Probability and Statistics
In a bag, there are 5 green marbles, 2 red marbles, 3 yellow, and 6 blue marbles. What is the probability that if a marble is selected, it is green?
Probability = green / total = 5 / (5+2+3+6) = 5/16
Ans: 5/16
Simplify the square root of 180
180 = 4 x 9 x 5 = 2 x 2 x 3 x 3 x 5
square root 180 = 2 x 3 x square root 5
= 6 square root 5
Solve for the value of x if
2(x+5) - 2 = 0
2(x+5) - 2 = 0
2(x+5) = 2
(x+5) = 1
x = -4
Is the number 15,438 divisible by 3?
Sum of digits = 1+5+4+3+8 = 21
21 is divisible by 3 so 15438 is divisible by 3
YES
Convert a speed of 6 inches per minute into feet per hour.
(6 in/min)(1 foot/12 inches)(60 min/1hr) =
30 feet per hour
What is the mean of the following values?
60, 70, 75, 79
Mean = sum of all values / number of values
Mean = (60 + 70 + 75 + 79) / 4
Mean = 284 / 4
Ans: 71
Simplify 2-4
2-4 = 1/24 = 1/16
ANS: 1/16
What is the LCM of 10, 20, and 24?
10 = 2 x 5
20 = 2 x 2 x 5
24 = 2 x 2 x 2 x 3
LCM = 2 x 2 x 2 x 3 x 5 = 120
A polygon has 900 degrees for the sum of its interior angles. How many sides does this polygon have?
sum of interior angles = (n-2)(180)
900 = 180n - 360
1260 = 180n
n = 1260 / 180 = 7
ANS: 7 sides
Convert 3 miles per hour into feet per minute. Note that 1 mile = 5280 feet.
(3 miles/hr)(1hr/60min)(5280 feet/1mile) =
264 miles per hour
In a bag, there are 3 different types of candies. There are 5 Kit Kats, 8 Twix bars, and 9 Charleston Chews. If a person chooses two pieces of candy without replacement, what is the probability, in simplest form, they would choose 2 Kit Kats?
P(1st Kit Kat) x P(2nd Kit Kat)
(5/22)(4/21)
= (4/22)(5/21)
= (2/11)(5/21)
= 10/231
Simplify the following expression:
The square root of 20 minus the square root 45
square root 20 = square root 4 x square root 5
square root 20 = 2 x square root 5
square root 45 = square root 9 x square root 5
square root 45 = 3 x square root 5
2 x square root 5 - 3 x square root 5
= -1 square root 5
Ans: - square root 5
Simplify the following expression:
(2 + (32 - 5)) ÷ (5 - 2 x 4)
(2 + (32 - 5)) ÷ (5 - 2 x 4)
(2 + 9 - 5) ÷ (5 - 8)
(6) ÷ (-3)
-2
Ans: -2
Given the area of circle is 121pi, calculate the circumference of the circle. Leave your answer in terms of pi.
Area circle = (pi)r2
121pi = (pi)r2
r = 11
C = 2(pi)r
C = 2(pi)11 = 22pi
ANS: 22pi
A drawing of a rectangular fence is drawn on a piece of paper. Its dimensions are 4 inches by 5 inches. The scale for the drawing is 1 inch on the drawing = 3.5 feet in real life. Calculate the area of the rectangular fence in real life.
4 inches x 3.5 = 14 feet
5 inches x 3.5 = 17.5 feet
Area = length x width = 14 x 17.5 = 245 feet2
ANS: 245 feet2
Find the interquartile range (IQR) for the following list of numbers:
15, 2, 6, 10, 3, 3, 3, 5, 10, 12, 11
Rearrange in numerical order first:
2, 3, 3, 3, 5, 6, 10, 10, 11, 12, 15
Median = 6
Q1 = 3, Q3 = 11
IQR = 11 - 3 = 8
Multiply and simplify: (2x3y2)3 (3x-2)2
(2x3y2)3 = 8x9y6
(3x-2)2 = 9x-4
(8x9y6)(9x-4) = 72x5y6
ANS: 72x5y6
Simplify the following expression:
(x ÷ 2y) - (2y ÷ x)
Find the LCM of 2y and x: 2xy
(x/2y)(x/x) - (2y/x)(2y/2y)
(x2/2xy) - (4y2/2xy)
(x2 - 4y2) / (2xy)
ANS: (x2 - 4y2) ÷ (2xy)
A shirt is on sale and after an 18% discount, the shirt costs $123. What is the original price of the shirt?
100 - 18 = 82%
Let y = original cost of shirt
(0.82)y = 123
y = (123) / 0.82
y = $150
ANS: 150
The original price of a textbook is $80. It goes on sale and there is a 15% discount. You decide to purchase the textbook, and you are charged an 8% sales tax on the book. How much did you pay for the book?
$80 x 0.85 = $68
$68 x 1.08 = 73.44
ANS: $73.44
At the ice cream shop, there are 7 different flavors to choose from. You decide to get two scoops of two different flavors. How many different combinations are possible?
Let flavors be A, B, C, D, E, F, G
A-B B-C C-D D-E E-F F-G
A-C B-D C-E D-F E-G
A-D B-E C-F D-G
A-E B-F C-G
A-F B-G
A-G
ANS: 21
Fully simplify: (16x4y6z0)1/2 ÷ (xy2)
(16x4y6z0)1/2 = 161/2x2y3z0 = 4x2y3
(4x2y3) ÷ (xy2)
ANS: 4xy
A school is going on a field trip to the museum and the students will be accompanied by teachers. A student ticket costs $4.50 and a teacher ticket costs $10.00. The number of teachers that go on the field trip is equal to one-third the number of students that go on the field trip. If the total cost for all the tickets is $164.50, how many teachers were on the field trip?
let y = number of students, # teachers = (1/3)(y)
Total cost = cost of student tix + cost teacher tix
Total cost = 4.50y + 10(1/3)y
164.50 = 4.50y + (10/3)y
164.50 = (9/2)y + (10/3)y
164.50 = (27/6)y + (20/6)y
164.50 = (47/6)y
(164.50)(6) = 47y
y = 21
Teachers = (1/3)21 = 7
ANS: 7
If you triple the diameter of a circle, by what multiple does the area of the circle change?
Area = (pi)r2
New area = (pi)(3r)2 = (pi)9r2
ANS: 9
In a jar of coins, there are 2 quarters for every 5 nickels. There are 3 quarters for every 4 dimes. There are also 85 total pennies in the jar. If the total amount of money in the jar is $10.00, how many quarters are there in the jar?
$10.00 - 85(0.01) = $9.15
q:n = 2:5
q:d = 3:4
Need same number of quarters to compare nickels and dimes. LCM of 2 and 3 is 6
q:n = 6:15
q:d = 6:8
q:n:d = 6:15:8
6(0.25) + 15(0.05) + 8(0.1) = 3.05
9.15 / 3.05 = 3
q = 6 x 3 = 18
ANS: 18 quarters