| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.78 |
| Score | 0% | 56% |
Convert 5,481,000 to scientific notation.
| 54.81 x 105 | |
| 5.481 x 106 | |
| 5.481 x 105 | |
| 0.548 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:
5,481,000 in scientific notation is 5.481 x 106
A triathlon course includes a 200m swim, a 40.8km bike ride, and a 4.0km run. What is the total length of the race course?
| 56km | |
| 56.1km | |
| 40.7km | |
| 45km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.2km + 40.8km + 4.0km
total distance = 45km
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 11 small cakes per hour. The kitchen is available for 2 hours and 38 large cakes and 230 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 15 | |
| 12 | |
| 10 | |
| 13 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 38 large cakes are needed for the party so \( \frac{38}{10} \) = 3\(\frac{4}{5}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 11 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 11 x 2 = 22 small cakes during that time. 230 small cakes are needed for the party so \( \frac{230}{22} \) = 10\(\frac{5}{11}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 11 = 15 cooks.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 40% larger than the original. By what percentage has the area of the logo increased?
| 25% | |
| 15% | |
| 20% | |
| 22\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
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commutative property for division |
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distributive property for multiplication |
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commutative property for multiplication |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).