| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.71 |
| Score | 0% | 54% |
A triathlon course includes a 400m swim, a 30.5km bike ride, and a 12.7km run. What is the total length of the race course?
| 58.6km | |
| 55.5km | |
| 43.6km | |
| 60.9km |
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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 30.5km + 12.7km
total distance = 43.6km
Solve 3 + (4 + 3) ÷ 5 x 2 - 32
| -3\(\frac{1}{5}\) | |
| \(\frac{7}{9}\) | |
| \(\frac{6}{7}\) | |
| 2 |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
3 + (4 + 3) ÷ 5 x 2 - 32
P: 3 + (7) ÷ 5 x 2 - 32
E: 3 + 7 ÷ 5 x 2 - 9
MD: 3 + \( \frac{7}{5} \) x 2 - 9
MD: 3 + \( \frac{14}{5} \) - 9
AS: \( \frac{15}{5} \) + \( \frac{14}{5} \) - 9
AS: \( \frac{29}{5} \) - 9
AS: \( \frac{29 - 45}{5} \)
\( \frac{-16}{5} \)
-3\(\frac{1}{5}\)
Which of the following statements about exponents is false?
b0 = 1 |
|
b1 = b |
|
all of these are false |
|
b1 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 10 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?
| 24 | |
| 12 | |
| 10 | |
| 11 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{55}{100} \) = \( \frac{55 x 10}{100} \) = \( \frac{550}{100} \) = 5 shots
The center makes 45% 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 = \( \frac{5}{\frac{45}{100}} \) = 5 x \( \frac{100}{45} \) = \( \frac{5 x 100}{45} \) = \( \frac{500}{45} \) = 11 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{2}{9} \) - \( \frac{7}{15} \)?
| -\(\frac{11}{45}\) | |
| 2 \( \frac{9}{45} \) | |
| 1 \( \frac{1}{45} \) | |
| \( \frac{7}{16} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 5}{9 x 5} \) - \( \frac{7 x 3}{15 x 3} \)
\( \frac{10}{45} \) - \( \frac{21}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{10 - 21}{45} \) = \( \frac{-11}{45} \) = -\(\frac{11}{45}\)