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Word Knowledge

The drab winter scene made Keisha long for the vibrant colors of spring.

dreary

Dull, monotonous.

Mechanical Comprehension

What is the efficiency of a machine has work input of 100 ft⋅lb and work output of 35 ft⋅lb?

35%

Due to friction, a machine will never be able to utilize 100% of its work input. A certain percentage of that input will be lost in overcoming friction within the machine. Effeciency is a measure of how much of a machine's work input can be turned into useful work output and is calculated by dividing work output by work input and multiplying the result by 100:
\( Efficiency = \frac{Work_{out}}{Work_{in}} \times 100 \) \( = \frac{35 ft⋅lb}{100 ft⋅lb} \times 100 \) \( = 35% \) %

Arithmetic Reasoning

The total water usage for a city is 50,000 gallons each day. Of that total, 32% is for personal use and 59% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?

13,500

59% of the water consumption is industrial use and 32% is personal use so (59% - 32%) = 27% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 50,000 gallons = 13,500 gallons.

Automotive Information

Which of the following is the name for a transmission that incorporates the differential in one package?

transaxle

A differential is designed to drive a pair of wheels while allowing them to rotate at different speeds. A transaxle is a transmission that incorporates the differential in one package. Most front-wheel drive cars use a transaxle while rear-wheel drive cars use a transmission and separate differential connected via a drive shaft. The differential is incorporated into the drive axle which splits engine power delivered by the drive shaft between the two drive wheels. All-wheel drive cars typically use a transaxle that includes an output shaft to the rear differential.

Electronics Information

The valence shell of n insulator is how full of electrons?

more than half full

Insulators have valence shells that are more than half full of electrons and, as such, are tightly bound to the nucleus and difficult to move from one atom to another.

Word Knowledge

Rail most nearly means:

upbraid

To scold in harsh language.

Math Knowledge

Find the value of a:
5a + y = -1
-2a - 3y = -3

-\(\frac{6}{13}\)

You need to find the value of a so solve the first equation in terms of y:

5a + y = -1
y = -1 - 5a

then substitute the result (-1 - 5a) into the second equation:

-2a - 3(-1 - 5a) = -3
-2a + (-3 x -1) + (-3 x -5a) = -3
-2a + 3 + 15a = -3
-2a + 15a = -3 - 3
13a = -6
a = \( \frac{-6}{13} \)
a = -\(\frac{6}{13}\)

Mechanical Comprehension

If 15 lbs. of force is applied 8 ft. from the fulcrum at the blue arrow and the green box is 7 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?

17.14 lbs.

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

Solving for R_a, our missing value, and plugging in our variables yields:

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{15 lbs. \times 8 ft.}{7 ft.} \) = \( \frac{120 ft⋅lb}{7 ft.} \) = 17.14 lbs.

Word Knowledge

The judge issued a lenient sentence because it was Frank's first offense.

merciful

Mild or tolerant.

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