Cumulative Exam review final math essentials

Vickie conducts a survey of home builders to determine the average cost of building a new home. She samples 10 home builders who are building in the town in which she lives. Under which conditions will her sample be a representative sample? Check all that apply. The builders were chosen at random. The population included only builders who build in Vicki's town. The population included builders who build homes in any town. The population included builders who do not build homes in Vicki's town. The builders were referred to Vicki by the realtor who will be selling the houses.

1 2

When is choosing a sample from a population least likely to be appropriate? Choose all that apply. when the population is small when the population is large when the sample contains proportions of items/events/people that are different from those of the population when the sample contains only items/events/people that reflect the population when surveying the entire population is time consuming when surveying the entire population is expensive

2 3

Adita has two options for how to invest $1,000. Plan A: Put the $1,000 in an account that pays $100 per year. Plan B: Put the $1,000 in an account that pays 5 percent interest per year. Which statement is true? Plan A will be worth more than plan B after two years. Plan A will be worth the same amount as plan B after one year. Plan B will be worth more than plan A after three years. Plan B will be worth more than plan A after four years.

A

An employer asks the survey question "How much money do you spend on gasoline per week to get to work?" of her employees that drive to work. Which best describes why she chose to only ask the employees that drive to work rather than all of her employees? The employees that drive to work were the target of her survey. The employees that drive to work adequately represented the sample. All employees were adequately represented by the sample that drives to work. All employees were too difficult to survey because the group was too large.

A

Eugene knows the circumference of a circle is 125.6 meters. Does he have enough information to find the area? Yes, because he could divide by 3.14 to find the diameter and then divide that result by 2 to find the radius. Once he has the radius, he can use the formula. Yes, because the area will just be twice the circumference so all he has to do is multiply by 2. No, because the circumference equals mc007-1.jpg and there is no mc007-2.jpg in 125.6. No, because the circumference equals mc007-3.jpg so he could only find the diameter. He needs the radius for the area formula.

A

Khalid wrote the sequence below. Which formula can be used to find the 10th term of the sequence?

A

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation? {-7, 1}

A

The number of bacteria in a sample after x days is represented using the equation mc015-1.jpg. By what approximate percent does the population change per day? 4.8% decrease 5.0% increase 95.2% decrease 105.0% increase

A

The table shows the average number of hours of daylight per day for the last four months of the year. What is the correlation coefficient for the data in the table? -0.993 -0.791 0.791 0.993

A

What is the most specific name that can be given to a figure with the following coordinates? (-10, 8), (-7, 13), (3, 7), and (0, 2) A. rectangle B. square C. trapezoid D. parallelogram

A

What is the range of the function f(x) = −(x + 3)2 + 7? all real numbers less than or equal to 7 all real numbers greater than or equal to 7 all real numbers less than or equal to −3 all real numbers greater than or equal to −3

A

What values of b satisfy 4(3b + 2)2 = 64?

A

Which value of a in the exponential function below would cause the function to shrink? f(x) = a{3/2}

A

A line of best fit is drawn for the set of points shown on the graph. Which point is an approximate extrapolation for x = 30 from the line of best fit? (23, 30) (30, 38) (44, 30) (30, 72)

B

Analyze the diagram below and answer the question that follows. In the diagram, 2004-05-02-04-00_files/i0190000.jpg 2004-05-02-04-00_files/i0190001.jpg 2004-05-02-04-00_files/i0190002.jpg, AG = 6, DG = 3, and CD = 10. What additional information is necesssary to calculate the area of ABCDE? A. AB and BC B. BG and EG C. DF and DE D. AB and BF

B

Fiona is completing the square to solve the polynomial equation. x2 - 4x + 1 = 0 What should be her first step? isolating the constant 1 adding 4 to both sides of the equation isolating the second term, -4x adding 1 to both sides of the equation

B

Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph? (2, 12) (2, 18) (2, 7) (3, 7)

B

The curve produced by the water coming from a fountain is sketched on the graph. Which function does the graph represent? f(x) = (x - 2)2 + 3 f(x) = -(x - 2)2 + 3 f(x) = (x + 2)2 + 3 f(x) = -(x + 2)2 + 3

B

The equation for the line of best fit is f(x) ≈ 1.8x − 5.4 for the set of values in the table. Using the equation for the line of best fit, what is a good approximation for x when f(x) = 30? 14 20 45 54

B

The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)? g(x) = (x − 7)2 − 3 g(x) = (x + 7)2 − 3 g(x) = (x − 3)2 − 7 g(x) = (x − 3)2 + 7

B

The graph shows a distribution of data with a standard deviation of 6. Which statement is true about the data point 84? It is within 1 standard deviation of the mean. It is within 2 standard deviations of the mean. It is exactly 3 standard deviations from the mean. It is exactly 4 standard deviations from the mean.

