| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.22 |
| Score | 0% | 64% |
In a class of 26 students, 12 are taking German and 5 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 23 | |
| 25 | |
| 26 | |
| 12 |
The number of students taking German or Spanish is 12 + 5 = 17. Of that group of 17, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 17 - 3 = 14 who are taking at least one language. 26 - 14 = 12 students who are not taking either language.
Convert 0.000975 to scientific notation.
| 9.75 x 10-4 | |
| 9.75 x 105 | |
| 9.75 x 10-3 | |
| 9.75 x 10-5 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.000975 in scientific notation is 9.75 x 10-4
The total water usage for a city is 15,000 gallons each day. Of that total, 19% is for personal use and 48% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 7,200 | |
| 3,000 | |
| 4,800 | |
| 4,350 |
48% of the water consumption is industrial use and 19% is personal use so (48% - 19%) = 29% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{29}{100} \) x 15,000 gallons = 4,350 gallons.
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = -7 |
|
a = 7 or a = -7 |
|
a = 7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is \( \frac{16\sqrt{35}}{8\sqrt{5}} \)?
| 2 \( \sqrt{7} \) | |
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{2}} \) | |
| \(\frac{1}{7}\) \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{16\sqrt{35}}{8\sqrt{5}} \)
\( \frac{16}{8} \) \( \sqrt{\frac{35}{5}} \)
2 \( \sqrt{7} \)