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Convert 4,235,000 to scientific notation.
| 4.235 x 10-6 | |
| 0.424 x 107 | |
| 4.235 x 106 | |
| 4.235 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:
4,235,000 in scientific notation is 4.235 x 106
Simplify \( \sqrt{18} \)
| 3\( \sqrt{2} \) | |
| 8\( \sqrt{4} \) | |
| 4\( \sqrt{4} \) | |
| 5\( \sqrt{4} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{18} \)
\( \sqrt{9 \times 2} \)
\( \sqrt{3^2 \times 2} \)
3\( \sqrt{2} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 45% off." If Charlie buys two shirts, each with a regular price of $25, how much money will he save?
| $11.25 | |
| $2.50 | |
| $3.75 | |
| $5.00 |
By buying two shirts, Charlie will save $25 x \( \frac{45}{100} \) = \( \frac{$25 x 45}{100} \) = \( \frac{$1125}{100} \) = $11.25 on the second shirt.
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 25 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 38 | |
| 33 | |
| 31 | |
| 57 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{55}{100} \) = \( \frac{55 x 25}{100} \) = \( \frac{1375}{100} \) = 13 shots
The center makes 40% 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 = \( \frac{13}{\frac{40}{100}} \) = 13 x \( \frac{100}{40} \) = \( \frac{13 x 100}{40} \) = \( \frac{1300}{40} \) = 33 shots
to make the same number of shots as the guard and thus score the same number of points.
What is c2 + 3c2?
| 4c-4 | |
| -2c-2 | |
| 4c2 | |
| 2c2 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
1c2 + 3c2
(1 + 3)c2
4c2