Algebra 2

What is an equation for a direct variation whose graph passes through the point (-5, 3)?

Which line, having the given slope and passing through the given point, represents a direct variation?

The length of an object's shadow varies directly with its height. If a can that is 13 cm tall casts a shadow that is 7.5 cm long, a bottle that is 25 cm tall will cast a shadow that is approximately 14.42 cm long.

A linear model for the situation below passes through the origin. A manufacturer can produce 4,200 gears in 8 hours. How many gears can be made in 1 hour?

The scatter plot below contains the points (2, 7), (-2, 1), (5, 13), (-4, 5), and (0,5). What equation best represents the trend line drawn on the scatter plot?

A data set that appears to be a random group of dots spread throughout the graph has a negative correlation.

What is the vertex of the graph of y = |x| - 6?

Which is the graph of the equation y = |x - 1|?

The graph of an absolute value function will always be an upward-pointing V shape.

Which is the graph of 0.4x + 0.1y ≥ 1?

What is the graph of

This is the graph of y < |x - 3|.

Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.

What is true about the system

A dependent system of equations will have infinitely many answers.

Jim's wages vary directly with the numbers of hours he works. For 7 hours, he makes $38.85. How much will he make in 37 hours?

Which line, having the given slope and passing through the given point, represents a direct variation?

The graph below models the burning of a candle. At time t = 0, the candle was 8 inches tall. If the candle burns at a rate of 2 inches per hour, what equation models the height h of the candle after burning for t hours?

The scatter plot below shows the weights in ounces of several kittens at various ages. What is the best equation of the trend line through these points?

What is the equation of the graph?

What is an inequality for this graph?

Which is the graph of

Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.

Which ordered pair is the solution to the given system of equations?

Two parallel lines form an inconsistent system of equations that has no solution.

Solve the system of equations. 2x - 4y = 3 -3x + 5y = 1

Use substitution to solve the system of equations given below.

Using substitution, the equations 2x - y = 4 and 3x + 2y = 13 give a solution of (3,2).

Use elimination to solve the system given below. 5x - 2y = 25 5x + 3y = 5

Use elimination to solve the system of equations given by 10x - 40y = 60 and 15x + 40y = -10.

Using elimination, the equations 3x - 4y = 12 and x + 4y = 20 can be solved to show that x = 8 and y = 3.

Which point is in the solution set of this system of inequalities?

Identify the graph that shows the solution to the system of inequalities.

A graph showing the inequalities "greater than or equal to" or "less than or equal to" will use dotted lines.

What is the maximum for the objective function for this graph?

A factory can produce two products, x and y, with a profit P approximated by P = 12x + 15y. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y ≤ 1000. What production levels yield maximum profit?

When finding the maximum value for an objective function, it is necessary to check the vertices of the graph.

Which point lies in the plane represented by the equation 2x + 7y + 3z = 25?

A point (x, y, z) can be used to represent the location of a geographical point in space, where x represents the latitude in degrees, y represents the longitude in degrees, and z represents the elevation in feet above or below sea level. Jerimoth Hill is the highest point of elevation in Rhode Island. It is 812 feet above sea level and lies at about 42° north latitude and 72° west longitude. What ordered triple represents the location of Jerimoth Hill?

An equation using three variables is graphed in coordinate space.

A bus leaves a terminal traveling at a rate of 45 miles per hour. When the bus has traveled 90 miles, a car leaves the same terminal, traveling at a rate of 60 miles per hour. Which pair of equations model the distances d covered by each vehicle after t hours?

An electronics store makes a profit of $55 for every standard CD player sold and $77 for every portable CD player sold. The manager's goal is to make at least $385 a day on sales of both standard and portable CD players. If s represents the number of standard CD players sold, and p represents the number of portable CD players sold, which inequality and graph represent the manager's daily goal?

Classify the system.

If you use the elimination method to solve the system of equations 3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method?Method I: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3. Then add the two equations.Method II: Multiply both sides of the first equation by 3, and multiply both sides of the second equation by 4. Then add the two equations.

A computer supply store sells two types of printers. Type A, costs $135, and the store makes a $40 profit on each sale. Type B, costs $120, and the store makes a $35 profit on each sale. The store manager expects to sell at least 100 printers this month and to make at least $4,400 profit on them. If x represents the number of type A printers sold, and y represents the number of type B printers sold, what are the constraints for a linear program that models this problem?

A graph of a system of three linear equations in three variables is shown below. How many solutions does the system have?

In chemistry, Charles Law states that if the pressure remains constant, the volume of an ideal gas varies directly with the temperature in degrees Kelvin. Suppose a gas has a volume of 100 mL at 250°K. Which proportion could you use to find the volume v of the gas if the temperature decreases to 150°K?

Brenda and Anne left their homes for their morning runs at the same time. Brenda can run a 10-minute mile and Anne can run a 12-minute mile. Combined, they ran 15 miles in a total of 2 hours and 42 minutes (162 minutes). How many miles did each woman run?

Solve the system of equations. x = 3y + 2z 2x + 3y + 2z = 3 -x + y - z = 6

Solve the system of equations. 2x + y - z = 3 x + y + z = 5 x - 2y + z = 2

Solve the system of three equations by elimination: 5x + 2y - 3z = 10 2x - 2y + 4z = 6 x - y + 2z = 3

The value of y varies directly with x. If y = 64 when x is 16, what is x when y is 288?

The value of y varies directly with x. If y is 24 when x is 72, what is the value of y when x is 144?

