| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.63 |
| Score | 0% | 73% |
What is the next number in this sequence: 1, 8, 15, 22, 29, __________ ?
| 38 | |
| 36 | |
| 29 | |
| 32 |
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
Simplify \( \frac{40}{76} \).
| \( \frac{3}{5} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{2}{7} \) | |
| \( \frac{10}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{76} \) = \( \frac{\frac{40}{4}}{\frac{76}{4}} \) = \( \frac{10}{19} \)
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 32,000 seats in a stadium are filled, how many home fans are in attendance?
| 41,667 | |
| 25,600 | |
| 33,333 | |
| 27,500 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
32,000 fans x \( \frac{4}{5} \) = \( \frac{128000}{5} \) = 25,600 fans.
Bob loaned Christine $700 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $763 | |
| $742 | |
| $735 | |
| $707 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $700
i = 0.06 x $700
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $700 + $42What is \( \frac{27\sqrt{40}}{9\sqrt{8}} \)?
| 3 \( \sqrt{5} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{5}} \) | |
| 5 \( \sqrt{\frac{1}{3}} \) | |
| \(\frac{1}{3}\) \( \sqrt{5} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{27\sqrt{40}}{9\sqrt{8}} \)
\( \frac{27}{9} \) \( \sqrt{\frac{40}{8}} \)
3 \( \sqrt{5} \)