Quantitive Reasoning, Algebra, and Statistics

What is the solution to the equation 1/2X + 3/2(x + 1) - 1/4 = 5 ? A. 5/2 B. 13/8 C. 15/8 D. 17/8

C. 15/8 The equation can be rewritten as 1/2X + 3/2X + 3/2 - 1/4 = 5, which simplifies to 2X = 5 + 1/4 - 3/2 = 5/14. Therefore, X = 15/4 / 2 = 15/8.

What is the number of grams in 500 kilograms? (1 kilogram = 1,000 grams) A. 0.5 B. 5,000 C. 50,000 D. 500,000

D. 500,000 To convert from kilograms to grams, multiply 500 kg x 1,000g/1kg, which results in 500,000 grams.

(graph) Robert sells four different flavors of jam at an annual farmers market. The graph above shows the number of jars of each type of jam he sold at the market during the first two hours. Which flavor of jam had the greatest increase in number of jars sold from Year 1 to Year 2? A. Blueberry B. Grape C. Peach D. Strawberry

A. Blueberry The graph shows that he sold 10 jars if blueberry jam the first year and 18 the second year, for an increase of 8 jars. This is the largest increase of any of the flavors.

L= {0, 20, 40, 80, 100} M= {5, 10, 15, 20, 25} N= {10, 20, 30, 40, 50} Sets L, M, and N are shown above. Which of the following sets represents LU(M(upside down U)N) (the union of L with the intersection of sets M and N)? A. {0, 5, 10, 15, 29, 25, 30, 40, 50, 80, 100} B. {0, 10, 20, 40, 80, 100} C. {20, 40} D. {20}

B. {0, 10, 20, 40, 80, 100} The intersection of sets M and N is all the numbers that appear in both of the sets, so M (upside down U) N = {10, 20}. The union of this and L is all the numbers that aero in this set or in set L, therefore L U (M (upside down U) N) = {0, 10, 20, 40, 80, 100}.

(graph) The table above shows a survey of 50 registered voters in a city. Each voter was asked whether they planned to vote "yes" or "no" on two different issues. If a voter who plans to vote "yes" on issue P is randomly selected, what is the probability that voter also plans to voter also plans to vote "yes" on issue Q? A. 0.16 B. 0.36 C. 0.40 D. 0.67

C. 0.40 There are 8 voters who plan to vote "yes" on both issues. There are 20 voters who plan to vote "yes" on issue P. This is represented by 8 + 20 = 0.4.

Jacoby followed a recipe that requires 2 cups of water for every 3 cups of flour. If he used 8 cups of flour, how many cups of water did he use? A. 2 2/3 B. 4 C. 5 1/3 D. 12

C. 5 1/3 The ratio of water to flour is 2/3.Since there were 8 cups of flour used, the expression 8 x 2/3 can be used to determine the amount of water used, which is 5 1/3.

It took Khalid 90 minutes to complete40 tasks. Which of the following is an equivalent rate? A. 10 tasks in 0.9 minutes B. 10 tasks in 2.25 minutes C. 10 tasks in 9 minutes D. 10 tasks in 22.5 minutes

D. 10 tasks in 22.5 minutes Ninety minutes to complete 40 tasks in an average rate of 22.5 minutes per task (90 minutes / 40 tasks). Multiplying this rate by 10 gives the average number of tasks Khalid completed every 10 minutes (2.25 x 10 = 22.5).

4(X + 5) + 4X + 8 Which of the following is equivalent to the expression above? A. 4(2X + 7) B. 8(X + 4) C. 5X + 17 D. 8X + 13

A. 4(2X + 7) The expression 4(X + 5) + 4X + 8 can be expanded to 4X + 20 + 4x + 8, which is equivalent to 8X + 28. Since 4 can be factored from each term in this expression, it can be rewritten as 4(2X + 7).

The volume of a right rectangular prism is found by multiplying the length of the base by the width of the base by the height of the prism. A right rectangular prism has a volume of 30 cubic inches. If the height of the prism is 6 inches, what is the area of the base of the prism? A. 5 square inches B. 24 square inches C. 36 square inches D. 180 square inches

A. 5 square inches Volume of a right rectangular prism is equal to the area of the base times the height. Since the height is known, divide the volume by height to find the area of the base. This is represented by 30 / 6 = 5.

In the xy- plane, a line crosses the y-axis at the point (0,3) and passes through the point (4,5). Which of the following is an equation of the line? A. y = 1/2X + 3 B. y = 2X + 3 C. y = 1/2X - 4 D. y = 2x - 4

A. y = 1/2X + 3 An equation in the form y = ax + b has a slope of a and a y-intercept of b. The line described has a y-intercept of 3 because it crosses the y-axis at y = 3 and has a slope of 1./2 because the value of y increases by 1 for every x increase of 2. Therefore, an equation of the line is y = 1/2X + 3.

