| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.25 |
| Score | 0% | 65% |
What is \( \frac{7}{8} \) + \( \frac{7}{16} \)?
| 2 \( \frac{3}{16} \) | |
| 1 \( \frac{4}{16} \) | |
| 1 \( \frac{8}{15} \) | |
| 1\(\frac{5}{16}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 2}{8 x 2} \) + \( \frac{7 x 1}{16 x 1} \)
\( \frac{14}{16} \) + \( \frac{7}{16} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{14 + 7}{16} \) = \( \frac{21}{16} \) = 1\(\frac{5}{16}\)
a(b + c) = ab + ac defines which of the following?
distributive property for division |
|
commutative property for division |
|
distributive property for multiplication |
|
commutative 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.
What is (z3)2?
| 2z3 | |
| z6 | |
| z-1 | |
| z |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(z3)2A triathlon course includes a 100m swim, a 50.5km bike ride, and a 11.8km run. What is the total length of the race course?
| 54.1km | |
| 25.6km | |
| 62.4km | |
| 29.5km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.1km + 50.5km + 11.8km
total distance = 62.4km
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 45% 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?
| 17 | |
| 24 | |
| 18 | |
| 15 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{45}{100} \) = \( \frac{45 x 15}{100} \) = \( \frac{675}{100} \) = 6 shots
The center makes 35% 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 = \( \frac{6}{\frac{35}{100}} \) = 6 x \( \frac{100}{35} \) = \( \frac{6 x 100}{35} \) = \( \frac{600}{35} \) = 17 shots
to make the same number of shots as the guard and thus score the same number of points.