PT 6 - MATH

The price of a car is three times the price of a motorcycle. If the motorcycle costs $8,976 less than the car, what is the price of the car?

$13,464

The dimensions of a rectangular break room ceiling are 20 ft by 12 ft. If one sticker costs $0.50 and covers 2 feet, what is the cost of decorating the perimeter of the ceiling with stickers?

$16

The dimensions of a rectangular pond are 30 ft. x 36 ft. x 12 ft. After a drought, only two-thirds of it is filled with water. If it costs $0.06 per cubic feet of water, how much will it cost to completely fill up the rest of the pond?

$259

Factor the following expression: 81a^42 - 16b^8 A. (3a21 + 4b4)(27a21 - 4b4) B. 9a21 + 4b4)(9a21 + 4b4) C. (9a21 - 4b4)(9a21 - 4b4) D. (3a21 - 4b4)(27a21 - 4b4) E. (9a21 + 4b4)(9a21 - 4b4)

(9a^21 + 4b^4)(9a^21 - 4b^4)

[-9 - (2 - 5)] ÷ (-6)

1

4|x+2| - 7 = 9, x < 0 Quantity A: X^2 Quantity B: -6x - 1 A. Quantity A is greater B. Quantity B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given

A.

A group of 260 children responded to a survey about the average pieces of candy they consume per week. Quantity A: # of children who eat more than 5 pieces of candy per week Quantity B: One-hundred forty-two A. Quantity A is greater B. Quantity B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given

A.

0 < a < b Quantity A: (a/b) Quantity B: (b/a) A. Quantity A is greater B. Quantity B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given

B.

Fourteen liters of an 80% milk solution and 2 twelve liters of a 45% milk solution are poured into one container. Quantity A: the final concentration of milk Quantity B: 63.8% A. Quantity A is greater B. Quantity B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given

B.

Max rolls two six-sided dice. Quantity A: the probability that Max rolls two even prime numbers Quantity B: (1/18) A. Quantity A is greater B. Quantity B is greater C. the two quantities are equal D. the relationship cannot be determined from the information given.

B.

The state fair holds a coloring contest every year, awarding the top 3 winners with prizes. First place gets a gold medal, second place gets silver, and third place bronze. If 12 kids participate, how many ways can this contest be won?

1,320

What is 35% more than 10% of y, if y = 4x and 9x - 3 = 15?

1.08

A container has 4 blue marbles, 2 green marbles, and 2 yellow marbles. If you draw 3 marbles with replacement, what is the probability the third marble is the only blue marble that is drawn?

1/8

Sam is training for a marathon. Every morning, Sam leaves his house to run 3 miles West, 2 miles North, 5 miles East, 2 miles South, then 2 miles West, ending exactly where he started. Find the area enclosed by the path of Sam's run.

10 square miles

What is the area encompassed underneath the following line equation in the first quadrant? y + 3x - 9 = 0

13.5

A circle and square have the same area. If the diameter of the circle is 4 inches, what is the perimeter of the square?

14.2

#26. Evaluate the following expression. SEE EXPRESSION

16/5

The following pie charts break down the number of kids pursuing piano, violin, and guitar, from Groups A and B, where n is the number of kids in each group. What is the ratio of the number of kids pursuing guitar in Group A to kids pursuing guitar in Group B? Group A: n = 40 Piano - (30%) Guitar - (40%) Violin - (30%) Group B: n = 64 Piano - (15%) Guitar - (50%) Violin - (35%)

1:2

Solve the following expression: (2/3) + (2/5) + (8/15) + (7/25) + (9/75) = ?

2

Moe's candy jar has 4 red candies and 6 blue candies. If Moe wants the probability of choosing a red candy to be four-fifths, how many more red candies must be added to the jar?

20

Two planes left the airport at the same time, one heading east and the other heading west. The plane heading east travels at 540 miles per hour, while the plane heading west travels at 480 miles per hour. How many minutes will it take for the planes to be exactly 400 miles apart?

23 minutes

In a class of 20 students, 5 students do not own any pets. Of the remaining students, everyone either owns a dog, a cat, or both. If 10 have a dog and 8 have a cat, how many students have both?

3

A student leaves his dorm and drives east in a straight line. After driving for 150 miles, he encounters a sign stating that the rest of the road is closed, so he heads back. If the street wasn't closed and he continued for 25 more miles, he would have been located exactly halfway between his dorm and his parents' house. How far away is the student's dorm from his parents' house?

350 miles

If there are 10 people in a room, and each person shakes hands with every other person once, how many handshakes will there be?

45

Max puts $5,000 into a saving account that pays a 3% interest rate compounded annually. Which expression below represents how much money will Max have in his savings account after 10 years?

5000 x 1.03^10

A weather forecast for the next 4 days includes the temperatures: 20, 21, 25, and 34. If a represents the average temperature, d represents the median temperature, and r represents the range, find a + d + r.

62

The following is the graph for the equation x + y = 4. Find the area of the shaded region. SEE GRAPH #19

7.5

If f(x) = x^2 +2 and g(x) = (x + 1)^2, then what is f(g(2)))?

83

Alex and Chris leave the gym at the same time. From the gym, Alex and Chris walk 5 miles west to get to Alex's house. From there, Chris drives 8 miles north to get to his apartment. How far does Chris live from the gym?

9.4 miles

In an airplane, 12 passengers on board are in business class, 1/5 of the passengers are in first class, while 2/3 of the passengers are in economy class. How many total passengers are onboard?

90

SEE #22 Simplify the expression

9x^6y^6

Line A is represented by the equation: y = -3/2 x + 5. Line B is perpendicular to Line A. Quantity A: (Slope of Line A) (Slope of Line B) Quantity B: (Slope of Line B) / (Slope of Line A) A. Quantity A is greater B. Quantity B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given.

B. Quantity B is greater

{3, 4, 5, 6, 7} Quantity A: the standard deviation of the data set Quantity B: 2 A. Quantity A is greater B. Quantity B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given

B. Quantity B is greater

Is X a positive number? 1. x^2 = 1 2. x cannot equal 1 A. Statement 1 alone is sufficient but statement 2 alone is NOT sufficient to answer the question B. Statement 2 alone is sufficient but statement 1 alone is NOT sufficient to answer the question C. Both Statement 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone D. Each statement alone is sufficient to answer the question E. Statement 1 and 2 together are not sufficient to answer the question.

C.

SEE #35 Quantity A: Slope of Line X Quantity B: Slope of Line Y A. Quantity A is greater B. Quantity B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given

C. The two quantities are equal

Jeff takes 8 hours to paint a house. If he works with his cousin, Simon, it takes them 3 hours to paint. How many hours does it take for Simon to paint the house alone? A. 1 hour and 52 minutes B. 2 hours and 16 minutes C. 3 hours and 34 minutes D. 4 hours and 48 minutes E. 5 hours and 8 minutes

D.

If a person averages 7 hours of sleep per day, how many seconds does the person spend sleeping per week? A. 24 × 60 × 60/7 B. 7 × 24 × 60 × 60 C. 7 × 60 × 60/24 D. 7 × 7 × 24 × 60 E. 7 × 7 × 60 × 60

E.

A lab researcher weighed 50 lab mice and found the mean to be 225 g and the standard deviation to be 15 g. To adjust for inaccuracies, the researcher added 5 g to each data in the set. What is the new mean and standard deviation of the new set of data?

mean is 230 g and standard deviation = 15 g

6x (x + 1) = 36 what is x? (there are two solutions)

x = -3, x = 2