| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.74 |
| Score | 0% | 55% |
In a class of 30 students, 10 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 8 | |
| 25 | |
| 19 | |
| 15 |
The number of students taking German or Spanish is 10 + 14 = 24. Of that group of 24, 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 24 - 2 = 22 who are taking at least one language. 30 - 22 = 8 students who are not taking either language.
The total water usage for a city is 15,000 gallons each day. Of that total, 29% is for personal use and 56% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 6,400 | |
| 6,600 | |
| 4,050 | |
| 6,000 |
56% of the water consumption is industrial use and 29% is personal use so (56% - 29%) = 27% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 15,000 gallons = 4,050 gallons.
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 13 small cakes per hour. The kitchen is available for 3 hours and 30 large cakes and 400 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?
| 8 | |
| 15 | |
| 13 | |
| 11 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 30 large cakes are needed for the party so \( \frac{30}{9} \) = 3\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 13 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 13 x 3 = 39 small cakes during that time. 400 small cakes are needed for the party so \( \frac{400}{39} \) = 10\(\frac{10}{39}\) 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 4 + 11 = 15 cooks.
What is \( \frac{-9b^8}{3b^3} \)?
| -3b5 | |
| -3b-5 | |
| -\(\frac{1}{3}\)b11 | |
| -\(\frac{1}{3}\)b-5 |
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:
\( \frac{-9b^8}{3b^3} \)
\( \frac{-9}{3} \) b(8 - 3)
-3b5
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 7:6 | |
| 3:1 | |
| 49:2 | |
| 3:2 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.