| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.73 |
| Score | 0% | 55% |
Which of the following statements about exponents is false?
b1 = b |
|
b1 = 1 |
|
b0 = 1 |
|
all of these are false |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
Solve 4 + (5 + 2) ÷ 2 x 5 - 52
| 4 | |
| \(\frac{4}{9}\) | |
| -3\(\frac{1}{2}\) | |
| \(\frac{3}{4}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
4 + (5 + 2) ÷ 2 x 5 - 52
P: 4 + (7) ÷ 2 x 5 - 52
E: 4 + 7 ÷ 2 x 5 - 25
MD: 4 + \( \frac{7}{2} \) x 5 - 25
MD: 4 + \( \frac{35}{2} \) - 25
AS: \( \frac{8}{2} \) + \( \frac{35}{2} \) - 25
AS: \( \frac{43}{2} \) - 25
AS: \( \frac{43 - 50}{2} \)
\( \frac{-7}{2} \)
-3\(\frac{1}{2}\)
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 102.6 | |
| 82.8 | |
| 98.7 | |
| 142.9 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 5 = \( \frac{8 \times 5}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour
So, in an average hour, the machine will produce 5 - 0.4 = 4.6 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 4.6 = 82.8 error free parts were produced yesterday.
Damon loaned Betty $400 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $416 | |
| $432 | |
| $412 | |
| $424 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $400
i = 0.06 x $400
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $400 + $24A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Ezra buys two shirts, each with a regular price of $39, how much will he pay for both shirts?
| $46.80 | |
| $40.95 | |
| $68.25 | |
| $56.55 |
By buying two shirts, Ezra will save $39 x \( \frac{25}{100} \) = \( \frac{$39 x 25}{100} \) = \( \frac{$975}{100} \) = $9.75 on the second shirt.
So, his total cost will be
$39.00 + ($39.00 - $9.75)
$39.00 + $29.25
$68.25