| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.02 |
| Score | 0% | 60% |
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 46 | |
| 38 | |
| 48 | |
| 42 |
The equation for this sequence is:
an = an-1 + 3(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
If all of a roofing company's 16 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 5 | |
| 14 | |
| 12 | |
| 8 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 6 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 6 x 4 = 24 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 24 - 16 = 8 new staff for the busy season.
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 45% 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?
| 8 | |
| 11 | |
| 17 | |
| 9 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{45}{100} \) = \( \frac{45 x 10}{100} \) = \( \frac{450}{100} \) = 4 shots
The center makes 35% 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 = \( \frac{4}{\frac{35}{100}} \) = 4 x \( \frac{100}{35} \) = \( \frac{4 x 100}{35} \) = \( \frac{400}{35} \) = 11 shots
to make the same number of shots as the guard and thus score the same number of points.
Convert 8,976,000 to scientific notation.
| 8.976 x 10-5 | |
| 8.976 x 106 | |
| 89.76 x 105 | |
| 0.898 x 107 |
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:
8,976,000 in scientific notation is 8.976 x 106
Ezra loaned Bob $600 at an annual interest rate of 8%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $24 | |
| $35 | |
| $42 | |
| $48 |
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 $600
i = 0.08 x $600
i = $48