| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.13 |
| Score | 0% | 63% |
If \( \left|a + 2\right| \) - 6 = -2, which of these is a possible value for a?
| -8 | |
| 23 | |
| -6 | |
| 6 |
First, solve for \( \left|a + 2\right| \):
\( \left|a + 2\right| \) - 6 = -2
\( \left|a + 2\right| \) = -2 + 6
\( \left|a + 2\right| \) = 4
The value inside the absolute value brackets can be either positive or negative so (a + 2) must equal + 4 or -4 for \( \left|a + 2\right| \) to equal 4:
| a + 2 = 4 a = 4 - 2 a = 2 | a + 2 = -4 a = -4 - 2 a = -6 |
So, a = -6 or a = 2.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 178.6 | |
| 124.2 | |
| 109.4 | |
| 129.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 6 = \( \frac{4 \times 6}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour
So, in an average hour, the machine will produce 6 - 0.24 = 5.76 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 5.76 = 109.4 error free parts were produced yesterday.
Which of the following is not a prime number?
9 |
|
7 |
|
5 |
|
2 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
A bread recipe calls for 1\(\frac{7}{8}\) cups of flour. If you only have 1\(\frac{3}{4}\) cups, how much more flour is needed?
| 2 cups | |
| 1\(\frac{1}{4}\) cups | |
| 3\(\frac{3}{8}\) cups | |
| \(\frac{1}{8}\) cups |
The amount of flour you need is (1\(\frac{7}{8}\) - 1\(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{15}{8} \) - \( \frac{14}{8} \)) cups
\( \frac{1}{8} \) cups
\(\frac{1}{8}\) cups
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
|
distributive property for division |
|
commutative property for division |
|
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.