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- Ohio
- Columbus State Community College
- Mathematics
- Mathematics 100
- Choose An Instructor
- Quantitative Reasoning

Thanh T.

• 310

cards
In Gainesville, one in four people have blonde hair. What is the chance that if four people are chosen at random from Gainesville, at least one person has blonde hair?

A. 1/256

B. 81/256

C. 175/256

D. 255/256

E. 1

1- the chance of not happening * the choices allowed (in this case the chance of not blond is 3/4 since 1/4 is blond so which means 3/4 is not blond) so take that number x it four time since we are picking four peopel. and take 1 and subtract that number.

C. 175/256

What is the volume of a cube that has a surface area of 54?

A. 1

B. 8

C. 16

D. 27

E. 64

know this formula

Area of cub = 6s^2

volume of cube= s^3

54= 6s^2

9=s^2

s= 3

3^3 = 27

A stock falls in price by 30%. The next day it rises by 17%. The third day, it falls to 6% of the second day value. What is the approximate overall percent change in the stock price?

100 stocks x .70 = 70 stocks (day 1)

70 stocks x 1.17= 81.9 stocks (day 2)

81.9 stocks x .06= 4.914 stocks (day 3)

What is the approximate overall percent change in the stock price?

You had 100 stocks and now you have 4.914 stocks on day 3. 100-4.9= 95.1 or 95.1% decrease or you kept 4.91% of the original value.

The mean and standard deviation of a set of data is given by m and s, respectively. If 10 additional data points are added exactly at the mean, which of the following is true?

A. m stays the same, s decreases

B. m stays the same, s increases

C. m decreases, s stays the same

D. m increases, s stays the same

E. both m and s decreaseTerm

answer: A m stays the same, s decreases

A mean- measure of center and describes the “middle value” of a data set. Therefore, if you add ANY number of data points directly at the center, the mean value will not change.

Standard deviation,- a measure of spread. This describes how far the data set expands around the “middle value.” **By adding 10 additional data points at the mean, you are “compressing” the data set around the mean. This decreases the standard deviation.**

The length of symptoms of the flu is normally distributed with an average of 7 days and a standard deviation of 2 days. What is the probability that someone with the flu will have symptoms for less than 5 days?

A. 16%

B. 34%

C. 50%

D. 84%

E. 95%

To answer this problem, you must know the 68-95-99.7 rule of normal distributions. This is explained in the picture below.

In a normally distributed data set, 68% of the data lies between 1 standard deviation above and below the mean (μ ± σ), 95% of the data lies between 2 standard deviations above and below the mean (μ ± 2σ), and 99.7% of the data lies between 3 standard deviations above and below the mean (μ ± 3σ).

This problem gives you both the mean of experiencing flu symptoms, μ = 7 days, and the standard deviation, σ = 2 days, and asks you to determine the probability that someone with the flu will have symptoms for less than 5 days.

5 days is one standard deviation below the mean, μ-σ. You are trying to determine the percent of the population that is beneath this threshold. From the 68-95-99.7 rule and the picture below, you know that 68% of the population lies between 1 standard deviation above and below the mean; therefore, 32% of the population is both above and below 1 standard deviation from the mean. However, we only want the percent of the population below 1 standard deviation below the mean, which is half of 32%, or 16%, so the answer is [A].

https://s3.amazonaws.com/datbootcamp/math/math-4-21-1.png

https://s3.amazonaws.com/datbootcamp/math/math-4-21-2.png

If you have 2 distinct black playing cards and 2 distinct red playing cards, how many ways can you arrange the four cards given that the red cards can never be next to each other?

A. 2

B. 4

C. 8

D. 12

E. 24

The first step is to determine the total number of all possible positions. Given that there are 4 distinct cards, the total number is 4! = 4 * 3 * 2 * 1 = 24.

**Possible combinations if the cards are identical:****RBRB, RBBR, BRBR**

**There are 3 possible combinations if the red and black cards are identical. If the red cards are different, we can double the number of combinations, so there are 6 total combinations. Since both the red and black cards are different, we will double it again and find that there are 12 possible configuration**s (I will enumerate them here, but on the test it is faster to not to do this!).

Now we will determine how many combinations have the red cards NOT next to each other. At first, we will assume the red and black cards are the same, and then double the number of combinations to account for the fact that the red cards are different, and then double that value again to account for the fact that the black cards are different.

Possible combinations(R=red, B=black):

R1B1R2B2, R2B1R1B2, R2B2R1B1, R1B2R2B1, R1B1B2R2, R2B1B2R2, R1B2B1R2, R2B2B1R2, B1R1B2R2, B1R2B2R1, B2R1B1R2, and B2R2B1R1.

So there are 12 possible combinations, and the answer is [D].

How many ways can the letters in MJOLNIR be arranged?

A. 5040

B. 7! / [2! 2!]

C. 6062

D. 77

E. 267

A. 2

B. 4

C. 6

D. 12

E. 24

Which of the following fractions is the largest?

A. 5/8

B. 10/13

C. 2/5

D. 11/14

E. 1/4

A. -0.1/0.01

B. -0.1/0.1

C. -0.1/-0.01

D. -0.1/-0.1

E. -0.1/-1

A. 100

B. 340

C. 621

D. 929

E. 1344

A. 5%

B. 10%

C. 45%

D. 50%

E. 55%

A. 12

B. 35

C. 64

D. 125

E. 210

A. 0.44

B. 1.5

C. 2.25

D. 3.66

E. 4.25

A. 25 degrees

B. 30 degrees

C. 45 degrees

D. 60 degrees

E. 75 degrees

A. 2/x

B. 4/x2

C. https://s3.amazonaws.com/datbootcamp/math/math-4-35-4.png

D. https://s3.amazonaws.com/datbootcamp/math/math-4-35-5.png

E. https://s3.amazonaws.com/datbootcamp/math/math-4-35-6.png

A. $50

B. $160

C. $405

D. $574

E. $762

A. 10 seconds

B. 12 seconds

C. 15 seconds

D. 20 seconds

E. 30 seconds

A. 15

B. 17

C. 19

D. 21

E. 23

A. 1/2

B. 2/5

C. 1/3

D. 3/5

E. 2/3

A. 16 liters

B. 12 liters

C. 32/3 liters

D. 94/5 liters

E. 18 liters

Solve for x: (x+7)2 ⁄ 3 = 9

A. 1

B. 8

C. 13

D. 20

E. 33

https://s3.amazonaws.com/datbootcamp/math/math-4-2-1.png

A. -6

B. -3

C. 3

D. 6

E. 8

https://s3.amazonaws.com/datbootcamp/math/math-4-4-1.png

A. (3x^6) ÷ (4y^4)

B. (5x^5) ÷ (3y^15)

C. (8x^12) ÷ (8y^4)

D. (16y^-3) ÷ (5x^4)

E. (3y^2) ÷ (16x^15)

A. (4,0)

B. (3,0)

C. (-4,0)

D. (0,3)

E. (0,4)

If 4^(2+x) = 2 × 16 × 32, what is x?

