| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
What is (b5)4?
| b | |
| 5b4 | |
| b20 | |
| b-1 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(b5)4A tiger in a zoo has consumed 45 pounds of food in 9 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 65 pounds?
| 7 | |
| 3 | |
| 10 | |
| 4 |
If the tiger has consumed 45 pounds of food in 9 days that's \( \frac{45}{9} \) = 5 pounds of food per day. The tiger needs to consume 65 - 45 = 20 more pounds of food to reach 65 pounds total. At 5 pounds of food per day that's \( \frac{20}{5} \) = 4 more days.
What is \( \frac{9}{3} \) + \( \frac{7}{7} \)?
| 1 \( \frac{7}{16} \) | |
| 1 \( \frac{4}{9} \) | |
| 4 | |
| \( \frac{6}{21} \) |
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 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 7}{3 x 7} \) + \( \frac{7 x 3}{7 x 3} \)
\( \frac{63}{21} \) + \( \frac{21}{21} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{63 + 21}{21} \) = \( \frac{84}{21} \) = 4
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 20% off." If Monty buys two shirts, each with a regular price of $32, how much will he pay for both shirts?
| $6.40 | |
| $36.80 | |
| $57.60 | |
| $25.60 |
By buying two shirts, Monty will save $32 x \( \frac{20}{100} \) = \( \frac{$32 x 20}{100} \) = \( \frac{$640}{100} \) = $6.40 on the second shirt.
So, his total cost will be
$32.00 + ($32.00 - $6.40)
$32.00 + $25.60
$57.60
Which of these numbers is a factor of 72?
| 54 | |
| 34 | |
| 46 | |
| 72 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.