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Math Knowledge

Simplify (9a)(8ab) + (7a²)(8b).

128a²b

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(9a)(8ab) + (7a²)(8b)
(9 x 8)(a x a x b) + (7 x 8)(a² x b)
(72)(a¹⁺¹ x b) + (56)(a²b)
72a²b + 56a²b
128a²b

Mechanical Comprehension

If the radius of the axle is 5 and the radius of the wheel is 6, what is the mechanical advantage of this wheel and axle configuration?

1.2

The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 6 and the output radius (where the resistance is being applied) is 5 for a mechanical advantage of \( \frac{6}{5} \) = 1.2

Arithmetic Reasoning

A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.

How many error-free parts did the machine produce yesterday?

84.6

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{6}{100} \) x 5 = \( \frac{6 \times 5}{100} \) = \( \frac{30}{100} \) = 0.3 errors per hour

So, in an average hour, the machine will produce 5 - 0.3 = 4.7 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 4.7 = 84.6 error free parts were produced yesterday.

Math Knowledge

What is the area of a circle with a radius of 2?

4π

The formula for area is πr²:

a = πr²
a = π(2²)
a = 4π

General Science

The coldest point in the Earth's atmosphere is reached in which atmospheric layer?

mesosphere

In the mesosphere, temperature again drops as altitude increases until the coldest point in the Earth's atmosphere, the mesopause, is reached where temperatures fall to −225 °F (−143 °C).

Mechanical Comprehension

Depending on where you apply effort and resistance, the wheel and axle can multiply:

force or speed

If you apply the resistance to the axle and the effort to the wheel, the wheel and axle will multiply force and if you apply the resistance to the wheel and the effort to the axle, it will multiply speed.

Word Knowledge

The soldiers cherished the kindly Nurse Nightingale for her pathos.

compassion

Sympathetic pity.

Mechanical Comprehension

If A = 9 ft. and the green box weighs 30 lbs. what is the torque acting on the A side of this lever?

270 ft⋅lb

For a lever, torque is weight x distance from the fulcrum which, in this case, is: 30 ft. x 9 lbs. = 270 ft⋅lb

Mechanical Comprehension

The force required to initally get an object moving is __________ the force required to keep it moving.

higher than

For any given surface, the coefficient of static friction is higher than the coefficient of kinetic friction. More force is required to initally get an object moving than is required to keep it moving. Additionally, static friction only arises in response to an attempt to move an object (overcome the normal force between it and the surface).

General Science

Which of the following does not represent the freezing point of water?

0°F

The Fahrenheit scale fixes the freezing point of water at 32°F, the Celsuis scale at 0°C, and the Kelvin scale at 273K.