What steps would you use to plot (-3, -4, 0) in a three-dimensional coordinate system?

Which statement about 5y = 2x is true?

Which steps would you use to plot the point (7, -6, -5) in a three-dimensional coordinate system?

The capacity of the gas tank in a car is 16.5 gallons. The car uses 10.5 gallons to travel 178.5 miles. After driving 85 more miles, only 1 gallon of gasoline remains in the tank. Which linear equation and graph model the amount of gas g left in the tank after driving m miles?

The points in the table have been graphed in the scatter plot below. What is the best equation for the trend line, and the value of y when x is 16?

You can use a linear model to represent the relationship between the hours worked h and the money earned m. When h = 0, then m = 0. If a person earned $39 after working 6 hours, how much will the person earn after working 25 hours?

Which system of equations is graphed below?

Solve the system of equations by using substitution. -2x + 3y = 7 4x - 6y = 8

Solve the system of equations by using substitution. y = 2x + 1 3x - y = 4

Use substitution to solve the system of equations given below.

Use elimination to solve the system of equations given by -7x + 3y = 14 and 7x - 2y = -11.

Use elimination to solve the system of equations given by 3x - 2y = 10 and 5x + 2y = 6.

Use elimination to solve the system of equations. -x + 2y = 18 x + 8y = -38

Which of the following describes the system of equations 2x - y + 4 = 0 and 4x - 2y + 7 = 0?

Graph the system of inequalities.

Which system of inequalities has this graph?

A small fish market sells only tuna and salmon. A tuna costs the fish market $0.75 per pound to buy and $2.53 per pound to clean and package. A salmon costs the fish market $3.00 per pound to buy and $2.75 per pound to clean and package. The fish market makes $2.50 per pound profit for each tuna it sells and $2.80 per pound profit for each salmon it sells. The fish market owner can spend only $159.00 per day to buy fish and $197.34 per day to clean and package the fish. The graph below represents the feasible region for this linear programming model. What are the coordinates of the vertices of the feasible region, and what are the vales of t and s that maximize the objective function?

An ice cream shop makes $1.25 on each small cone and $2.25 on each large cone. On a typical Saturday, it sells between 60 and 80 small cones and 120 and 150 large cones. The total sales have never exceeded 200 cones. If x represents the number of small cones sold, and y represents the number of large cones sold, what inequalities represent the constraints and what is the objective function in this linear programming problem?

Find the values of x and y that maximize the objective function for this graph.

The objective function for this graph is P = 5x + y. What values of x and y maximize this function?

Using substitution, the equations 2x - 3y = -21 and 3x + 3y = -24 give a solution of (-9,-1).

Which set of numbers best describes the number -4?

Which set of numbers best describes the number π (pi)?

The expression | -2 | - |-7 | simplifies to 5.

The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 0.75 seconds.

The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 2.5 seconds.

The expression 2y - 7x + 3y + 3x evaluated for x = 2 and y = 4 is 12.

Solve 3(x - 5) - 15 = 48.

Solve w + 12 = -6 - 2w.

In the expression 2(x+4) - 12 = 44, x = 24.

Solve and graph -2x + 7 ≥ 2(3 - x).

A car salesman receives $50 for each car sale plus 2% of the purchase price. How much must a car sell for in order for the salesperson to earn at least $500?

The image shows the graph of 3x + 2 < 11 and - x + 2 < 3.

Solve |5x - 3| ≤ 3.

Solve |8 - m| + 4 = 21.

The expression | 2 + 4n | - 4 = 14 produces the answers n = 4 and n = 5.

Simplify the expression |-3| - |-5|.

Evaluate 2a - 5b - 3a for a = -2 and b = 5.

Find the perimeter of the figure shown below. Simplify the answer. 8a + 2b 10a + 4b 10a + 2b 10a - 2b

One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. The perimeter is 38 cm. Find the dimensions of the triangle.

A certain box of cereal should have a net weight that is within 1.5 grams of 510. After the first phase of production, the weight of the cereal is 308 grams. By how much should the weight of the cereal increase to remain within the specified weight?

Graph the solution of -7x + 4 ≥ 11 and 10 - 3x > 1.

Solve and graph 13 - 3y < -5.

Solve |5x - 7| = 3.

In the expression 3(x - 6) - 12 = 33, x = 21.

Suppose that 80% of people surveyed answered 'Yes' to a certain question. Let the digits 0-7 to represent 'Yes' and let 8 and 9 represent 'No.' Use the random numbers shown below to determine how many people out of 20 answered 'No.'

Suppose you take a true/false quiz that contains five true/false questions. Let an even digit represent a correct answer and an odd digit represent an incorrect answer. In the five trials shown, how often did you get at least 3 questions correct? (Note: Assume there is a 0 before the number 4908 in the first trial.)

A jar contains 7 red marbles, 4 blue marble, and 6 green marbles. You draw one marble from the jar. The probability of drawing a blue or red marble is 11/17.

Find f(-5) if f(x) = -8x - 1.

Find the slope of the line that passes through (5, -5) and (9, -5).

The slope of the line that passes through (-2, 6) and (1, 15) is 3.

Find the equation of the line that passes through the point (-7, 2) and has a slope m = -5 in point-slope form.

Find the equation of the line that passes through the points (-6, 3), (5, -2) in point-slope form.

The point-slope formula of a line that passes through the point (8,5) and has a slope of ¼ is y = 1/4x + 3.

Which equation represents the line whose slope is 1 and whose y-intercept is (0, 0).