A. 3

B. 4

C. 5

D. 6

E. 7

Solve for x: 17 ≤ 2 - 3x

A. x ≤ 5

B. x ≥ 5

C. x ≥ -5

D. x ≤ -5

E. x > -5

A. 18 degrees

B. 46 degrees

C. 56 degrees

D. 62 degrees

E. 70 degrees

What is the largest possible value of x in the solution to 3 – x ≥ 7?

A. -10

B. -4

C. 4

D. 10

E. 14

Solve for x: https://s3.amazonaws.com/datbootcamp/math/math-4-10-1.png

A. 0

B. 1

C. 2

D. 3

E. 4

https://s3.amazonaws.com/datbootcamp/math/math-4-3-1.png

A. -2

B. -1

C. 0

D. 1

E. 2

1/2 added to 1/5 is 70% of what number?

A. 1

B. 3/2

C. 2

D. 5/3

E. 9/4

A. $100

B. $120

C. $140

D. $156

E. $188

A. 25

B. 50

C. 75

D. 110

E. 150

Simplify: (9^(5 )– 27^4) ⁄ 3^9

A. -10

B. 14

C. -24

D. 81

E. 6

A. +10%

B. -23%

C. -31%

D. -91%

E. -95%

Which of the following fractions is the largest?

A. 5/8

B. 10/13

C. 2/5

D. 11/14

E. 1/4

A. √20

B. √29

C. √35

D. √42

E. √50

https://s3.amazonaws.com/datbootcamp/math/math-4-29-1.png

A. 2 – π/8

B. 2 – π/4

C. 2 – π/2

D. 2 – π

E. 2

https://s3.amazonaws.com/datbootcamp/math/math-4-30-10.png

In the diagram, point A is at the intersection of the minor axis and the ellipse, and point B is at the intersection of the major axis and the ellipse. What is the length of the line segment AB?

https://s3.amazonaws.com/datbootcamp/math/math-4-30-1.png

A. 2

B. 3

C. 3√2

D. 4

E. 5

A. 2

B. 3

C. 4

D. 4√2

E. 7

https://s3.amazonaws.com/datbootcamp/math/math-4-34-1.png

A. sin a/c

B. sin b/c

C. arcsin a/c

D. arcsin b/c

E. arctan a/c

A. x = 1

B. x = 29/21

C. x = 3/2

D. x = 2

E. x = 54/21

If , https://s3.amazonaws.com/datbootcamp/math-1-2-1.png

what is the value of x?

A. 3

B. 6

C. 10

D. 15

E. 16

Johnny has 15 toys with a total value of $125. If some of Johnny’s toys are worth $5 and the others are worth $10, how many toys does Johnny have that are worth $5?

A. 5

B. 7

C. 8

D. 10

E. 13

Simplify

https://s3.amazonaws.com/datbootcamp/math/math-1-4-1.png

A. 16x / z^3 y

B. 2x / z^3 y

C. 2x / z^3 y^2

D. 2x / zy^2

E. 16x / zy^2

Find suitable expressions for x and y such that log(245) = x + 2y.

A. x = 4 log(2) and y = 3 log (5)

B. x = log(13) and y = log(11)

C. x = log(337.5) and y = log(225)

D. x = log(3) and y = log(9)

E. x = log(5) and y = log(7)

Solve the inequality: |3 – x| < 14

A. x > -11

B. -11 < x < 17

C. x < 17

D. x < -11 and x > 17

E. x < -11

If ab + 2 = 9 – 4a, what is the value of a?

A. 3b

B. 7

C. 7 / b

D. 7 / (b + 4)

E. 3 / (b - 2)

Solve for x:

https://s3.amazonaws.com/datbootcamp/math/math-1-8-1.png

8 ^(3x-4) = (2^x ) * 16

A. -1

B. 0.5

C. 2

D. 3.5

E. 4

Solve for x: 3^ (x^3 – 4) = 81

x cube minus 4

A. 2

B. 3

C. 4

D. 5

E. 6

A. √2

B. 2√2

C. 3 √2

D. √3

E. 2√3

A. 1

B. 3.5

C. 5

D. 7.5

E. 10.5

Express (4 x 10^3) ^2 in scientific notation:

A. 1 x 106

B. 1.6 x 106

C. 4 x 106

D. 1 x 107

E. 1.6 x 107

If a stack of 12 identical books is 24.12 inches tall, how tall is each book?

A. 1.01 inches

B. 1.02 inches

C. 2.01 inches

D. 2.02 inches

E. 3.03 inches

An apple tree yields 40 apples one harvest year. The next year is a particularly good harvest, and the same apple tree yields 100 apples. What is the percent increase between the two years of harvest?

A. 50%

B. 100%

C. 150%

D. 200%

E. 250%

Question 15 of 40

Round down to the next integer: log2 (80)

A. 4

B. 5

C. 6

D. 7

E. 8

A class of 20 students averages a score of 80 on a test (out of 100). How many students would need to do the 5 point extra credit to bring the average up to 82?

A. 2

B. 3

C. 5

D. 7

E. 8

Question 17 of 40

Approximate √√40,000 ( square root of square root 40,000) A. 8

B. 10

C. 14

D. 20

E. 25

Given that 1 inch = 2.54 centimeters, approximately how many yards are there in 10 meters?

A. 8

B. 9

C. 10

D. 11

E. 12

The standard deviation of {10, 15, 20, 25, 30} can be best approximated by which of the following?

A. 3.3

B. 7.5

C. 12.2

D. 14.6

E. 15.7

What is the probability of pulling two cards from the same suit in a row, with each card coming from a separate 52 card deck?

