| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.94 |
| Score | 0% | 59% |
What is a4 - 6a4?
| -5a4 | |
| 7a4 | |
| 7a-8 | |
| 7a8 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
1a4 - 6a4
(1 - 6)a4
-5a4
What is the distance in miles of a trip that takes 4 hours at an average speed of 45 miles per hour?
| 450 miles | |
| 100 miles | |
| 180 miles | |
| 420 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 45mph \times 4h \)
180 miles
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 100.4 | |
| 126.9 | |
| 95.6 | |
| 112.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 6 = \( \frac{7 \times 6}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour
So, in an average hour, the machine will produce 6 - 0.42 = 5.58 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 5.58 = 100.4 error free parts were produced yesterday.
Which of the following statements about exponents is false?
b1 = b |
|
all of these are false |
|
b1 = 1 |
|
b0 = 1 |
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).
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 30 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 31 | |
| 36 | |
| 28 | |
| 38 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{50}{100} \) = \( \frac{50 x 30}{100} \) = \( \frac{1500}{100} \) = 15 shots
The center makes 40% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{15}{\frac{40}{100}} \) = 15 x \( \frac{100}{40} \) = \( \frac{15 x 100}{40} \) = \( \frac{1500}{40} \) = 38 shots
to make the same number of shots as the guard and thus score the same number of points.