3x - 2y = 15 x = 3 The two lines given by the equations above intersect in the xy-plane. What is the value of the y-cordinate of the point of intersection? A. -7 B. -3 C. 3 D. 7

B. -3 substituting 3 for x in the first equation gives 3(3) - 2y = 15. This simplifies to 9 - 2y = 15. Subtracting 9 from both sides of 9 - 2y = 15 gives -2y = 6. Finally, dividing both sides of -2y = 6 by -2 gives y = -3.

Which of the following values is equivalent to 5(^-3)? A. 1/15 B. 1/125 C. -15 D. -125

B. 1/125 The expression 5(^-3) can be rewritten as 1/5(^3), which is equal to 1/5x5x5 = 1/125.

Water runs from a pump at a rate of 1.5 gallons per minute. At this rate, how long would it take to fill a tub with a 150-gallon capacity? A. 10 minutes B. 100 minutes C. 225 minutes D. 2,250 minutes

B. 100 minutes The time it would take to fill the tub can be found by dividing the number of gallons the tub can hold by the rate the water rungs from the pump. This is represented by 150 gallons / 1.5 gallons per minute = 100.

Which of the following fractions is equivalent to -6 - (-9)/8? A. -3/8 B. 3/8 C. -15/8 D. 15/8

B. 3/8 The fraction -6 - (-9)/8 = -6 + 9/8, which is equivalent to 3/8.

The elevation at the summit of Mount Whitney is 4,418 meters above sea level. Climbers begin at a trailhead that has an elevation of 2,550 meters above sea level. What is the change in elevation, to the nearest foot, between the trailhead and the summit? (1 foot = 0.3048 meters) A. 569 feet B. 5,604 feet C. 6,129 feet D. 14,495 feet

C. 6,129 feet The difference between the elevations is 4,418 - 2,550 = 1,868 meters. Since each meter is 0.3048 of a foot, divide the change of elevation in meters by the conversion factor to find the number of feet (1,868 / 0.3048 = 6,129).

(graph) The table gives the population of the 5 largest countries in the European Union in the year 2014. Which of the following is closest to the mean population of these countries? A. 80.8 million B. 64.3 million C. 63.7 million D. 60.8 million

C. 63.7 million To find the mean, find the total population of all 5 countries and divide by the total number of countries: 65.9 + 80.8 + 60.8 + 46.5 + 64.3 = 318.3 and 318.3 / 5 = 63.66, which rounds to 63.7. The values in the table are given in millions, so the mean population is about 63.7 million.

(graph) Triangle PQR lies in the xy-plane, and the coordinates of vertex Q are (2, -3). Triangle PQR is rotated 180 degrees clockwise about origin and then reflected across the y-axis to produce triangle P'Q'R', where vertex Q' corresponds to vertex Q of triangle PQR. What are the coordinates of Q'? A. (-3, -2) B. (3, -2) C. (-2, 3) D. (2, 3)

D. (2, 3) When triangle PQR is rotated 180 degrees clockwise about the origin (0, 0), point Q is translated from (2, -3) to (-2, 3) in the xy-plane. Then, after the triangle is reflected, or flipped, across the y-axis, point Q is translated from (-2, 3) to (2, 3).

Which of the following expressions is 5 times as much as the sum of r and s? A. 5 x r + s B. 5 + r + s C. r + s x 5 D. (r + s) x 5

D. (r + s) x 5 The order of operations was used properly to write the expression. The sum of r and s in parenthesis is found first, then multiplication is used to find the number that is 5 times the sum of r and s.

The amount of money M, in dollars, Paul earns can be represented by the equation M = 12.5h + 11, where h is the number of hours Paul works. Which of the following is the best interpretation of the number 11 in the equation? A. The amount of money, in dollars, Paul earns each hour. B. The total amount of money, in dollars, Paul earns after working for h hours. C. The total amount of money, in dollars, Paul earns after working for one hour D. The amount of money, in dollars, Paul earns in addition to an hourly wage.

D. The amount of money, in dollars, Paul earns in addition to an hourly wage.

Which of the following expressions is equivalent to (x(^3) x X(^2))(^5)? A. X(^10) B. X(^15) C. X(^25) D. X(^30)

Using the rules of exponents, (X(^3) x X(^2))(^5) can be rewritten as (X(^(3 + 2))(^5) = (X(^5))(^5) = X(^5 x 5) = X(^25).