A. 4/13

B. 1/4

C. 1/8

D. 1/16

E. 1/32

Three dice are rolled. What is the probability that all three dice come up with the same number?

A. 1/216

B. 1/108

C. 1/72

D. 1/36

E. 1/2

In a group of people, 30 of them wear glasses and 17 of them wear earrings. If 12 people wear both glasses and earrings, how many people wear only earrings or only glasses?

A. 17

B. 23

C. 30

D. 35

E. 42

If x is a random variable whose probability distribution function is given by a normal distribution with mean of 7 and standard deviation of 2, which of the following values of x is the least likely?

A. 5

B. 2.5

C. 7

D. 8

E. 10

A standard deck of playing cards consists of 52 cards, half of which are black and half of which are red. If three cards are picked at random from the deck with replacement, what is the probability that either all three are black or all three are red?

A. 1/2

B. 1/4

C. 1/8

D. 3/8

E. 1/16

A. 26 * 26 * 10 * 10 * 10

B. 26 * 26 * 9 * 9 * 9

C. 26 * 25 * 10 * 10 * 9

D. 26 * 25 * 9 * 8 * 7

E. 26 * 25 * 10 * 9 * 8

Constantine picks two letters at random from the word CONSTANTINOPLE with replacement. What is the probability that both letters picked are consonants?

A. 9/14

B. 81/196

C. 5/14

D. 25/196

E. 14/196

Which of the following data sets has the largest standard deviation?

A. {1, 3, 5, 7, 9}

B. {1, 2, 3, 4, 5}

C. {1, 3, 5, 7, 10}

D. {2, 3, 5, 7, 9}

E. {1, 3, 6, 7, 9}

Two lines in the two-dimensional plane are perpendicular. If one line passes through the points (2,4) and (6,11), what is the slope of the other line?

A. 4/7

B. -4/7

C. 7/4

D. -7/4

E. -1

A rectangle perfectly bounds an ellipse. If the rectangle’s long side is of length 26 and the short side is of length 10, determine the area of the shaded region.

https://s3.amazonaws.com/datbootcamp/math/math-1-29-1.png

A. 40π - 130

B. 40 - 130π

C. 120 - 60π

D. 260 - 55π

E. 260 - 65π

A semi-circular piece of paper with a radius of 3 inches is attached to a stick along the diameter AB, as seen in the figure. If the paper is horizontally rotated a full revolution around the stick, what volume does the piece of paper generate, in cubic inches?

https://s3.amazonaws.com/datbootcamp/math/math-1-30-1.png

A. 10π

B. 24π

C. 36π

D. 48π

E. 80π

A square of side length 1 has two half-circles etched into it as shown in the figure. What area of the square is outside of either of the half-circles?

https://s3.amazonaws.com/datbootcamp/math/math-1-31-1.png

A. 1 – π

B. 1 – (π/2)

C. 1 – (π/4)

D. π/2

E. π

A tin can is a closed cylinder of radius 3 centimeters and height 9 centimeters. If the top of the can was removed to get at the contents inside, what fraction of the surface area of the can is left?

A. 1/2

B. 5/8

C. 3/4

D. 7/8

E. 1/8

A cylindrical can has a volume of 48π. If the can has a height of 3, what is the circumference of the circular cross section of the can?

A. 2π

B. 3π

C. 4π

D. 6π

E. 8π

Two adjacent sides of a triangle have lengths 3 and 7. If the total area of the triangle is 10, which of the following represents the angle between the two adjacent sides?

A. arcsin (20/21)

B. arcsin (10/21)

C. arccos (20/21)

D. arccos (10/21)

E. arctan (6/7)

Question 35 of 40

If cos(θ) = 12/13, find csc(θ).

A. 13/5

B. 13/12

C. 5/13

D. 169/144

E. 169/25

A military aircraft is travelling from Norfolk to McKinley, a 50-mile, straight line journey, with a refueling station on the route between the two. 30 miles into the flight, the pilot is recalled back to Norfolk, but must refuel. Given that the refueling station is in the direction of Norfolk and that the distance from the pilot’s current position to the refueling station is 1/4 the remaining distance to McKinley, how far is the refueling station from Norfolk?

A. 17 miles

B. 19 miles

C. 21 miles

D. 23 miles

E. 25 miles

Daniel is four years older than Greg. In 8 years, Daniel will be two years older than three times Greg’s current age. How old is Greg now?

A. 1

B. 3

C. 4

D. 5

E. 6

Bob can chop down 10 trees in 30 minutes, while Frank can chop down 15 trees in 30 minutes. Working together, how long will it take them to chop down 100 trees?

A. 40 minutes

B. 50 minutes

C. 60 minutes

D. 80 minutes

E. 120 minutes

A. $0.10

B. $0.15

C. $0.20

D. $0.25

E. $0.30

McDowell’s sells x burgers at a price of $10. How much would 2 burgers cost at McDowell’s?

A. 10 / x

B. 5 / x

C. x / 5

D. x / 20

E. 20 / x

February 13, 2017

A. 45 seconds

B. 20 seconds

C. 30 seconds

D. 40 seconds

E. 1 minute

What expression describes the shaded region in the picture, between the lines y = -x and y = 2x + 5?

https://s3.amazonaws.com/datbootcamp/math/math-2-1-1.png

A. y ≥ -x and y ≤ 2x + 5

B. y ≥ -x and y ≥ 2x + 5

C. y ≤ -x and y ≤ 2x + 5

D. y ≤ -x and y ≥ 2x + 5

E. y = x and y ≤ 2x + 5

What is a possible value of x – 3 given that (4x + 3)2 = 289?

A. -1/2

B. 0

C. 1/2

D. 2

E. 3

For which of the following could set {-100, -50, -25, 25, 50, 100} satisfy G ∪ F?

