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Arithmetic Reasoning

What is $ \frac{3}{3} $ - $ \frac{5}{5} $?

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

$ \frac{3 x 5}{3 x 5} $ - $ \frac{5 x 3}{5 x 3} $

$ \frac{15}{15} $ - $ \frac{15}{15} $

Now, because the fractions share a common denominator, you can subtract them:

$ \frac{15 - 15}{15} $ = $ \frac{0}{15} $ =

Math Knowledge

$\sqrt{80}$

If side a = 8, side b = 4, what is the length of the hypotenuse of this right triangle?

$ \sqrt{80} $

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = $ \sqrt{80} $

Arithmetic Reasoning

Convert x^-3 to remove the negative exponent.

$ \frac{1}{x^3} $

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

Word Knowledge

My parents banned Chad from our house because of his indecorous behavior at dinner.

vulgar

In bad taste.

Word Knowledge

Civility most nearly means:

courtesy

Politeness.

Electronics Information

Electrical power is measured in:

watts

Electrical power is measured in watts (W) and is calculated by multiplying the voltage (V) applied to a circuit by the resulting current (I) that flows in the circuit: P = IV. In addition to measuring production capacity, power also measures the rate of energy consumption and many loads are rated for their consumption capacity. For example, a 60W lightbulb utilizes 60W of energy to produce the equivalent of 60W of heat and light energy.

Mechanical Comprehension

What is the power output of a 9 hp engine that's 85% efficient?

4207.5 $ \frac{ft⋅lb}{s} $

$ Efficiency = \frac{Power_{out}}{Power_{in}} \times 100 $
Solving for power out: $ P_{o} = \frac{E \times P_{i}}{100} $
Knowing that 1 hp = 550 $ \frac{ft⋅lb}{s} $, P_i becomes 9 hp x 550 $ \frac{ft⋅lb}{s} $ = 4950 $ \frac{ft⋅lb}{s} $
$ P_{o} = \frac{E \times P_{i}}{100} = \frac{85 \times 4950 \frac{ft⋅lb}{s}}{100} $ $ = \frac{420750 \frac{ft⋅lb}{s}}{100} $ = 4207.5 $ \frac{ft⋅lb}{s} $

General Science

The two heart chambers that collect blood are called:

atria

The heart is the organ that drives the circulatory system. In humans, it consists of four chambers with two that collect blood called atria and two that pump blood called ventricles. The heart's valves prevent blood pumped out of the ventricles from flowing back into the heart.

Electronics Information

Resistance is opposition to which of the following?

current

Resistance is opposition to the flow of current and is measured in ohms (Ω). One ohm is defined as the amount of resistance that will allow one ampere of current to flow if one volt of voltage is applied. As resistance increases, current decreases as resistance and current are inversely proportional.

Arithmetic Reasoning

Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 20 small cakes per hour. The kitchen is available for 2 hours and 26 large cakes and 480 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?

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. 26 large cakes are needed for the party so $ \frac{26}{10} $ = 2$\frac{3}{5}$ cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 20 x 2 = 40 small cakes during that time. 480 small cakes are needed for the party so $ \frac{480}{40} $ = 12 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 3 + 12 = 15 cooks.