Determine the coordinates of the y-intercept of 2x + 4y = 8.

The line y = 7x - 2 has a slope of 7 and a y-intercept of (-2 ,0).

A farmer wished to construct a rectangular fence with one side along a barn. The farmer has 240 feet of fence and wishes to have the length be three times the width. If the side of the barn accounts for the length of the fence, find the dimensions of the fence.

Solve |x + 4| ≥ 1.

A group of students rolled two number cubes 100 times and recorded a sum of six 14 times. Find the experimental probability of rolling a sum of six.

A line passes through the point (-6, 1) and has slope m = -4. Find the equation in point-slope form.

Find the slope and the y-intercept of the line. y = 5x - 7

Determine the coordinates of the x-intercept of 3x - 4y = 24.

The image shows the graph of 3x + 2 < 11 and - x + 2 < 3.

Point M is at the coordinates (-5, 5).

Find the opposite and reciprocal of -1.8.

Name the property of real numbers illustrated by the equation 3(2x - 14) = 6x - 42.

Evaluate -1x + 7y + 4x + 1y for x = 4 and y = -2.

Evaluate 3(2m - 3n) - 2(m + 2n) for m = -9 and n = -7.

Solve 11c - 2(2c + 1) = 3(c - 6).

Solve and graph 5x - 2 ≤ 8.

Solve |x + 8| ≤ 5.

Solve |x + 9| = 8.

Write the specification 14.35 ≤ d ≤ 15.15 as an absolute value inequality.

A jar contains 12 blue marbles, 8 red marbles, and 20 green marbles. You pick one marble from the jar. Find the theoretical probability, P(blue or green).

There are 135 girls in the junior class at West High School. Of these 135 girls, 16 are on the volleyball team (V), 22 are on the softball team (S), and 8 are on both the volleyball and softball team. One student is selected at random. Find the probability that the student plays on the softball team but not the volleyball team.

You roll a twelve-sided die with the numbers 1 through 12 on the faces of the die. You roll the die once. Find the theoretical probability P(factor of 12).

Find g(-2) if g(x) = 4x + 3.

What is the domain and range of this function? Domain: all real numbers; Range: y ≥ -4 Domain: -2 ≤ x ≤ 2; Range: y ≥ -4 Domain: x ≥ -4; Range: all real numbers Domain: x ≥ 0; Range y ≥ 0

What is the domain and range of this function? Domain: x > 0; Range: y > 0 Domain: x ≥ 0; Range: y ≥ 0 Domain: all real numbers; Range: all real numbers Domain: positive integers; Range: positive integers

What point has coordinates of (-5, 4)?

Graph 2x + 3y = 9.

Match the given graph with its corresponding equation.

What is the slope of the line through the points P(-5, -6) and Q(-12, 5)?

Write the point-slope form of an equation of the line that passes through (4, -3) and (2, 1).

The expression 2y - 5x + 3y + 2x evaluated for x = 3 and y = 2 is -11.

Solve the question below.

Is y = (2x)2 + 5x - 7 + 1 linear or quadratic? Identify the quadratic, linear, and constant terms.

Find a quadratic model for the values in the table.

The vertex of a parabola will never be on the axis of symmetry.

Find the quadratic function

Graph

The minimum value of a parabola that opens upward will be its vertex.

Write y = -4x2 - 64x - 265 in vertex form.

Graph y = - (x - 1)2 + 4.

The vertex of f(x) = 3(x+2)2 - 4 is (-2,-4).

Factor x2 - 81.

Use the GCF to factor 15x2 + 6x.

4y is the greatest common factor of 4y2 + 6y.

Factor x2 - 6x + 8.

Factor 5r2 + 13r - 6.

3x2 -5x - 2 factors to (3x+1)(x-2).

A biologist took a count of the number of migrating waterfowl at a particular lake and recounted the lake's population of waterfowl for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of waterfowl at the lake on week 8.

Identify the vertex and the axis of symmetry of the parabola.

Graph

Graph y = (x - 3)2 + 1.

Identify the vertex and y-intercept of the graph of f(x) = -4(x + 3)2 + 7.

Write y = -3x2 + 12x - 21 in vertex form.

Factor x2 - 16.

Factor 4x2 - 49.

What is the GCF of 3n3 + 5np2 + n2p2?

Factor t2 - 10t + 25.

Factor 4y2 - 3y - 1.

The vertex of f(x) = 2(x-2)2 +10 is (-2, 10).

Factor 8ac + 12ad + 10bc + 15bd.

Factor 3xy - 2by + 3ax - 2ab.

4n3 + 5n2 + 6n + 15 factors to (3n2 + 2) (3n + 5).

Solve 6x2 = 48. If necessary, round your answer to the nearest hundredth.

Solve x2 - 6x = 0 by graphing or by factoring.

A quadratic equation factored to 0 = (x-4)(x+3) would have solutions of x = -4 and x = 3.

Simplify C. -500i

The square root of a negative number is an imaginary number.

Solve 9x2 + 6x + 1 = 64.

Rewrite y = x2 + 4x + 5 in vertex form. Then find the vertex.

When solving a quadratic equation by completing the square, the coefficient of the highest power must be any positive integer.

Solve 3x2 - 9x - 12 = 0 using the Quadratic Formula.

Without graphing, tell how many x-intercepts y= 2x2 + 4x + 2 has.

Using the quadratic formula allows you to find the x-intercepts of a quadratic equation.

A biologist took a count of the number of migrating geese in a state park and recounted the park's population of geese for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of geese at the lake on week 8.

