| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
What is 5\( \sqrt{9} \) x 7\( \sqrt{6} \)?
| 35\( \sqrt{15} \) | |
| 105\( \sqrt{6} \) | |
| 12\( \sqrt{6} \) | |
| 35\( \sqrt{9} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
5\( \sqrt{9} \) x 7\( \sqrt{6} \)
(5 x 7)\( \sqrt{9 \times 6} \)
35\( \sqrt{54} \)
Now we need to simplify the radical:
35\( \sqrt{54} \)
35\( \sqrt{6 \times 9} \)
35\( \sqrt{6 \times 3^2} \)
(35)(3)\( \sqrt{6} \)
105\( \sqrt{6} \)
What is the distance in miles of a trip that takes 4 hours at an average speed of 20 miles per hour?
| 80 miles | |
| 125 miles | |
| 300 miles | |
| 135 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 = \( 20mph \times 4h \)
80 miles
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 1:2 | |
| 25:2 | |
| 5:8 | |
| 9:2 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.
Damon loaned Bob $1,400 at an annual interest rate of 3%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $99 | |
| $42 | |
| $3 | |
| $12 |
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 $1,400
i = 0.03 x $1,400
i = $42
Convert 0.0003407 to scientific notation.
| 0.341 x 10-3 | |
| 3.407 x 10-5 | |
| 34.07 x 10-5 | |
| 3.407 x 10-4 |
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:
0.0003407 in scientific notation is 3.407 x 10-4