Question

gateway to tech iii math (act prep) unit #1 basic mathematics (2017)

1. a beaker of liquid cools from 19°f to - 6°f. by how many degrees has it cooled?

a. 6
b. 13
c. 19
d. 25
e. 26
hint. find the difference between 19 and - 6.

1. the student council at grace high school has 10 freshmen, 8 sophomores, 15 juniors and 7 seniors. sophomores are what fraction of the council?

f. 1/3
g. 1/4
h. 1/5
j. 3/8
k. 7/40

1. which power of ten is equivalent to.00000072?

a. 7.2×10^(-7)
b. 7.2×10^(-6)
c. 7.2×10^(-5)
d. 7.2×10^(6)
e. 7.2×10^(7)

1. which number is the best estimate of (489)(982)/(302 + 690)?

f. 50
g. 400
h. 450
j. 500
k. 2000

1. ceramic bowls regularly priced at $9.95 each are on sale, three for $19.98. how much do three regular - priced bowls cost?

a. 3 times ($19.98 minus $9.95)
b. $9.95 times three
c. $9.95 divided by three
d. $19.98 times three
e. $19.98 divided by three
hint. one regular - priced bowl costs $9.95.

1. marty found that he had an average of 81 for his four math tests. he forgot to average in a grade of 76. what is his true average?

f. 100
g. 80
h. 65
j. 39
k. 31

1. mike’s electric bills over six months were $28.84, $18.96, $29.32, $16.22, $17.98, and $21.80. to the nearest cent, find the average of the six bills.

a. $26.62
b. $22.19
c. $22.18
d. $22.00
e. $18.55
do not simply guess!
work problems out.
check your answers.
stop here.

Explanation:

Step1: Calculate temperature difference

To find how many degrees the liquid has cooled, we subtract the final temperature from the initial temperature. So, we calculate $19-(- 6)$. Subtracting a negative number is the same as adding the positive of that number. So, $19-(-6)=19 + 6=25$.

Step2: Cost of three regular - priced bowls

Since one regular - priced bowl costs $\$9.95$, the cost of three regular - priced bowls is $9.95\times3$.

Step3: Fraction of sophomores in the council

First, find the total number of students in the council: $10 + 8+15 + 7=40$. The number of sophomores is 8. The fraction of sophomores in the council is $\frac{8}{40}=\frac{1}{5}$.

Step4: Scientific notation conversion

For the number $0.00000072$, in scientific notation, we move the decimal point 7 places to the right to get a number between 1 and 10. So, it is $7.2\times10^{-7}$.

Step5: Estimation of a fraction

Estimate $489\approx500$, $982\approx1000$, $302\approx300$, and $690\approx700$. Then $\frac{(489)(982)}{302 + 690}\approx\frac{500\times1000}{300+700}=\frac{500000}{1000}=500$.

Step6: Correcting the average

Marty had an average of 81 for 4 tests, so the sum of his original 4 - test scores is $81\times4 = 324$. He forgot to average in a grade of 76. The sum of all 5 scores is $324+76 = 400$. The true average is $\frac{400}{5}=80$.

Step7: Calculating the average of bills

The sum of the six electric bills is $28.84 + 18.96+29.32+16.22+17.98+21.80=133.12$. The average is $\frac{133.12}{6}\approx22.19$.

Answer:

1. D. 25
2. H. $\frac{1}{5}$
3. A. $7.2\times10^{-7}$
4. J. 500
5. B. $\$9.95$ times three
6. G. 80
7. B. $\$22.19$