| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.89 |
| Score | 0% | 58% |
Which of the following statements about exponents is false?
all of these are false |
|
b1 = b |
|
b0 = 1 |
|
b1 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 37 | |
| 43 | |
| 46 | |
| 51 |
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
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
|
greatest common factor |
|
least common factor |
|
least common multiple |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
The total water usage for a city is 50,000 gallons each day. Of that total, 13% is for personal use and 46% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 3,500 | |
| 16,500 | |
| 750 | |
| 8,050 |
46% of the water consumption is industrial use and 13% is personal use so (46% - 13%) = 33% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{33}{100} \) x 50,000 gallons = 16,500 gallons.
In a class of 15 students, 6 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 5 | |
| 13 | |
| 11 |
The number of students taking German or Spanish is 6 + 8 = 14. Of that group of 14, 4 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 14 - 4 = 10 who are taking at least one language. 15 - 10 = 5 students who are not taking either language.