| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.81 |
| Score | 0% | 56% |
What is -6z7 - 2z7?
| 8z7 | |
| -8z-7 | |
| -8z7 | |
| 8z-7 |
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:
-6z7 - 2z7
(-6 - 2)z7
-8z7
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 10 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?
| 17 | |
| 8 | |
| 18 | |
| 22 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{50}{100} \) = \( \frac{50 x 10}{100} \) = \( \frac{500}{100} \) = 5 shots
The center makes 30% 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 = \( \frac{5}{\frac{30}{100}} \) = 5 x \( \frac{100}{30} \) = \( \frac{5 x 100}{30} \) = \( \frac{500}{30} \) = 17 shots
to make the same number of shots as the guard and thus score the same number of points.
Convert 957,000 to scientific notation.
| 9.57 x 104 | |
| 9.57 x 105 | |
| 9.57 x 106 | |
| 95.7 x 104 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
957,000 in scientific notation is 9.57 x 105
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 133.9 | |
| 84.6 | |
| 154.7 | |
| 71.3 |
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 8 = \( \frac{7 \times 8}{100} \) = \( \frac{56}{100} \) = 0.56 errors per hour
So, in an average hour, the machine will produce 8 - 0.56 = 7.4399999999999995 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 7.4399999999999995 = 133.9 error free parts were produced yesterday.
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
|
commutative property for division |
|
distributive property for multiplication |
|
commutative property for multiplication |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).