Factor 18ab + 9ax -4b - 2x.

A rocket is launched from atop a 54-foot cliff with an initial velocity of 119 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t2 + 119t + 54. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest hundredth of a second.

Evaluate the discriminant of 25x2 + 350x + 49 = 0. Tell how many solutions the equation has and whether the solutions are real or imaginary.

An expression for the area of a rectangle is xy - 2x + 3y - 6. Express this area in factored form.

Complete the square: x2 + 2x + ____ .

Identify the vertex and the axis of symmetry of the parabola.

Solve -11x + 9 + 5x2 = 0 using the Quadratic Formula.

Solve -9x + 6 + 5x2 = 0 using the Quadratic Formula.

Graph y = -x2 - 1.

Randex Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = -2x2 + 4x + 2 where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. Find the maximum weekly profit.

Write the equation of the parabola in vertex form.

Factor 8a4b - 3ab2c.

Find the GCF of 14a2b4c and 56ab2c2.

Factor 4x2 + 5x - 21.

Factor m3 - 4m2 + 6m - 24.

Factor xy - 6 + 2y - 3x.

Solve x2 - 4x - 5 = 0 by factoring.

Find the additive inverse of 6 - 3i.

Simplify (3 + 3i) - (7 + 6i).

Simplify 2i(5 - i).

Write A. 1 - 4i B. 1 + 4i C. 3i D. -3i

Complete the square: x2 + 6x + ____ .

Rewrite y = x2 - 10x + 3 in vertex form. Then find the vertex.

Solve 7x2 + 28x = 49 by completing the square.

Solve 8x2 - 80x = -24 by completing the square.

15x3 - 10x2 + 3x -2 factors to (5x2 + 1) (3x - 2).

Classify 2x3 - 2x by degree and by number of terms.

The table shows the number of oak trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of oaks planted in 1998.

4x3y4 is a 4th degree monomial.

The roots of a certain polynomial are -2/5, -6 and 4/3. What might the linear factors of the polynomial be?

Write 2r3 + 8r2 - 10r in factored form.

The polynomial 3x2 - 7 + 4x3 + x6 is written in standard form.

Find the zeros of y = (x - 2)(x + 1)(x + 3).

Find the zeros of y = (x - 2)(x + 9).

A multiple zero has a multiplicity equal to the number of times the zero occurs.

Divide (5x3 - 6 - 5x) ÷ (10 + 5x) using synthetic division.

Use synthetic division and the Remainder Theorem to find P(-3) if P(x) = x4 + 19x3 + 108x2 + 236x + 176.

When dividing polynomials, every term of the numerator must be divided by the entire denominator.

Solve x2 - 12x + 41 = 0

Factor 3q3 - 81.

4x2 - 36 = 0 has a solution of x = +/- 3.

Classify -4x3 - 2x2 - 2x by degree and by number of terms.

Classify 2 by degree and by number of terms.

Find a polynomial function to model the data.

Find the zeros of y = (x - 1)(x + 2).

Find the zeros of y = x(x + 5)(x - 8).

Divide (3x3 + 4x2 - 5x - 2) ÷ (x + 2) using long division.

Factor x4 - 8x2 + 15.

Solve x - x3 = 2x4 + 3x2 - 5.

Solve x2 - 10x + 29 = 0.

Solve 8x3 + 27 = 0.

The polynomial x4- 2x2 + x4 - x is written in standard form.

Find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3 + i.

Use the Rational Root Theorem to determine all possible rational roots of 5x3 + 4x2 + 4x + 10 = 0. Do NOT find the actual roots.

The possible rational roots of x3 + 3x2 - 4x + 2 are +/- 3 and +/- 2.

For 3x9 -7x6 + 4x3 + 15 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

For 8 - 4x3 + 4x6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

The equation f(x) = 4x4 + 4x2 + 9x - 2 can have at most four distinct real roots.

Evaluate. 9!/6!

There are 17 students participating in a spelling bee. How many ways can the students who go first and second be chosen?

7! Is another way of writing 7 * 6 * 5.

Determine whether the following situation would require calculating a permutation or a combination. Assigning students to their seats on the first day of school.

Ten candidates are running for three seats in the student government. You may vote for as many as three candidates. In how many ways can you vote for three or fewer candidates?

Order does not matter when examining combinations, but order does matter in permutations.

What is the probability of getting two heads when tossing a coin four times?

Use Pascal's Triangle to expand (s - v)5.

If flipping a coin is equally likely to result in heads or tails, the odds of flipping a coin six times and getting only one head are 3 out of 16.

A fifth-degree polynomial equation with rational coefficients has the roots 2, -7i, and -7 + i. Find the remaining roots.

Divide (x4 - 11x3 - 49x2 + 899x - 2506) ÷ (x - 8).

Assume red and green are equally likely occurrences. What is probability that you will get one green light in a row of five lights?

A school bought a special type of lock for all student lockers. Every student had to create his or her own pass code made up of 4 different numbers from 0-9. How many different pass codes are possible?

A summer reading list has 20 books on it. In how many ways can you choose four books to read?

Use Pascal's Triangle to expand (3a - b)4.

Write in standard form. Then classify by degree and by number of terms.

Write (x - 2)(x + 9) as a polynomial in standard form.

Find the zeros of the function. State the multiplicity of multiple zeros. y = (x - 4)2

Divide (2x3 + 4x2 + 3x + 4) ÷ (x + 1) using long division.

Which polynomial is NOT a factor of 3x4 - 10x3 - 29x2 + 16x + 20?

