| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 18 small cakes per hour. The kitchen is available for 3 hours and 31 large cakes and 390 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?
| 12 | |
| 14 | |
| 11 | |
| 13 |
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. 31 large cakes are needed for the party so \( \frac{31}{9} \) = 3\(\frac{4}{9}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 18 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 18 x 3 = 54 small cakes during that time. 390 small cakes are needed for the party so \( \frac{390}{54} \) = 7\(\frac{2}{9}\) 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 + 8 = 12 cooks.
What is \( \frac{20\sqrt{42}}{4\sqrt{6}} \)?
| 5 \( \sqrt{\frac{1}{7}} \) | |
| 5 \( \sqrt{7} \) | |
| 7 \( \sqrt{5} \) | |
| \(\frac{1}{5}\) \( \sqrt{7} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{20\sqrt{42}}{4\sqrt{6}} \)
\( \frac{20}{4} \) \( \sqrt{\frac{42}{6}} \)
5 \( \sqrt{7} \)
21 members of a bridal party need transported to a wedding reception but there are only 4 4-passenger taxis available to take them. How many will need to find other transportation?
| 5 | |
| 2 | |
| 7 | |
| 1 |
There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 21 people needing transportation leaving 21 - 16 = 5 who will have to find other transportation.
How many 10-passenger vans will it take to drive all 32 members of the football team to an away game?
| 3 vans | |
| 4 vans | |
| 10 vans | |
| 6 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{32}{10} \) = 3\(\frac{1}{5}\)
So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.
a(b + c) = ab + ac defines which of the following?
commutative property for division |
|
commutative property for multiplication |
|
distributive 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.