B

Which is the graph of ? 3/2{1/3}

B

Which recursive formula describes the sequence below? 5, 13, 29, 61, 125, ...

B

Which rule can be used to describe the growth of the y-values of the function mc018-1.jpg over each interval from mc018-2.jpg to mc018-3.jpg? add 12 multiply by 12 add 1, then 12, then 144 multiply by 1, then by 12, then by 144

B

A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3 seconds, the ball lands on the ground. The ball's motion can be modeled using the function f(x) = -10x2 + 20x + 8. What is the height of the ball 1.5 seconds after it is thrown? 11.7 meters 13.8 meters 15.5 meters 17.5 meters

C

A quadratic equation of the form 0 = ax2 + bx + c has one real number solution. Which could be the equation? 0 = 2x2 - 4x + 1 0 = 2x2 - 5x + 3 0 = -2x2 - 4x - 2 0 = -2x2 - 3x - 1

C

A sequence can be defined by the explicit formula mc020-1.jpg. Which recursive formula represents the same sequence of numbers?

C

Analyze the diagram below and complete the instructions that follow. A home plate marker for a softball field is a pentagon with three right angles and two congruent angles, as shown in the diagram. The ground crew for a softball complex has 4 home plate markers to paint. Calculate the area of the 4 home plate markers. The measurements shown in the diagram are in inches. A. 50 in.² B. 162 in.² C. 648 in.² D. 848 in.² Please select the best answer from the choices provided A B C D

C

Find the surface area of a ping-pong ball if the diameter of the ping-pong ball is 1.4882 inches. Round your answer to the nearest hundredth. A. 3.90 B. 5.18 C. 6.96 D. 27.83

C

Marisa recorded the number of hours she babysat each day last summer. She plotted the data in the box plot. Which statement must be true according to the box plot? The data is symmetric and shows that she was equally likely to work more than 3.5 hours or less than 5 hours. The data is symmetric and shows that she never worked more than 5 hours. The data is skewed and shows that she was equally likely to work more than 3.5 hours or less than 5 hours. The data is skewed and shows that she never worked more than 5 hours.

C

Over which interval are the exponential and linear function approximately the same? mc003-1.jpg from 0.25 to 0.5 from 0.5 to 0.75 from 0.75 to 1.0 from 1.25 to 1.5

C

The graph of the function f(x) = (x + 2)(x − 4) is shown. Which describes all of the values for which the graph is negative and increasing? all real values of x where x < −2 all real values of x where −2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0

C

The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants. According to the line of best fit, about how many ounces of frozen yogurt can someone purchase for $5?

C

The radius of Venus is 3760.4 miles. What is the approximate surface area of Venus, to the nearest whole number? A. 47,255 B. 9,090,143 C. 177,696,123 D. 7,014,989,521

C

What is a solution to (x + 6)(x + 2) = 60? x = −6 x = −4 x = 4 x = 12

C

What is the missing value in the following arithmetic sequence? 9.2 7.1 7.2 7.4 7.5

C

Which function has a vertex on the y-axis? f(x) = (x - 2)2 f(x) = x(x + 2) f(x) = (x - 2)(x + 2) f(x) = (x + 1)(x - 2)

C

A satellite view of a hurricane is placed on a coordinate plane. The outside edges of the hurricane are located at (4, 6) and (11, 6). Determine the width and the center of the hurricane. A. width = 4 center = (7.5, 6) B. width = 4 center = (8, 6) C. width = 19 center = (5, 8.5) D. width = 7 center = (7.5, 6)

D

Analyze the graph below and answer the question that follows. Which of the following is true? A. All sides of the figure are of equal length. The figure is a rhombus. B. Both pairs of opposite sides of the figure are of equal length. The figure is a parallelogram. C. The diagonals are of equal length. The figure is a rectangle. D. There are two disjoint pairs of congruent sides. The figure is a kite.

D

Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = -6. Which function could Heather be writing? f(x) = x2 + 36x + 12 f(x) = x2 - 36x - 12 f(x) = -x2 + 12x + 36 f(x) = -x2 - 12x - 36

D

Kristin wants to ask the managers of the fast food restaurants in a large city "How do you retain employees?" What condition must be true to justify surveying only a sample of the managers instead of surveying the entire population of managers? The population is small. The population is diverse. The population is not the target of the survey question. The population is expensive and time-consuming to survey.

D

The frequency table shows the results of a survey comparing weekly gasoline costs to the average number of miles a car can drive on a gallon of gasoline. Marcel converts the frequency table to a conditional relative frequency table by row. Which value should he use for Y? Round to the nearest hundredth. 0.19 0.45 0.82 0.90

D

The function f(x) = -x2 - 4x + 5 is shown on the graph. Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.

D