Which polynomial is NOT a factor of 3x4 - 16x3 - 3x2 + 36x + 20?

Factor 3q3 - 81.

Solve x3 + 4x2 - x - 4 = 0.

Solve x3 + 5x2 - 9x - 45 = 0.

Find only the rational roots of x4 - 9x3 + 16x2 + 18x - 36 = 0.

Find the roots of x3 - x2 + 2 = 0.

For x7 - 2x6 + 3x2 - 2x + 5 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

For 3x3 -2x + 6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

Which polynomial function has the highest degree?

Seven skiers enter a downhill race. First, second, and third places will be given to the three fastest skiers. How many arrangements of first, second, and third places are possible with seven skiers?

Evalute 9!

Find 8P3.

How many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available?

In how many ways can the three letters A, B, and C be arranged?

Determine whether the following situation would require calculating a permutation or a combination. Selecting four teachers to attend a math seminar.

Four cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of four cards are possible?

How many combinations of four can you make from the set? {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

The polynomial 5x3 - 2x2 + x - 13 is written in standard form.

What is the vertex of the graph of y = |x| - 6?

Which statement describes the relationship between the graph of the equation

Graph y = x2 - 6.

Write the equation of the parabola in vertex form.T

The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998.

Use Pascal's Triangle to expand (s - v)6.

Evaluate 8C3.

Solve 5x - 4 = |2x + 1|. Check for extraneous solutions.

Assume red and green are equally likely occurrences. What is the probability that you will get zero green lights in a row of five lights?

Write an explicit formula for the sequence

Write a recursive formula for the sequence 15, 26, 48, 92, 180, .... Then find the next term.

The next three terms of the sequence 1, 3, 5, 7, ... are 9, 11, 13.

A grocery clerk sets up a display of 12-pack cartons of cola. There are 40 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display?

Is the sequence -9.9, -13, -16, -19.2, ... arithmetic? If so, identify the common difference.

The missing term of the arithmetic sequence 13, __, 27 is 21.

Find the missing terms of the geometric sequence 480, ___, ___, ___, 12.288, .... (Hint: The geometric mean of the first and fifth terms is the third term.)

Is the sequence

The sequence 3, 6, 9, 12 is geometric.

For the sum

Write the related series for the finite sequence 7.6, 6.3, 5, ... , -1.5. Then evaluate the series.

5, 7, 11, 15, 21 is an infinite series.

Which series will converge?

Evaluate the infinite geometric series 2.1 + 0.21 + 0.021 + ... .

The sum of a geometric series containing five terms, a common ratio of 3, and a first term of 1/2 is 62.5.

Describe the pattern

Describe the pattern 16, -8, 4, -2, 1, ....

Which formula does NOT describe the sequence 8, 6, 3, -1, -6, ... ?

Find the arithmetic mean an of the terms

Find the missing term of the arithmetic sequence 25, ___, 49, ....

Determine whether the series -1024 + 256 -64 + 16 - ... is arithmetic or geometric. Then evaluate the series to the ninth term.

Evaluate the infinite geometric series

Evaluate the series 3 - 12 + 48 - 192 + ... to the seventh term. Round your answer to the nearest hundredth, if necessary.

The sequence 2, 6, 18, 54, ... is a geometric sequence.

Evaluate the area under g(x) = -x2 - 3x + 7 for -4 ≤ x ≤ 1.

Use inscribed rectangles to approximate the area under g(x) = -0.5x2 + 7 for -3 ≤ x ≤ 0 and rectangle width 0.5.

The area approximated by circumscribed rectangles is greater than the area under the curve.

Use the frequency table to find P(more than 3 children).

Use the frequency table to find P(0 - 2 children).

A situation may not be described by more than one sample space.

The probability that a city bus is ready for service when needed is 85%. The probability that a city bus is ready for service and has a working radio is 64%. Find the probability that a bus chosen at random has a working radio given that it is ready for service.

Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.

If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second.

Find the mean, the median, and mode of the set of values. 5, 20, 6, 5, 15, 18, 12, 13, 14

The cost of ten different portable MP3 players is shown in the table. What is the mean cost?

The mode of the set 2, 3, 3, 4, 5, 8, 9, 10 is 3.

The scores of 36 students on a recent geography test are in the table. If Lupe got a 69 on the test, what percentile would that score represent?

The box-and-whisker plot represents the test scores of 25 students. What percent of the scores were between 88.5 and 65?

If x is at the 63rd percentile, then 37% of the data are less than or equal to x.

A rubber ball dropped on a hard surface takes a sequence of bounces,

Evaluate the infinite geometric series 1.9 + 0.19 + 0.019 + ....

Decide whether the formula an = -4n(n - 1) is explicit or recursive. Then find the first five terms of the sequence.

A spinner is divided into eight equally-sized areas. The central angle for pink is 90°, for teal is 225°, and for blue is 45°. Which is the correct frequency table for this spinner?

Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.

A box-and-whisker plot is a method of displaying data that uses quartiles to form the center box and the minimum and maximum values to form the whiskers.

How do the medians of the two sets of exam scores compare?

Make a box-and-whisker plot for the set of values. 5.2, 9.2, 5.2, 3.2, 3.2, 7.2, 6.2, 8.2, 5.2, 4.2, 5.2, 6.2, 9.2, 9.2, 8.2

Make a box-and-whisker plot for the set of values. 7.2, 3.2, 5.2, 3.2, 4.2, 7.2, 5.2, 3.2, 6.2, 4.2, 6.2, 3.2, 6.2, 2.2, 4.2

Is the sequence 5.1, 10.5, 15.9, 21.3, ... arithmetic? If so, identify the common difference.

