| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.54 |
| Score | 0% | 71% |
A bread recipe calls for 2\(\frac{1}{8}\) cups of flour. If you only have 1\(\frac{1}{4}\) cups, how much more flour is needed?
| \(\frac{7}{8}\) cups | |
| 1\(\frac{7}{8}\) cups | |
| 1\(\frac{1}{2}\) cups | |
| 3\(\frac{3}{8}\) cups |
The amount of flour you need is (2\(\frac{1}{8}\) - 1\(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{17}{8} \) - \( \frac{10}{8} \)) cups
\( \frac{7}{8} \) cups
\(\frac{7}{8}\) cups
What is the next number in this sequence: 1, 8, 15, 22, 29, __________ ?
| 36 | |
| 29 | |
| 34 | |
| 35 |
The equation for this sequence is:
an = an-1 + 7
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 + 7
a6 = 29 + 7
a6 = 36
What is the distance in miles of a trip that takes 2 hours at an average speed of 15 miles per hour?
| 30 miles | |
| 50 miles | |
| 195 miles | |
| 105 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 15mph \times 2h \)
30 miles
Simplify \( \frac{24}{52} \).
| \( \frac{1}{2} \) | |
| \( \frac{9}{14} \) | |
| \( \frac{8}{19} \) | |
| \( \frac{6}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{52} \) = \( \frac{\frac{24}{4}}{\frac{52}{4}} \) = \( \frac{6}{13} \)
What is \( 8 \)\( \sqrt{63} \) + \( 5 \)\( \sqrt{7} \)
| 29\( \sqrt{7} \) | |
| 40\( \sqrt{9} \) | |
| 13\( \sqrt{9} \) | |
| 40\( \sqrt{7} \) |
To add these radicals together their radicands must be the same:
8\( \sqrt{63} \) + 5\( \sqrt{7} \)
8\( \sqrt{9 \times 7} \) + 5\( \sqrt{7} \)
8\( \sqrt{3^2 \times 7} \) + 5\( \sqrt{7} \)
(8)(3)\( \sqrt{7} \) + 5\( \sqrt{7} \)
24\( \sqrt{7} \) + 5\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
24\( \sqrt{7} \) + 5\( \sqrt{7} \)