| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
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Convert 6,578,000 to scientific notation.
| 6.578 x 10-5 | |
| 6.578 x 105 | |
| 6.578 x 106 | |
| 6.578 x 107 |
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:
6,578,000 in scientific notation is 6.578 x 106
If a rectangle is twice as long as it is wide and has a perimeter of 48 meters, what is the area of the rectangle?
| 8 m2 | |
| 2 m2 | |
| 128 m2 | |
| 50 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 48 meters so the equation becomes: 2w + 2h = 48.
Putting these two equations together and solving for width (w):
2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8
Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m2
What is the distance in miles of a trip that takes 2 hours at an average speed of 20 miles per hour?
| 60 miles | |
| 40 miles | |
| 210 miles | |
| 250 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 = \( 20mph \times 2h \)
40 miles
Which of the following is not a prime number?
9 |
|
5 |
|
7 |
|
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.
What is \( \frac{4}{4} \) - \( \frac{8}{12} \)?
| \( \frac{1}{12} \) | |
| \(\frac{1}{3}\) | |
| 2 \( \frac{6}{12} \) | |
| 1 \( \frac{2}{9} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 3}{4 x 3} \) - \( \frac{8 x 1}{12 x 1} \)
\( \frac{12}{12} \) - \( \frac{8}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{12 - 8}{12} \) = \( \frac{4}{12} \) = \(\frac{1}{3}\)