A number in scientific notation has the format 0.000 x 10^exponent. 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:

0.0001342 in scientific notation is 1.342 x 10^-4

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{65}{100} \) = \( \frac{65 x 25}{100} \) = \( \frac{1625}{100} \) = 16 shots

The center makes 45% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{16}{\frac{45}{100}} \) = 16 x \( \frac{100}{45} \) = \( \frac{16 x 100}{45} \) = \( \frac{1600}{45} \) = 36 shots

to make the same number of shots as the guard and thus score the same number of points.

There are 3 5-passenger taxis available so that's 3 x 5 = 15 total seats. There are 20 people needing transportation leaving 20 - 15 = 5 who will have to find other transportation.

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.

The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 40 and 56 have in common.