| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.78 |
| Score | 0% | 56% |
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 49,000 seats in a stadium are filled, how many home fans are in attendance?
| 32,667 | |
| 40,000 | |
| 30,000 | |
| 34,500 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
49,000 fans x \( \frac{2}{3} \) = \( \frac{98000}{3} \) = 32,667 fans.
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 40% of his shots. If the guard takes 15 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 15 | |
| 20 | |
| 10 | |
| 24 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{40}{100} \) = \( \frac{40 x 15}{100} \) = \( \frac{600}{100} \) = 6 shots
The center makes 30% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{6}{\frac{30}{100}} \) = 6 x \( \frac{100}{30} \) = \( \frac{6 x 100}{30} \) = \( \frac{600}{30} \) = 20 shots
to make the same number of shots as the guard and thus score the same number of points.
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 105.6 | |
| 147.8 | |
| 104.5 | |
| 73.6 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 5 = \( \frac{8 \times 5}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour
So, in an average hour, the machine will produce 5 - 0.4 = 4.6 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 4.6 = 73.6 error free parts were produced yesterday.
A bread recipe calls for 3\(\frac{3}{8}\) cups of flour. If you only have 1\(\frac{1}{8}\) cups, how much more flour is needed?
| 1\(\frac{3}{4}\) cups | |
| 2\(\frac{1}{4}\) cups | |
| 3\(\frac{1}{4}\) cups | |
| 2\(\frac{1}{8}\) cups |
The amount of flour you need is (3\(\frac{3}{8}\) - 1\(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{27}{8} \) - \( \frac{9}{8} \)) cups
\( \frac{18}{8} \) cups
2\(\frac{1}{4}\) cups
a(b + c) = ab + ac defines which of the following?
distributive property for division |
|
commutative property for multiplication |
|
commutative property for division |
|
distributive property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.