A. F = {x ≥ 100}, G = {x ≤ -100}

B. F = {|100|}, G = {-50, -25}

C. F = {x < 100}, G = {x < -100}

D. F = {x < 25}, G = {x < -25}

E. F = {x ≥ 14}, G = {x ≤ -14}

A. -5 ≥ x ≥ -15

B. 5 ≥ x and ≥ 15

C. 5 ≤ x ≤ 15

D. 3 ≤ x ≤ 12

E. 3 ≥ x ≥ 12

A. (-∞, ∞)

B. (-∞, -3)

C. (-∞, -3) ∪ (0, ∞)

D. (0, ∞)

E. (-∞, 0)

Question 6 of 40

Solve for x: 0.003 = √.0036x

A. 0.0025

B. 0.0081

C. 0.009

D. 0.012

E. 0.05

Simplify (5 ⁄ x)^3 + 7x^4

A. (7x7+125) ⁄ x3

B. 25x4 ⁄ 7x3

C. (5x3 + 343) ⁄ x4

D. (125x + 7) ⁄ x3

E. 7x4 ⁄ 5x3

Solve for x: (x-1)^(4/3) = 16

https://s3.amazonaws.com/datbootcamp/math/math-2-8-1.png

A. 4

B. 8

C. 9

D. 12

E. 16

What is the solution set to the following inequality: |3x + 1| < 4?

A. -5/3 < x < 1

B. x < 1

C. x > -5/3

D. x < -5/3 or x > 1

E. x > 1

Which of the following fractions is the largest?

A. 5/8

B. 8/14

C. 16/30

D. 3/4

E. 11/20

Which of the following fractions is the largest?

A. 5/8

B. 8/14

C. 16/30

D. 3/4

E. 11/20

What is the smallest positive number that is divisible by both 15 and 21?

A. 15 * 21

B. 3 * 21

C. 5 * 21

D. 15 * 3

E. 15 * 15

Determine

https://s3.amazonaws.com/datbootcamp/math/math-2-13-1.png

A. 13

B. 18

C. 22

D. 31

E. 36

Of the 10,000 people graduating from the State College this year, 30% are engineers, and 17% of the engineers are nuclear engineers. How many nuclear engineers are graduating from the State College this year?

A. 130

B. 310

C. 440

D. 510

E. 670

Jimmy buys 12 oranges at $1 an orange, and 4 apples at $2 an apple. What is the average price per fruit of the two fruits Jimmy bought?

A. $1.00

B. $1.25

C. $1.50

D. $1.75

E. $2.00

Simplify https://s3.amazonaws.com/datbootcamp/math/math-2-16-1.png

A. 5 x 4

B. 5 x 4^10

C. 5 x 4^14

D. 5 / 4^4

E. 5 / 4^10

It takes 28 minutes to polish 7/9 of a mirror. How long does it take to polish the entire mirror?

A. 36 minutes

B. 40 minutes

C. 44 minutes

D. 50 minutes

E. 54 minutes

A farmer has a piece of land with an area of 4 square yards. If a cow can graze grass at a rate of 2 square feet per hour, how long will it take 3 cows to graze the entire piece of land?

A. 1 hour

B. 2 hours

C. 3 hours

D. 4 hours

E. 6 hours

There are 8 marbles in a bag: 4 are blue, 3 are green, and 1 is red. What is the probability that of two randomly chosen marbles without replacement, 1 is blue and 1 is red?

A. 1/7

B. 1/6

C. 2/5

D. 1/2

E. 3/4

The odd numbers on a regular die are painted red. On a second regular die, the numbers that are one less than a perfect square are painted red. If both dice are thrown, what is the chance that both come up red?

A. 1/12

B. 1/6

C. 1/3

D. 3/12

E. 7/12

According to a survey, the average number of keys kept on a given person’s keychain is normally distributed with a mean of 4 and a standard deviation of 1. If a person is chosen at random, what is the probability that this person has less than 3 keys on their key chain?

A. 5%

B. 16%

C. 34%

D. 50%

E. 68%

Isotope A has a 1/4 chance of decaying in an hour, while isotope B has a 1/9 chance of decaying in an hour. In one hour, what is the chance that isotope A decays and isotope B does not decay?

A. 2/9

B. 1/4

C. 5/9

D. 3/4

E. 1

13 business men all have to shake each others’ hands. How many handshakes will take place in total? Assume that each businessman only shakes hands with everyone once.

A. 13

B. 39

C. 52

D. 78

E. 156

A group of 100 people were asked to pick a random number between 1 and 20. If 52 of them picked the number 17, which of the following must be true?

A. Only the median of the dataset is 17

B. Only the mode of the dataset is 17

C. The mean of the dataset is 17

D. The median and the mode of the dataset is 17

E. The median and the mean of the dataset is 17

How many lines can be drawn between a set of 7 distinct points?

A. 10

B. 12

C. 15

D. 19

E. 21

Half of the population of Cool Town owns a bicycle, and 25% of the population owns a car. If 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from Cool Town owns either a car or a bicycle or both?

A. 10%

B. 50%

C. 65%

D. 75%

E. 100%

How many distinct amounts of money can be made from any combination of 1 quarter, 3 dimes, and 1 nickel?

A. 8

B. 9

C. 10

D. 11

E. 12

What is the distance in the x-y plane between the points (1,4) and (3,7)?

A. 3

B. √13

C. 4

D. √17

E. √21

An ellipse is defined by the equation x^2 ⁄ 9 + y^2 ⁄ 16 = 1. A square is made with side length equal to the distance between the two foci, as seen in the picture. What is the area of this square?

https://s3.amazonaws.com/datbootcamp/math/math-2-29-1.png

A. 10

B. 15√2

C. 20√7

D. 28

E. 34

The location of the foci is given by another constant c, which is defined by:

https://s3.amazonaws.com/datbootcamp/math/math-2-30-1.png

A. 4√3 + 2π

B. 4√3 + 4π

C. 2√3 + 2π

D. 2√3 + 4π

E. 4√3 + 6π

30-60-90 triangles

45-45-90 angles

The hypotenuse of a right triangle has a length of 13, and one of its sides has a length of 12. What is the area of the triangle?

A. 20

B. 30

C. 45

D. 60

E. 120

A square has an area equal to 49. What is the length of the largest bisecting line going between opposite points of the square?

A. 4

B. 4√2

C. 6

D. 7

E. 7√2

A basketball of diameter 10 inches is places in a cube box of side length 10 inches. What is the difference in volume between the box and the basketball (in cubic inches)?

A. 1000 – (500/3)π

B. 1000 – (1000/3)π

C. 1000 – 500π

D. 1000 – (200/3)π

E. 100 – 25π

tanx * (sinx – cosx) = ?

