| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.42 |
| Score | 0% | 68% |
How many hours does it take a car to travel 130 miles at an average speed of 65 miles per hour?
| 2 hours | |
| 5 hours | |
| 9 hours | |
| 1 hour |
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 = \( \frac{130mi}{65mph} \)
2 hours
A bread recipe calls for 3\(\frac{3}{4}\) cups of flour. If you only have 1\(\frac{5}{8}\) cups, how much more flour is needed?
| 2\(\frac{1}{2}\) cups | |
| 1\(\frac{3}{4}\) cups | |
| 1\(\frac{1}{2}\) cups | |
| 2\(\frac{1}{8}\) cups |
The amount of flour you need is (3\(\frac{3}{4}\) - 1\(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{30}{8} \) - \( \frac{13}{8} \)) cups
\( \frac{17}{8} \) cups
2\(\frac{1}{8}\) cups
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 49 | |
| 44 | |
| 47 | |
| 46 |
The equation for this sequence is:
an = an-1 + 3(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
What is \( \frac{9\sqrt{6}}{3\sqrt{3}} \)?
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{2} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{2}} \) | |
| \(\frac{1}{2}\) \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{9\sqrt{6}}{3\sqrt{3}} \)
\( \frac{9}{3} \) \( \sqrt{\frac{6}{3}} \)
3 \( \sqrt{2} \)
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
|
distributive property for multiplication |
|
commutative property for multiplication |
|
commutative property for division |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).