Forth flashcards
The density d of an object is given by d=mv , where m is the mass of the object (measured in grams) and v is its volume (measured in cubic inches). What is the volume of an object with mass 16 grams that has a density of 20 grams per cubic inch?
0.80 cubic inches
1.25 cubic inches
4.00 cubic inches
8.00 cubic inches
Answer: The correct answer is A. Substitute 20 in for d and 16 in for m in the formula. Then multiply both sides by v and divide by 20:
d=mv
20=16v
20v=16
v=1620=0.80
So, the volume of the object is 0.80 cubic inches.
What is the value of the following arithmetic expression?
(9−4+2)2√(3⋅2−5)3
3
7
14
49
Answer: The correct answer is B. Follow the order of operations to simplify the expressions within the parentheses first. Then simplify the radical using the fact that a2−−√=a when a > 0 and simplify the denominator using the fact that 1 raised to any power is 1. Doing so yields the following:
(9−4+2)2√(3⋅2−5)3=(5+2)2√(6−5)3=72√13=71=7
Compute the mean for the following data set.
9, 2, 4, 9, 10, 6, 12, 3
Round to the nearest tenth, if necessary.
6.1
6.9
7.5
9.5
Answer: The correct answer is B. Add the eight data values and divide the sum by 8:
9+2+4+9+10+6+12+38=558=6.875≈6.9
A company issues bonus awards to 3 employees each year in the amounts of $2,000 each. They select the award recipients from a shortlist of 11 employees. All employees on this list are considered equal and could receive any of the three awards, so they are selected randomly. No person can receive multiple bonus awards. How many ways can these bonus awards be assigned?
11 × 10 × 9
11!38!
11!8!3!
113
Answer: The correct answer is C. This is the number of combinations, which assumes that the order in which the employees are chosen doesn’t matter. This is the case here because all three awards are the same amount.
A deli employs dishwashers, hospitality staff, and cooks. The distribution of employees according to whether they are still high school students is summarized in the following table:
Dishwashers Hospitality Staff Cooks
In High School
4
2
2
Not In High School
1
6
5
What is the probability that a randomly chosen employee of the deli is either a dishwasher or is in high school?
0.25
0.40
0.45
0.65
Answer: The correct answer is C. The events “employee is a dishwasher” and “employee is in high school” are not mutually exclusive. So, you must use the addition rule. Specifically,
P(dishwasher OR in high school) = P(dishwasher) + P(in high school) − P(dishwasher AND in high school).
There are 20 employees in the table, and all choices are equally likely because an employee is being chosen at random. So, divide the number of outcomes by 20 in each case to find the individual probabilities.
P(dishwasher) = 520 = 0.25
P(in high school) = 820 = 0.40
P(dishwasher AND in high school) = 420 = 0.20
Substituting these into the formula yields:
P(dishwasher OR in high school) = 0.25 + 0.40 − 0.20 = 0.45
You decide to start saving for retirement at age 25. You invest $1,200 per year in an IRA that pays 5.5% interest compounded monthly. How much interest will you have earned on just $1,200 (the amount you invested at age 25) when you reach age 70? Round to the nearest dollar.
$12,152
$12,978
$13,352
$14,175
Answer: The correct answer is B. The future value, FV, of an investment of P dollars compounded n times annually for t years at an annual interest rate of r% is given by the following formula:
FV=P(1+rn)nt
Here, P = $1,200, r = 0.055, n = 12, and t = 70 − 25 = 45. Substituting these values into the formula and simplifying yields FV=P(1+0.05512)(12)(45) ≈ $14.175. The amount of interest earned is this amount minus the initial investment of $1,200, namely $14,175 − $1,200 = $12,975.
Seo-yeon borrowed $120,000 to purchase office space for her new business. The loan terms are 15 years at an annual interest rate of 2.4%. Which of these formulas represents her monthly payment?
0.024(120,000)1−(1+0.024)−180
0.002(120,000)1−(1−0.002)−180
0.002(120,000)1−(1+0.002)−120
0.002(120,000)1−(1+0.002)−180
Answer: The correct answer is D. The monthly payment P is given by the following formula:
P=rV1−(1+r)−n
where r is the monthly interest rate, V is the original amount of the loan, and n is the duration of the loan in months. Here, r=0.02412=0.002 and n = 15(12) = 180. Substituting these values into the formula yields
P=0.022(120,000)1−(1+0.002)−180
What is the perimeter of the rectangle shown below?
rectangle with sides 2 ft and 13 ft
15 feet
26 feet
30 feet
52 feet
Answer: The correct answer is C. The formula for the perimeter P of a rectangle with width w and length l is P = 2w + 2l. Here, w = 2 feet and l = 13 feet. So, the perimeter is P = 2(2) + 2(13) = 4 + 26 = 30 feet.
Compute (4.2 × 105) × (3.0 × 103).
1.26 × 107
1.26 × 109
1.26 × 1014
1.26 × 1016
Answer: The correct answer is B. Multiply the decimal parts and add the powers of 10 to initially get the product 1.26 × 108. Then to convert 1.26 × 108 to proper scientific notation, move the decimal point to the left one unit and increase the power of 10 by 1. This yields 1.26 × 109.
What is the missing number in the equality ?√ = 4.84?
4.8412
4.842
4.84×2
4.842
Answer: The correct answer is D. By definition, a2−−√ = a when a > 0. So, the number that goes in the box is 4.842.
Which of these statements is logically equivalent to this conditional?
If you are a first-year student, then you cannot live off-campus.
If you are not a first-year student, then you can live off-campus.
If you are a first-year student, then you can live off-campus.
If you can live off-campus, then you are not a first-year student.
If you cannot live off-campus, then you are a first-year student.
Answer: The correct answer is C. This is the contrapositive of the given statement. It is known that the conditional p ⇒ q is equivalent to the conditional ¬q ⇒ ¬p
Which of the following statements is the contrapositive of the conditional statement “If the meatloaf contains ketchup, then Sam will not eat it”?
If Sam will not eat it, then the meatloaf contains ketchup.
If Sam will eat it, then the meatloaf does not contain ketchup.
The meatloaf contains ketchup and Sam will eat it.
The meatloaf does not contain ketchup and Sam will not eat it.
Answer: The correct answer is B. Symbolically, let p be the statement “The meatloaf contains ketchup” and q be the statement “Sam will not eat it.” The contrapositive of the conditional p ⇁ q is (⇁ q) ⇒ (⇁ p). Applying this to the given statements yields “If Sam will eat it, then the meatloaf does not contain ketchup