A. sin2x

B. cos x

C. sin x * (tan x - 1)

D. sin x * (cos x - sin x)

E. tan2x

If 2 cos (x) – 1 = 0, what value of x between 0° and 90° satisfies this equation?

A. 5π/6

B. π/3

C. π/4

D. π/6

E. 5π/3

Cover degree to radian

Julia took 4 courses at her college this past semester. She earned an A in chemistry (3 credits), a B in chemistry lab (1 credit), an A in Spanish (4 credits), and a C in Fruit Science (1 credit). If grades are weighted such that an A is four grade points, a B is three grades points, and a C is two grade points, what is Julia’s grade point average from this past semester?

A. 2.89

B. 3.00

C. 3.50

D. 3.67

E. 4.00

A population of rabbits grows by 10% every month. If the population begins with 1000 rabbits, how many rabbits will there be in 6 months?

A. 1234

B. 1451

C. 1772

D. 2003

E. 2304

Jeff can paint a wall in 3 hours, while Will can paint the same size wall in 5 hours. If they work together and charge $40 an hour to paint walls, how much should they charge to paint 3 walls?

A. $80

B. $160

C. $175

D. $205

E. $225

Train A leaves a city traveling at 100 miles per hour. Train B leaves from the same city in the same direction of Train A traveling at 150 miles per hour. If train A leaves 3 hours before train B, how long will it take for train B to catch up to train A?

A. 3 hours

B. 4 hours

C. 5 hours

D. 6 hours

E. 8 hours

Kelly is twice as old as her friend Jess. In ten years, Kelly will be four more years older than three times Jess’ current age. How old is Kelly now?

A. 3

B. 5

C. 6

D. 8

E. 12

3 liters of 50% salt solution is mixed with 7 liters of 13% solution. What is the percent of salt in the mixture?

A. 13.6%

B. 17.4%

C. 24.1%

D. 33.2%

E. 50.1%

Which of the following expressions represents the shaded area in the graph below?

https://s3.amazonaws.com/datbootcamp/math/math-3-1-1.png

A. 5 ≥ y ≥ x2

B. y ≤ 5 and x ≤ x2

C. y ≥ 5 and x ≥ x2

D. 5 ≥ y ≤ x2

E. y ≥ -5 and x ≤ -x2

Factor x^6 – 4y^8 into two binomial factors.

A. (x^3 – 4y^4 )(x^3 + y^4)

B. (x^3 – 2y^4)^2

C. (x^3 – 2y^4 )(x^3 + 2y^4)

D. (x^3 + 2y^4)

E. (x^3 – 4y^4)^2

For which values of x is the following function undefined?

https://s3.amazonaws.com/datbootcamp/math/math-3-3-1.png

A. x = 2

B. x = -2

C. x = 3

D. x = -3

E. x = -2 and x = 3

Question 4 of 40

Solve for x: 3 + (x – 4) – 2(x + 7) = x – 10

A. -7

B. -5

C. -3

D. -5/2

E. 1/2

Find suitable expressions for x and y such that log(675)= 2x + 3y.

A. x = 2log(5) and y = 4log(3)

B. x = log(13) and y = log(11)

C. x = log(5) and y = log(3)

D. x = log(3) and y = log(5)

E. x = log(337.5) and y = log(225)

Solve for

https://s3.amazonaws.com/datbootcamp/math/math-3-6-10.png

A. 27

B. 32

C. 49

D. 64

E. 81

Which of the following is equivalent to the inequality ?

https://s3.amazonaws.com/datbootcamp/math/math-3-7-1.png

A. x < 15

B. x < -15

C. x > 15

D. x > -15

E. x = 15

Find f(g(x)) if f(x) = x^2 and g(x) = x + 1.

A. x

B. x2

C. x2 + 1

D. x2 + 2x + 1

E. x + 1

What is the equation of the line the that contains the point (1,0) and is perpendicular to the line

2y + 3x = 1?

A. y = x + 1

B. y= (1/2) x - 1

C. y= (2/3) x + 1

D. y = x - 1

E. y = (2/3) x - (2/3)

Question 10 of 40

Six tenths of 500 is what percent of 250?

A. 120%

B. 130%

C. 150%

D. 170%

E. 200%

The price of a video game console is increased by 20%. If you have a coupon to buy the video game console for 10% off, what is the net percent change from the original price of the console?

A. 8% decrease

B. 8% increase

C. 10% decrease

D. 10% increase

E. 12% increase

Question 12 of 40

How many positive integer factors does 210 have?

A. 1

B. 4

C. 10

D. 16

E. 22

Which of the following is the highest apples to oranges ratio?

A. 3 apples for 9 oranges

B. 300 apples for 800 oranges

C. 0.8 apples for 0.4 oranges

D. 0.8 apples for 0.04 oranges

E. 10 apples for 1 orange

On average, beer is 5% alcohol by volume (ABV), wine is 12% ABV, and liquor is 37% ABV. What would be the alcohol content in mL of a 1 L bargain drink that is 3 parts beer, 4 parts liquor, and 3 parts wine? (1000 mL = 1 L)

A. 96 mL

B. 199 mL

C. 299 mL

D. 359 mL

E. 499 mL

The State of Florida voted to increase sales tax an additional 0.25%. What is the extra amount paid on a $70 jacket from this sales tax increase?

A. $0.02

B. $0.07

C. $0.18

D. $0.25

E. $1.75

How many millimeters are there in two feet, given that 1 inch = 2.54 centimeters?

A. 30.48

B. 60.96

C. 304.80

D. 609.60

E. 1219.2

The National Institute of Science and Technology reviewed several commercially available clocks to determine the number of seconds they lost per year. They found that this data followed a Gaussian distribution with a mean of 450 seconds lost per year and a standard deviation of 50 seconds. What percentage of clocks lose 500 or more seconds per year?

A. 84%

B. 32%

C. 16%

D. 4%

E. 2%

How many different ways (orders) can you arrange 6 different playing cards?

A. 6

B. 36

C. 720

D. 1296

E. 46656

How many ways can you choose 7 people from a group of 10?

A. 70

B. 120

C. 140

D. 240

E. 300

Which of the following is the closest to the standard deviation of the following data set? {10, 13, 19, 14, 16}

A. 0.03

B. 0.3

C. 3

D. 30

E. 300

How many ways can the letters in **APPALOOSA** be arranged?

