| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.41 |
| Score | 0% | 68% |
What is the distance in miles of a trip that takes 1 hour at an average speed of 20 miles per hour?
| 20 miles | |
| 30 miles | |
| 55 miles | |
| 360 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 = \( 20mph \times 1h \)
20 miles
Solve for \( \frac{4!}{2!} \)
| \( \frac{1}{210} \) | |
| \( \frac{1}{56} \) | |
| 12 | |
| 60480 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{4!}{2!} \)
\( \frac{4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{4 \times 3}{1} \)
\( 4 \times 3 \)
12
What is \( \frac{4}{3} \) + \( \frac{5}{9} \)?
| 1\(\frac{8}{9}\) | |
| \( \frac{8}{14} \) | |
| \( \frac{4}{9} \) | |
| \( \frac{7}{9} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 3}{3 x 3} \) + \( \frac{5 x 1}{9 x 1} \)
\( \frac{12}{9} \) + \( \frac{5}{9} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{12 + 5}{9} \) = \( \frac{17}{9} \) = 1\(\frac{8}{9}\)
Which of these numbers is a factor of 36?
| 23 | |
| 28 | |
| 16 | |
| 6 |
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.
Convert 5,241,000 to scientific notation.
| 5.241 x 10-5 | |
| 5.241 x 105 | |
| 5.241 x 107 | |
| 5.241 x 106 |
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:
5,241,000 in scientific notation is 5.241 x 106