| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.32 |
| Score | 0% | 66% |
Find the average of the following numbers: 16, 12, 17, 11.
| 12 | |
| 19 | |
| 14 | |
| 18 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{16 + 12 + 17 + 11}{4} \) = \( \frac{56}{4} \) = 14
The total water usage for a city is 5,000 gallons each day. Of that total, 21% is for personal use and 47% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 5,250 | |
| 3,150 | |
| 3,750 | |
| 1,300 |
47% of the water consumption is industrial use and 21% is personal use so (47% - 21%) = 26% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{26}{100} \) x 5,000 gallons = 1,300 gallons.
How many hours does it take a car to travel 280 miles at an average speed of 70 miles per hour?
| 4 hours | |
| 6 hours | |
| 7 hours | |
| 2 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{280mi}{70mph} \)
4 hours
What is 7\( \sqrt{4} \) x 6\( \sqrt{7} \)?
| 84\( \sqrt{7} \) | |
| 42\( \sqrt{4} \) | |
| 42\( \sqrt{11} \) | |
| 13\( \sqrt{4} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
7\( \sqrt{4} \) x 6\( \sqrt{7} \)
(7 x 6)\( \sqrt{4 \times 7} \)
42\( \sqrt{28} \)
Now we need to simplify the radical:
42\( \sqrt{28} \)
42\( \sqrt{7 \times 4} \)
42\( \sqrt{7 \times 2^2} \)
(42)(2)\( \sqrt{7} \)
84\( \sqrt{7} \)
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
|
commutative property for multiplication |
|
commutative property for division |
|
distributive property for division |
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.