A. 2405

B. 2505

C. 9050

D. 13530

E. 15120

A hat contains 5 pieces of red paper and 12 pieces of blue paper. How many more pieces of red paper need to be added so that the probability of choosing a piece of red paper is 60%?

A. 2

B. 5

C. 9

D. 13

E. 17

Two normal dice are rolled. What is the probability of getting a sum of 7 or 11?

A. 1/36

B. 1/9

C. 2/9

D. 1/2

E. 3/4

Out of a group of 200 dogs, 20% have spots, 35% have brown fur, and 10% have both spots and brown fur. How many dogs have either spots or brown fur but not both?

A. 10

B. 25

C. 45

D. 65

E. 70

Which of the following best represents the standard deviation of the data set

{10, 12, 13, 14, 16}?

A. 2

B. 2.4

C. 2.8

D. 3

E. 3.2

The front wheel of a bicycle has a 1 foot radius and travels 84π inches. If the rear wheel has only a 3 inch radius, how many revolutions combined do both wheels undergo?

A. 3.5

B. 17.5

C. 20

D. 21

E. 25.5

how to find revolutions by wheel

A cube has side length of 1. What is the maximum distance between two points inside the cube?

A. 1

B. √2

C. 2

D. √3

E. 3

If the ratio of the interior angles of a strange quadrilateral is 1:3:5:9, what is the measure of the smallest angle?

A. 10 degrees

B. 12 degrees

C. 16 degrees

D. 20 degrees

E. 30 degrees

If the measures of the three angles of a triangle are x, x^2, and 7x, what is x?

A. 5 degrees

B. 10 degrees

C. 12 degrees

D. 15 degrees

E. 70 degrees

Four squares with side length 2 are lined up side by side as shown in the figure. A circle is etched into the four squares, with center at the point that all four square touch and such that the circle intersects each of the squares at half way along an edge. What is the ratio of the area of the circle to the area of the four squares together?

https://s3.amazonaws.com/datbootcamp/math/math-3-31-4.PNG

A. π/16

B. π/8

C. π

D. 2π

E. 3π/2

What is the measure of an internal angle of a regular 18-gon?

A. 150 degrees

B. 160 degrees

C. 175 degrees

D. 120 degrees

E. 30 degrees

If

https://s3.amazonaws.com/datbootcamp/math/math-3-33-10.png

A. 1/4

B. -1/4

C. 4

D. -4

E. 16

A 30 foot tall tree was knocked over during a hurricane. The top of the tree knocked into a nearby house at a point 14 feet up the wall of the house. What angle does the tree make with the ground?

A. Arctan (14/30)

B. Arcsin (30/14)

C. Arcsin (14/30)

D. Arccos (14/30)

E. Arccos (30/14)

An investment in Pear Computers has an initial value of $5000. A second investment in Macrosoft Computers has an initial value of $7500. The Pear stock falls by the same percentage as the Macrosoft stock rises. If the new combined investment value is $13,000, by what percentage did the Pear stock fall and the Macrosoft stock rise?

A. 10%

B. 15%

C. 20%

D. 30%

E. 45%

Richard is three times as old as Bryan. In six years, Richard will be twice as old as Bryan will be in six years. How old is Richard right now?

A. 12

B. 15

C. 18

D. 21

E. 28

While riding his bike, Mike travels 10 miles at 30 miles per hour, then an additional 20 miles at 10 miles per hour. What is Mike’s approximate average velocity for the entire trip?

A. 10 mph

B. 13 mph

C. 15 mph

D. 20 mph

E. 30 mph

Connie can file 100 papers an hour, while Eric can file 80 papers an hour. Working together, how long will it take them to file 900 papers?

A. 4 hours

B. 5 hours

C. 5.5 hours

D. 6 hours

E. 8 hours

A businessman puts $100,000 into a stock, which yields an interest rate of 10% compounded annually. After 3 years, how much is the investment worth?

A. $110,837

B. $130,000

C. $133,100

D. $146,410

E. $201,283

Karen buys enough cans of soda to last her 30 days. The next time Karen is at the store, she sees that the price of cans of soda is on-sale for 25% less than their original value. If Karen spends the exact same amount on cans of soda, how long will the new on-sale supply last her?

A. 20 days

B. 30 days

C. 40 days

D. 45 days

E. 50 days

John can mow a lawn in 2 hours, and Matt can mow the same lawn in 3 hours. How long will it take for John and Matt to mow the lawn working together, but John only works for 24 minutes?

A. 80 minutes

B. 120 minutes

C. 144 minutes

D. 164 minutes

E. 180 minutes

A. 8! / 5!

B. 8! / (5! × 3!)

C. 8!

D. 38

E. 8! / (5! × 3)

A. 45 seconds

B. 20 seconds

C. 30 seconds

D. 40 seconds

E. 1 minute

A. 95040

B. 792

C. 350

D. 4200

E. 18

When order matter use____

when order doesn't matter use___

A. 24

B. 48

C. 32

D. 40

E. 36

A. 2004 * 10^2

B. 200 * 10^3

C. 2 * 10^5

D. 2 * 10^3

E. 2 * 10^4

A. -14

B. 10

C. 32.4

D. -7.78

E. 25.2

To convert F to Celcius

Convert Celsius to F

A. 15

B. 16

C. 14

D. √236

E. √212

A. 5’8”

B. 5’4”

C. 5’7.33”

D. 5’7”

E. 5’9”

A. (13×13) / (52×52)

B. (13 / 52)

C. (13×12) / (52×51)

D. (13! / 52!)

E. (2 / 13)

A. 8 to 3

B. 5 to 3

C. 3 to 5

D. 3 to 11

E. 3 to 8

25x is to 40y as 25y is to what?

A. 40x

B. 40y2/x

C. 40x2/y

D. x/40

E. 40/xy

In how many different orders can six books be organized in a shelf?

A. 1

B. 64

C. 1296

D. 720

E. 36

a. 33%

b. 50%

c. 68%

d. 75%

e. 90%

A. 5:4

B. 3:2

C. 1:1

D. 4:5

E. 2:3

what is a composite number

What is prime number

a. Exponential

b. Logarithmic

c. Linear

d. Polynomial

e. Inversely proportional

Exponential plots would result in a greater increase in ____ over time,

logarithmic plots would result in ___ approaching an asymptote over time.

