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Arithmetic Reasoning

What is \( \frac{4}{6} \) + \( \frac{4}{14} \)?

\(\frac{20}{21}\)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

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

\( \frac{4 x 7}{6 x 7} \) + \( \frac{4 x 3}{14 x 3} \)

\( \frac{28}{42} \) + \( \frac{12}{42} \)

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

\( \frac{28 + 12}{42} \) = \( \frac{40}{42} \) = \(\frac{20}{21}\)

Mechanical Comprehension

Two gears are connected and the larger gear drives the smaller gear. The speed of rotation will __________ and the torque will __________.

increase, decrease

Connected gears of different numbers of teeth are used together to change the rotational speed and torque of the input force. If the smaller gear drives the larger gear, the speed of rotation will be reduced and the torque will increase. If the larger gear drives the smaller gear, the speed of rotation will increase and the torque will be reduced.

General Science

Scavengers break down the dead bodies of plants and animals into which of the following?

simple nutrients

Like decomposers, scavengers also break down the dead bodies of plants and animals into simple nutrients. The difference is that scavengers operate on much larger refuse and dead animals (carrion). Decomposers then consume the much smaller particles left over by the scavengers.

Automotive Information

Too much fuel results in a __________ air-fuel mixture that burns quicker and cooler.

rich

The stoichiometric ratio defines the proper ratio of air to fuel necessary so that an engine burns all fuel with no excess air. For gasoline fuel, the stoichiometric ratio is about 14.7:1 or for every one gram of fuel, 14.7 grams of air are required. Too much air results in a lean air-fuel mixture that burns more slowly and hotter while too much fuel results in a rich mixture that burns quicker and cooler.

General Science

Which of the following is the narrowest classification of life?

species

The narrowest classification of life, species, contains organisms that are so similar that they can only reproduce with others of the same species.

General Science

Convert -20C° to F°.

-4

To convert from C° to F° use:

\(F° = {9 \over 5}C° + 32\)

\(F° = {9 \over 5}(-20) + 32\)

\(F° = {-180 \over 5} + 32\)

\(F° = -36 + 32 = -4\)

Word Knowledge

Scamper most nearly means:

dash

To run quickly.

Word Knowledge

Advantageous most nearly means:

favorable

Giving an advantage.

General Science

Materials like metals that transfer heat efficiently are called:

conductors

Heat is always transferred from warmer to cooler environments and conduction is the simplest way this transfer can occur. It is accomplished through direct contact between materials and materials like metals that transfer heat efficiently are called conductors while those that conduct heat poorly, such as plastic, are called insulators.

Mechanical Comprehension

If A = 10 ft., B = 1 ft., C = 9 ft., the green box weighs 50 lbs. and the blue box weighs 60 lbs., what does the orange box have to weigh for this lever to balance?

48.89 lbs.

In order for this lever to balance, the torque acting on each side of the fulrum must be equal. So, the torque produced by A must equal the torque produced by B and C. Torque is weight x distance from the fulcrum which means that the following must be true for the lever to balance:

f_Ad_A = f_Bd_B + f_Cd_C

For this problem, this equation becomes:

50 lbs. x 10 ft. = 60 lbs. x 1 ft. + f_C x 9 ft.

500 ft. lbs. = 60 ft. lbs. + f_C x 9 ft.

f_C = \( \frac{500 ft. lbs. - 60 ft. lbs.}{9 ft.} \) = \( \frac{440 ft. lbs.}{9 ft.} \) = 48.89 lbs.