| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.59 |
| Score | 0% | 52% |
The total water usage for a city is 45,000 gallons each day. Of that total, 34% is for personal use and 59% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 9,200 | |
| 1,050 | |
| 14,400 | |
| 11,250 |
59% of the water consumption is industrial use and 34% is personal use so (59% - 34%) = 25% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{25}{100} \) x 45,000 gallons = 11,250 gallons.
What is \( 9 \)\( \sqrt{112} \) - \( 7 \)\( \sqrt{7} \)
| 2\( \sqrt{7} \) | |
| 63\( \sqrt{112} \) | |
| 2\( \sqrt{784} \) | |
| 29\( \sqrt{7} \) |
To subtract these radicals together their radicands must be the same:
9\( \sqrt{112} \) - 7\( \sqrt{7} \)
9\( \sqrt{16 \times 7} \) - 7\( \sqrt{7} \)
9\( \sqrt{4^2 \times 7} \) - 7\( \sqrt{7} \)
(9)(4)\( \sqrt{7} \) - 7\( \sqrt{7} \)
36\( \sqrt{7} \) - 7\( \sqrt{7} \)
Now that the radicands are identical, you can subtract them:
36\( \sqrt{7} \) - 7\( \sqrt{7} \)Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 20 small cakes per hour. The kitchen is available for 4 hours and 31 large cakes and 160 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 5 | |
| 8 | |
| 4 | |
| 9 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 31 large cakes are needed for the party so \( \frac{31}{16} \) = 1\(\frac{15}{16}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 20 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 20 x 4 = 80 small cakes during that time. 160 small cakes are needed for the party so \( \frac{160}{80} \) = 2 cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 2 = 4 cooks.
In a class of 17 students, 5 are taking German and 7 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 16 | |
| 12 | |
| 17 | |
| 7 |
The number of students taking German or Spanish is 5 + 7 = 12. Of that group of 12, 2 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 12 - 2 = 10 who are taking at least one language. 17 - 10 = 7 students who are not taking either language.
What is \( \frac{-4b^7}{1b^2} \)?
| -4b-5 | |
| -\(\frac{1}{4}\)b9 | |
| -4b5 | |
| -\(\frac{1}{4}\)b5 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-4b^7}{b^2} \)
\( \frac{-4}{1} \) b(7 - 2)
-4b5