A linear trend is one in which an increase in ___ results in a linear increase in ___

A. π

B. √2/2

C. (π√2)/4

D. √2/(2π)

E. (2√2)/π

isosceles triangle vs equilateral triangle

A. cos(x)

B. √x

C. -|x|

D. ex

E. x!

a) growing

2) decreasing

A. 4 cells

B. 64 cells

C. 128 cells

D. 256 cells

E. 512 cells

A. 63

B. 66

C. 132

D. 198

E. 496

A. 10

B. 12

C. 16

D. 18

E. 20

A. 17.4 minutes

B. 18 minutes

C. 16 minutes

D. 16.8 minutes

E. 15.5 minutes

A. 11 AM

B. 10 AM

C. 10:30 AM

D. 11:30 AM

E. Jason never passes Mark

A. A is divisible by C.

B. X is divisible by B.

C. Division of X by A equals B.

D. B is divisible by C.

E. A * X is always odd.

A. 2

B. 3

C. 4

D. 5

E. 6

A. $1025

B. $1130

C. $2050

D. $2155

E. $2260

A. 275

B. 235

C. 200

D. 247.50

E. 250

A. 83

B. 80.52

C. 52.8

D. 50.8

E. 62.5

A. $64

B. $112

C. $148

D. $172

E. $96

A. 0 to 60 mph in 4 seconds

B. 0 to 75 mph in 5 seconds

C. 0 to 55 mph in 3.5 seconds

D. 0 to 45 mph in 3 seconds

E. 0 to 65 mph in 4.5 seconds

A uniform acceleration implies that the speed increases ______.

A. 9

B. 11

C. 12

D. 13

E. 15

Know special right angles

A. 20

B. 20√2

C. 10/√2

D. 40

E. 20/√2

A. 82

B. 80

C. 79

D. 81

E. 78

A. {12,14,16}

B. {12, 14, 18}

C. {120, 140, 160}

D. {60, 61, 59}

E. {20, 20, 25}

A. 17

B. 8

C. 23

D. 28

E. 11

A. 1/2

B. 3/8

C. 1/8

D. 3/4

E. 5/8

A. 1/3

B. 3/10

C. 1/4

D. 1/8

E. 3/5

A. 16

B. 15

C. 16.5

D. 15.5

E. 14.5

A. (sin x + cos x)^2

B. 2(sin x + cos x)

C. (sin^2x / cos x) + (cos x / sin^2x)

D. cos x (tan x * sin x + cos x)

E. (sin x - cos x)^2

A. 1.11 x 10^-2

B. 1.11 x 10^-4

C. 111 x 10^-2

D. 10^-9

E. 3 x 10^-3

A. 62.1

B. 6.21

C. 16.1

D. 1.61

E. 52.8

2.4 * 10^-6 * (5 * 10^6)^2 = ?

A. 6 x 10^6

B. 1.2 x 10^6

C. 6 x 10^7

D. 2.4 x 10^7

E. 1.2 x 10^7

A. 10^12

B. 10^8

C. 10^6

D. 10^3

E. 10^2

http://datquestionoftheday.com/wp-content/uploads/2013/03/12.jpeg

A.) 15.925

B.) 21.35

C.) 24.5

D.) 29.575

E.) 31.85

A. 50 lbs.

B. 100 lbs.

C. 200 lbs.

D. 400 lbs.

E. The English and metric tons weigh the same.

Given that:

4y + 6x = 26

3y – 6x = -12

What is 2x – 5y?

A. -1

B. -4

C. 10

D. 5

E. 8/5

, what is the value of 45x?

A. -45

B. 25

C. 45

D. 81

E. -125

The following data was obtained.

http://datquestionoftheday.com/wp-content/uploads/2013/03/32.jpeg

Which is the best term to describe this data?

A.) Exponential

B.) Quadratic

C.) Linear

D.) Logarithmic

E.) S-Curve

Linear and s-curve functions don't increase rapidly

True or False

True or False

http://datquestionoftheday.com/wp-content/uploads/2013/03/1.jpeg

A.) 18.75 π mm^3

B.) 34.375 π mm^3

C.) 50 π mm^3

D.) 75 π mm^3

E.) 137.5 π mm^3

A. The area of the triangle is greater than 3000

B. The area of the triangle is less than 3000

C. The third side must have a length greater than 120

D. The third side has a length equal to 90

E. None of the above is correctTerm

A. 17

B. 8

C. 23

D. 28

E. 11

A. {12,14,16}

B. {12, 14, 18}

C. {120, 140, 160}

D. {60, 61, 59}

E. {20, 20, 25}

A. 82

B. 80

C. 79

D. 81

E. 78

A. {…, -5, -4, -3}

B. {-2, -1, 0, …}

C. {-5, -4, -3, -2, -1}

D. {-4, -3}

E. {-5, -4, -3}

|x + 4| ≥ 7

A. x ≥ 3 and x ≤ -11

B. -11 ≤ x ≤ 3

C. -3 ≤ x ≤ 11

D. x ≥ 11 and x ≤ -3

E. x ≥ 3

Solve for x: log_{a} (8x^{2}) – log_{a} (2x) = log_{a} 12

A. 0

B. 1

C. 2

D. 3

E. 4

A. 0

B. 1

C. 2

D. 3

E. 4

solve more quickly

What is ** √ f ( g(x) * g(f(x) (square root the whole thing)**

A. x

B. x^{2}

C. x^{2} - 3

D. x - 3

E. x + 3

If (x^{2.5}/ √x )^{2} = 9, what is the value of x

A. √3

B. 2√3

C. 3

D. 9

E. 3√3

A. (3+4x) / (xy)

B. (4x^{2}-xy +3) / (xy)

C. (4x - y + 3) / (xy)

D. (3 + 4x - 1) / (xy^{2})

E. 1

A. -2

B. 0

C. 2

D. 4

E. 6

( √(x^{18}y^{4}z^{12)} ) / (x^{5}y^{9}z)

A. xyz

B. x^{2} / y^{4} z

C. x^{4} y^{2} / z^{3}

D. x^{3} z^{5} / y

E. x^{4} z^{5} / y^{7}

A. -√2

B. 4

C. √3 / 2

D. -3

E. 5

Which of the following describes the shaded region in the figure?

