| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.11 |
| Score | 0% | 62% |
Convert 0.0003415 to scientific notation.
| 3.415 x 10-3 | |
| 34.15 x 10-5 | |
| 3.415 x 10-4 | |
| 0.342 x 10-3 |
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:
0.0003415 in scientific notation is 3.415 x 10-4
Which of these numbers is a factor of 36?
| 15 | |
| 6 | |
| 8 | |
| 33 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
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 25 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?
| 24 | |
| 36 | |
| 40 | |
| 39 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{50}{100} \) = \( \frac{50 x 25}{100} \) = \( \frac{1250}{100} \) = 12 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 = \( \frac{12}{\frac{30}{100}} \) = 12 x \( \frac{100}{30} \) = \( \frac{12 x 100}{30} \) = \( \frac{1200}{30} \) = 40 shots
to make the same number of shots as the guard and thus score the same number of points.
In a class of 26 students, 10 are taking German and 13 are taking Spanish. Of the students studying German or Spanish, 7 are taking both courses. How many students are not enrolled in either course?
| 18 | |
| 22 | |
| 21 | |
| 10 |
The number of students taking German or Spanish is 10 + 13 = 23. Of that group of 23, 7 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 23 - 7 = 16 who are taking at least one language. 26 - 16 = 10 students who are not taking either language.
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
|
distributive property for division |
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distributive property for multiplication |
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commutative property for division |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.