| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.06 |
| Score | 0% | 61% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 70% larger than the original. By what percentage has the area of the logo increased?
| 17\(\frac{1}{2}\)% | |
| 25% | |
| 27\(\frac{1}{2}\)% | |
| 35% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
How many hours does it take a car to travel 360 miles at an average speed of 40 miles per hour?
| 4 hours | |
| 8 hours | |
| 9 hours | |
| 7 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 = \( \frac{360mi}{40mph} \)
9 hours
What is 7\( \sqrt{4} \) x 7\( \sqrt{4} \)?
| 14\( \sqrt{4} \) | |
| 196 | |
| 49\( \sqrt{8} \) | |
| 14\( \sqrt{16} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
7\( \sqrt{4} \) x 7\( \sqrt{4} \)
(7 x 7)\( \sqrt{4 \times 4} \)
49\( \sqrt{16} \)
Now we need to simplify the radical:
49\( \sqrt{16} \)
49\( \sqrt{4^2} \)
(49)(4)
196
Betty scored 88% on her final exam. If each question was worth 4 points and there were 160 possible points on the exam, how many questions did Betty answer correctly?
| 35 | |
| 50 | |
| 29 | |
| 27 |
Betty scored 88% on the test meaning she earned 88% of the possible points on the test. There were 160 possible points on the test so she earned 160 x 0.88 = 140 points. Each question is worth 4 points so she got \( \frac{140}{4} \) = 35 questions right.
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.