https://s3.amazonaws.com/datbootcamp/math/math-5-10-1.png

A. y > 3, y > (10/3)x – 2

B. y < 3. y > (10/3)x–2

C. y > 3, y < (10/3)x – 2

D. y < 3, y < (10/3)x–2

E. y = 3, y > (10/3)x - 2

Which of the following describes the shaded region in the figure?

https://s3.amazonaws.com/datbootcamp/math/math-5-10-1.png

B. y < 3. y > (10/3)x–2

D. y < 3, y < (10/3)x–2

https://s3.amazonaws.com/datbootcamp/math/math-5-10-2.png

A. 11

B. 17

C. 23

D. 37

E. 41

Simplify: (3^{4} + 27^{2}) / 9^{3}

A. 10/9

B. 10/81

C. 28/9

D. 28/81

E. 81/9

Evaluate: https://s3.amazonaws.com/datbootcamp/math/math-5-12-1.png

A. 4

B. 8

C. 16

D. 32

E. 64

A. 1

B. 3

C. 5

D. 7

E. 9

To get the answer

1) determine the base unit of repetition In this problem. 12579 is the base unit repetition

2)** the base unit of repetition is in a group of 5 digits. Therefore, the 5th digit in each repeating unit will always be the same. and so the 55th digit in the 5th digit in the repeating unit **

What is the ratio of (3 ⁄ 4)^{6} to (3 ⁄ 4)^{8}?

A. 3/4

B. 9/16

C. 4/3

D. 16/9

E. 1

Which of the following is equivalent to log24 – log216 + log22?

A. -1

B. 0

C. 1

D. 2

E. 3

Solve the following:

(3/5) +(4/3) - (1/15)

A. 4/3

B. 28/15

C. 2

D. 34/15

E. 3

( √ (.0144 / .0036)

A. 4

B. 2

C. 0.2

D. 0.04

E. 0.016

A. 5%

B. 34%

C. 50%

D. 68%

E. 95%

A. 120

B. 240

C. 360

D. 720

E. 1000

A. {0, 1, 2, 3, 4}

B. {0, 1, 2, 3, 3}

C. {10, 11, 12, 13, 14}

D. {0, 1, 2, 4, 4}

E. {10, 11, 12, 12, 14}

A **data set** with larger standard deviation will have a larger spread of values & **usually a larger range. **

The **range** is the **difference between the largest & smallest value in a data set.**

A** dataset with a large range** will u**sually have a large standard deviation**

For example, the standard deviation of {x, y, z} is equal to the standard deviation of {x+10, y+10, z+10}.

__A& B have the same standard deviation. so if these were the the options in a multiple choice questions , they both CAN'T BE right because they are both the same. __

ex)

A [ 0, 1, 2, 3 , 4]

B [10, 11, 12, 13, 14]

data set B is the same as data set A +10

A. mode

B. median

C. mean

D. median and mean

E. mode and mean

The **median** is the middle value of a data set.

The **mode **is the value that occurs most often in the data set

The mode has no direct correlation upon the mean or median

A. 2.5%

B. 13.5%

C. 34%

D. 68%

E. 95

A. 30%

B. 40%

C. 50%

D. 60%

E. 70%

A. 1/256

B. 81/256

C. 175/256

D. 225/256

E. 1

A. 81

B. 72

C. 9! / 2!

D. 9^{9}

E. 18

5-12-13

45-45-90 angle

x- x - x√2

30-60-90 angle

x- x√3- 2x

A. Radius = 3, Area = 3π

B. Radius = 3, Area = 9π

C. Radius = √13, Area = 3π

D. Radius = √13, Area = √13π

E. Radius = √13, Area = 13π

https://s3.amazonaws.com/datbootcamp/math/math-5-29-1.png

A. 10

B. 20

C. 36

D. 45

E. 50

Ex if given perimeter of triangle is 9+3√3 in a 30-60-90 angles, figure out the other sides

Know that the sides are (remember from pythag

x- x√3- 2x

so perimeter would be

x+ 2x + 3√3 = 9 + 3√3 in the right side of the equation the number before the radical gives you what x is equal to. so x= 3 in this case

substitute

3 + 2(3) + 3√3 should = to 9 +3√3

3+ 6 + 3√3

9+3√3 = 9+3√3

A. 9√3

B. 9

C. 12√3

D. 21

E. 24√3

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A. 312 sin(148°) cos(148°)

B. 625 sin(74°)

C. 625 cos(74°)

D. 625 sin(74°) cos(74°)

E. 25 sin(45°) cos(45°)

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A. 4√12

B. 12

C. 36

D. 4√90

E. 48

A. 20 degrees

B. 38 degrees

C. 50 degrees

D. 75 degrees

E. 85 degrees

supplement angle= what angle you add up to make 180°

______ angle= what angle you add up to make 180°

Which one is complementary and which one is supplementary.

A. 0

B. 1

C. 2

D. 3

E. 4

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A. 3/4

B. 3/5

C. 4/3

D. 5/3

E. 5/4

A. 200 miles

B. 220 miles

C. 260 miles

D. 280 miles

E. 350 miles

A. 1 hour

B. 1.5 hours

C. 2 hours

D. 2.25 hours

E. 3 hours

A. Bank A, $2

B. Bank A, $7

C. Bank B, $2

D. Bank B, $7

E. They made the same amount of money

A. $1.00

B. $1.30

C. $2.00

D. $2.60

E. $3.90

A. 10

B. 20

C. 35

D. 50

E. 60

average speed

take the total distance divide by the total time

sin 2x = 2sin x cos x

Pythagorean triplets

3-4-5

5-12-13

8-15-17

total time.

i.e i can paint 1 wall in 12 hours. you can paint 1 wall in 6 hours. how long we can do it together

18 18 2 4 hours

In probability **"or" means addition**

the word** "and" means multiplication**

Length of the arc

s= degree in radian * the radius

1 REV= 60 MINUTES

1 REV= 2Π

Σ= summation-getting the sum or adding up the expression.

exterior angle= 360/n

n= number of sides.

Operation is division and if bases are the same, we subtract the exponents

Intersection= get the elements that are found in the interested set

A. 10^5

B. 10^9

C. 10^14

D. 10^4

E. 10^7

amplitude is found as an absolute value and therefore cannot be a negative number.

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