For the geometric sequence 2, -10, 50, -250, ..., find the seventh term.

Write the explicit formula for the sequence with a1 = 120 and r = 0.3. Then generate the first five terms.

Evaluate the series 3 + 9 + 15 + 21 + 27 + ... to the 16th term.

Tell whether 3, 10, 17, 24, ... , 73 is a sequence or a series. Then tell whether it is finite or infinite.

The sequence -12, -6, 0, 6, ... , 48 has 11 terms. Evaluate the related series.

Use summation notation to write the arithmetic series -3.9 + (-1.9) + 0.1 + ... for six terms.

Evaluate the series

A class of 30 students has 11 honor students and 13 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.

The table gives data about municipal waste collected and recycled by type. Find P(recycled | glass).

The table lists the results of a survey of the students at a community college. Suppose a student is selected at random. Find P(male | student takes physiology).

Find the arithmetic mean an of the terms

You cannot use a table or graph to show a probability distribution.

A percentile is a number from 0 to 100 which can be associated with x to indicate the percent of the data that are less than or equal to x.

A large asteroid crashed into a moon of another planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic progression 20, 60, 100, 140, .... Find the distance that the projectile traveled in the 9th second.

What does the dot at 47 represent?

The sequence -14, -9, -4, 1, ... , 41 has 12 terms. Evaluate the related series.

Inscribed rectangles are completely under the curve.

Evaluate the infinite series

Which number is an outlier in the data shown in the table?

The table gives data about municipal waste collected and recycled by type. Find P(paper | not recycled).

Evaluate the series

Write and evaluate a sum to approximate the area under y = (x - 4)2 - 1 for the domain 0 ≤ x ≤ 2. a. Use inscribed rectangles 0.5 units wide. b. Use circumscribed rectangles 0.5 units wide.

Write an explicit and a recursive formula for the sequence -7, -5.6, -4.2, -2.8, -1.4, ....

Probability over a continuous range of events is cumulative probability.

Use inscribed rectangles to approximate the area under f(x) = -x2 + 6 for -1.5 ≤ x ≤ 0 and rectangle width 0.5.

Given the set of axes y-axis: a car's velocity, x-axis: time, what does the area under the curve represent?

Identify the outlier in the temperature data shown.

The number of patients treated at Dr. Oster's dentist office each day was recorded for nine days. Using the data 7, 4, 18, 14, 14, 11, 13, 21, and 6, find the mean, median, and mode.

The number of patients treated at Dr. Holman's dentist office each day was recorded for seven days. Using the data 3, 10, 18, 9, 22, 20, and 2, find the mean, median, and mode.

A frequency table is a list of the outcomes in a sample space and the number of times each outcome occurs.

Ms. Chin collected data about how long students in two of her classes spent doing homework. This table shows the result. Suppose a student from her third or fourth period class is selected at random.

Use the frequency table to find P(2 or 3 children).

Find the mean and standard deviation for the set of values. 23, 16, 15, 18, 20, 17, 4, 7, 15

The range of the set 12, 18, 19, 22, 25 is 19.

Find the range and the interquartile range of the set of values. 31, 16, 39, 15, 18, 41, 24, 26, 21, 33, 9, 12

Which sample size will produce a margin of error of ±4.1%?

Which sample size will produce a margin of error of ±3.5%?

From a group of 1,268 people, 172 prefer chocolate ice cream over vanilla. The proportion who prefer vanilla is approximately 86.4%.

If a group of dogs has an average weight of 40 pounds and a standard deviation of 15.2 pounds, 16% of the dogs will weigh more than 55.2 pounds.

The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?

The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?

Find the mean and standard deviation for the set of values. 23, 16, 15, 18, 20, 17, 4, 7, 15

The range of the set 12, 18, 19, 22, 25 is 19.

Find the range and the interquartile range of the set of values. 31, 16, 39, 15, 18, 41, 24, 26, 21, 33, 9, 12

Which sample size will produce a margin of error of ±4.1%?

Which sample size will produce a margin of error of ±3.5%?

From a group of 1,268 people, 172 prefer chocolate ice cream over vanilla. The proportion who prefer vanilla is approximately 86.4%.

If a group of dogs has an average weight of 40 pounds and a standard deviation of 15.2 pounds, 16% of the dogs will weigh more than 55.2 pounds.

The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?

The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?

Find 49° in radians.

An angle in standard position with a positive measurement will extend below the x-axis.

pi/3 radians in degrees

The amplitude of y = 3 sin(2x) is 3.

Use the graph to find the value of y = sin θ for θ = 270°.

Find the amplitude and period of y = -5 sin (5x).

For a circle of radius 9 feet, find the arc length s cut off by a central angle of 6°.

In which quadrant does the terminal side of a 117° angle lie?

Find 311° in radians.

When 2251 voters were polled, 52% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.

Write an equation of the cosine function with amplitude 2 and period 8π.

The range of the set 2, 5, 8, 19, 33, 45 is 43.

Graph y= 2.5 tan 4x/5

Graph y = 5 cos x.

Evaluate sec 3.

Reciprocal functions cannot be evaluated in radians.

Evaluate sec 131°.

Simplify cos θ sec θ.

Simplify cot/cos

The tangent of an angle is equal to the ratio of its sine divided by its cosine.

The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse.

