| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.70 |
| Score | 0% | 54% |
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 39,000 seats in a stadium are filled, how many home fans are in attendance?
| 31,200 | |
| 33,000 | |
| 32,500 | |
| 28,000 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
39,000 fans x \( \frac{4}{5} \) = \( \frac{156000}{5} \) = 31,200 fans.
What is 3z2 - 2z2?
| -z2 | |
| -z-2 | |
| z2 | |
| 5z4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
3z2 - 2z2
(3 - 2)z2
z2
The total water usage for a city is 30,000 gallons each day. Of that total, 13% is for personal use and 46% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 7,800 | |
| 9,900 | |
| 16,500 | |
| 10,500 |
46% of the water consumption is industrial use and 13% is personal use so (46% - 13%) = 33% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{33}{100} \) x 30,000 gallons = 9,900 gallons.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Monty buys two shirts, each with a regular price of $29, how much will he pay for both shirts?
| $37.70 | |
| $50.75 | |
| $21.75 | |
| $36.25 |
By buying two shirts, Monty will save $29 x \( \frac{25}{100} \) = \( \frac{$29 x 25}{100} \) = \( \frac{$725}{100} \) = $7.25 on the second shirt.
So, his total cost will be
$29.00 + ($29.00 - $7.25)
$29.00 + $21.75
$50.75
What is \( 8 \)\( \sqrt{12} \) + \( 5 \)\( \sqrt{3} \)
| 40\( \sqrt{12} \) | |
| 13\( \sqrt{12} \) | |
| 21\( \sqrt{3} \) | |
| 40\( \sqrt{36} \) |
To add these radicals together their radicands must be the same:
8\( \sqrt{12} \) + 5\( \sqrt{3} \)
8\( \sqrt{4 \times 3} \) + 5\( \sqrt{3} \)
8\( \sqrt{2^2 \times 3} \) + 5\( \sqrt{3} \)
(8)(2)\( \sqrt{3} \) + 5\( \sqrt{3} \)
16\( \sqrt{3} \) + 5\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
16\( \sqrt{3} \) + 5\( \sqrt{3} \)