| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.61 |
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Convert 0.0006152 to scientific notation.
| 6.152 x 10-4 | |
| 6.152 x 10-3 | |
| 6.152 x 105 | |
| 6.152 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:
0.0006152 in scientific notation is 6.152 x 10-4
What is 4b4 + 5b4?
| -b-4 | |
| 9b4 | |
| 9b-8 | |
| 9b8 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
4b4 + 5b4
(4 + 5)b4
9b4
If a mayor is elected with 81% of the votes cast and 54% of a town's 13,000 voters cast a vote, how many votes did the mayor receive?
| 4,142 | |
| 6,037 | |
| 3,580 | |
| 5,686 |
If 54% of the town's 13,000 voters cast ballots the number of votes cast is:
(\( \frac{54}{100} \)) x 13,000 = \( \frac{702,000}{100} \) = 7,020
The mayor got 81% of the votes cast which is:
(\( \frac{81}{100} \)) x 7,020 = \( \frac{568,620}{100} \) = 5,686 votes.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 20 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?
| 28 | |
| 22 | |
| 42 | |
| 27 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{55}{100} \) = \( \frac{55 x 20}{100} \) = \( \frac{1100}{100} \) = 11 shots
The center makes 50% 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 = \( \frac{11}{\frac{50}{100}} \) = 11 x \( \frac{100}{50} \) = \( \frac{11 x 100}{50} \) = \( \frac{1100}{50} \) = 22 shots
to make the same number of shots as the guard and thus score the same number of points.
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 13 small cakes per hour. The kitchen is available for 2 hours and 24 large cakes and 310 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 15 | |
| 11 | |
| 5 | |
| 13 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 24 large cakes are needed for the party so \( \frac{24}{10} \) = 2\(\frac{2}{5}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 13 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 13 x 2 = 26 small cakes during that time. 310 small cakes are needed for the party so \( \frac{310}{26} \) = 11\(\frac{12}{13}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 12 = 15 cooks.