Solve 2 cos θ + 4 = 3 for 0 ≤ θ < 2π.

The diagram shows one solution to the equation 3 - sin θ = 5 sin θ. Find the complete solution of the equation.

The length of side RP is approximately 42 cm.

Find the area of the triangle. Round your answer to the nearest tenth, if necessary.

Solve the problem below.

The law of cosines is used to find the measures of a triangle when only the three sides are known, because the law of sines requires at least one angle measure.

Find the angles in the triangle when a = 19, b = 20, and c = 10. Round your answers to the nearest tenth.

Solve the problem below.

Determine the number of standard deviations which include all data values listed for the situation.The mean time employees take of a company to commute to work is 40.75 minutes; the standard deviation is 12.9 minutes.42 min, 45 min, 53 min, 34 min, 12 min, 48 min, 52 min, 24 min, 56 min, 47 min, 28 min, 48 min

Simplify cot θ tanθ.

A set of data that is normally distributed has a mean of 35.6 and standard deviation of 2.5. Which number is between 1 and 2 standard deviations of the mean?

In one survey, the shoe sizes of women are distributed normally about the mean. The mean of the data is 7.17, and the standard deviation is 1.44. About what percent of the women are within two standard deviations of the mean in shoe size?

Find the angles in the triangle when a = 13, b = 12, and c = 11. Round your answers to the nearest tenth.

Solve cot θ sin θ = 1/5 for 0 ≤ θ < 2π.

Find the range and the interquartile range of the set of values.37, 21, 44, 19, 22, 47, 26, 32, 25, 43, 11, 15

Which expression completes the equation to make it an identity? cos+ sin + cos / 1+ sin

In a survey of 368 people, 81 drink milk straight from the milk carton. For the sample, find the sample proportion, the margin of error, and the interval likely to contain the true population proportion.

Use the Law of Sines to solve for c to the nearest tenth.

Which expression completes the equation to make it an identity?

What is the period of y = 3 tan 4x + 5?

Write 11pi/18 radians in degrees

Find the value of csc 165°. Round your answer to the nearest hundredth.

In ΔABC, b = 4, c = 1, and ma =118

In ΔABC, b = 1, c = 3 ma= 138

Use the Law of Sines to solve for a to the nearest tenth.

The class average on a math test was 84.5 and the standard deviation was 4.4. Find the z-score for a test score of 94.

Find the degree measures of the angles whose tangent is sqr 3

Find the mean and standard deviation for the set of values. 25, 19, 5, 21, 18, 22, 17, 10, 7

Solve the problem below.

Graph Y=-pi/4 cot ( x-pi/4)

Solve 3 cos 0 = cos 0 - sqr2 for 0 < 0 < 2pi

Which sample size will produce a margin of error of ±6.3%?

Use the graph to find the value of y = sin θ for θ = 150°.

Simplify sin θ sec θ.

Find the radian measures of the angles whose sine is -0.8. Round to the nearest hundredth.

When 876 voters were polled, 67% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.

Use the Law of Sines to solve for a to the nearest tenth.

On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 265 feet at an angle of 35° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?

A matrix with 4 columns and 3 rows is a matrix of dimensions 4x3.

Identify a31 in the matrix.

What are the dimensions of the matrix?

Find

Two matrices can be subtracted if they have an equal number of rows, regardless of how many columns they have.

Solve for each variable

Find AB,

Two matrices with dimensions 2x2 and 2x2 will result in a product matrix with dimensions 2x2 when multiplied.

Graph the figure and its image after the given rotation.

Transforming a figure 3 units to the right and 2 units up can be accomplished by adding 3 to each x-coordinate of the vertices and subtracting 2 from the y-coordinates.

What are the coordinates of the image after a rotation of 90°?

Find the inverse of -2 2 -1

The determinant of this matrix is 7.

Which matrix has determinant -7?

Find

Find

Use matrices A, B, and C. Find B-C if possible.

Write the coordinates of the image after a dilation three times the original size.

Find

Find

Solve

Determine whether

Find

Simplify

-25 has no real 4th root.

Find all the real cube roots of

The fifth root of 12 is equal to the fifth root of 7 times the fifth root of 5.

Simplify

Divide and simplify sqr 24/ sqr 2

Rationalize the denominator of

Multiply

These are two like radicals.

17 1/3 is the same as the cube root of 17.

Simplify

Simplify

The solution to this equation is x = 11.

Refer to the question below.

Solve

Find AB,

Solve

Multiply and simplify

Multiply and simplify

Find the coordinates of the image after the reflection in the given line.

Find

Write

The formula for the volume of a sphere is

Two matrices with dimensions 3x1 and 2x4 will produce a product matrix with dimensions 3x4 when multiplied.

Find all the real square roots of 0.0036.

Solve

Multiply

Which matrix is the multiplicative inverse of

Simplify

What are the dimensions of the matrix?

The velocity of sound in air is given by the equation

Find the coordinates of the image of

Solve

Rationalize the denominator of

Determine whether

What are the dimensions of the matrix?

What are the dimensions of the matrix?

Find the real-number root of

Solve

Write the coordinates of the image after a translation 3 units right and 2 units down.

In May, Suzanne bought 32 styrofoam balls and decorated them as toy figurines. In June, she sold 12 figurines. In May, Carrie bought 36 styrofoam balls to decorate and in June, she sold 22 figurines. Which matrix represents all of their May purchases and their June sales?

Multiply

What are the dimensions of the matrix? Identify a12.

In May, Marcus bought 48 styrofoam balls and decorated them as toy figurines. In June, he sold 19 figurines. In May, Lin bought 44 styrofoam balls to decorate and in June, she sold 21 figurines. Which matrix represents all of their May purchases and their June sales?

Write

Let f(x) = 3x + 7 and g(x) = 4x - 2. Find (f composited with g) (-6).

Let f(x) = 3x2 + 10x- 8 and g(x) = x + 4.

If f(x) = 3x + 7 and g(x) = 5x - 2 then (f+g)(x) = 8x + 5.

The domain of a relation and its inverse are the same.

Find the inverse of f(x) = 3x2. Is the inverse a function?

Identify the graph of y = 2x2 - 5 and its inverse.

Write an exponential function to model this situation: a population of 260 animals increases at an annual rate of 9%.

For an annual rate of change of -31%, find the corresponding growth or decay factor.

An annual rate of change is -10%. The corresponding growth or decay factor is 0.10.

Graph y = 4x - 3 as a translation of its parent function.

Evaluate e4.

y = -4* 2x is a reflection of y = -1/4* 2x.

Log4 64 = 3

Given log 15 = B and log 3 = C , find log 5.

Use the properties of logarithms to evaluate log4 256.

Find the equation of the graph.

Solve the question below.

A continuously compounded account starts with $2500 in principal. The annual interest rate is 11.3%. What is the balance after 15 years?

Find the inverse of y = 3x2 + 4. Is the inverse a function?

Let f(x) = 4 - x2 and g(x) = 2 - x. Find f(x) • g(x).

Solve the question below.

Find the annual percent increase or decrease that y = 0.35(2.3)x models.

Write 5 log x - 4 log (x - 4) as a single logarithm.

How much money invested at 5% compounded continuously for 2 years will yield $1150?

Solve the question below.

Find the inverse of the relation. Graph the given relation and its inverse.

Suppose that x and y vary inversely. Write a function rule for the function that x = 4 when y = 7.

If m varies directly as the square root of y, inversely as p2, and directly as n, what happens to m when y is quadrupled, p is tripled, and n is multiplied by 5?

If y varies inversely with x and y = 6 when x = 9, then y = 96/x.

State the excluded values of x in the expression

Simplify

This statement simplifies to 16a2.

Divide

The only restriction of the variable in this equation is that x cannot equal positive or negative 5.

Multiply

Solve the question below.

A complex fraction is a fraction that has a fraction in either its numerator or denominator, or in both its numerator and denominator.

Simplify

Solve

An extraneous solution is a solution of the derived equation, but not of the original equation.

Solve

After taking 3 quizzes, your average is 79 out of 100. What must your average score be on the next five quizzes to increase your average to 84?

Expand

State the excluded value(s) of

Given log 5 = P and log 2 = Q , find log 10.

After taking 7 quizzes, your average is 75 out of 100. What must your average score be on the next five quizzes to increase your average to 80?

Simplify

Simplify

It is not necessary to check all solutions of the derived equation in the original equation to find whether any of them are not solutions of the original equation.

Write an exponential function to model this situation: a population of 300 animals increases at an annual rate of 13%.

State the excluded values of a and b in the expression

Simplify

State the excluded value(s) of

Find

Which property was used to rewrite log

Identify the graph of y = 2 x + 7 and its inverse.

Multiply

The Bangor Coat Factory found that the number of coats sold N varies directly as their advertising budget A and inversely as the price of each coat P . The Bangor Coat Factory sold 10,800 coats when $30,000 was spent on advertising and the price of a coat was set at $50. Determine the number of coats sold when the amount spent on advertising is increased to $70,000.

Graph y = 3 x + 1 as a translation of its parent function.

Solve the question below.

Simplify

Simplify

Use the properties of logarithms to evaluate

Let f ( x ) = x 2 + 2 x - 1 and g ( x ) = 2 x - 4. Find 2 f ( x ) - 3 g ( x ).

A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Nita can paint a certain room in 3 hours. Jorge can paint the same room in 4 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?

The selling price of x number of a certain stereo can be modeled by the function R ( x ) = 160 x . The total cost of making x stereos is C ( x ) = 71 x - 0.02 x 2. What is the percent markup for 31 stereos?

Use the properties of logarithms to evaluate log7343.

Graph f ( x ) = 2 x + 1 + 3 as a translation of its parent function.

For f ( x ) = 5 - 3 x and g ( x ) = x 2 - 1, find f ( g ( x )) and g ( f ( x )).

For the function f ( x ) = (4 - 2 x )2, find f -1 and the domain and range of f and f -1. Determine whether f -1 is a function.

Simplify

Find the next three terms in the sequence 1, 2, 4, 8, ....

Simplify csc θ sin θ.

Divide

Find

Find

Find the 11th term of the sequence 11, 19, 27, 35, ....

Solve the question below.

Simplify sin2 θ(1 - csc2 θ).

Divide

Find the next two terms in the sequence -5, 8, -13, 20, -29, .... Write a formula for the nth term. Identify the formula as explicit or recursive.

Multiply

A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Katalin can paint a certain room in 3 hours. Lena can paint the same room in 8 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?

Find the exact coordinates of the point at which the terminal side of -135° intersects the unit circle.

Solve

Find the values of cos θ and sin θ for -25°. Round your answers to the nearest hundredth.

Solve

In which quadrant does the terminal side of a 314° angle lie?

Is the sequence -5.4, 5.1, 15.6, 26.1, ... arithmetic? If so, identify the common difference.