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Arithmetic Reasoning

What is the least common multiple of 6 and 12?

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 have in common.

Electronics Information

The ampere is a unit of measurement for:

current

Current is the rate of flow of electrons per unit time and is measured in amperes (A). A coulomb (C) is the quantity of electricity conveyed in one second by a current of one ampere.

General Science

As part of the carbon cycle, plants release carbon into the atmosphere through which process?

decomposition

The carbon cycle represents the ciruit of carbon through Earth's ecosystem. Carbon dioxide (CO₂) in the atmosphere is absorbed by plants through photosynthesis. Plants then die and release carbon back into the atmosphere during decomposition or are eaten by animals who breathe (respiration) the carbon into the atmosphere they exhale and produce waste which also releases carbon as it decays.

Electronics Information

What type of current flows in only one direction in a circuit?

direct

Direct current flows in only one direction in a circuit, from the negative terminal of the voltage source to the positive. A common source of direct current (DC) is a battery.

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.

Electronics Information

Which of the following is not a purpose of a resistor in an electrical circuit?

multiply the current in the circuit

Resistors can be chosen in a wide variety of values to control the voltage in a circuit, limit the current, or moderate the heat produced by the components in the circuit.

Word Knowledge

Rashid made the untenable statement that George Washington was the second president of the United States.

baseless

Not able to be defended.

Word Knowledge

Revive most nearly means:

reanimate

To bring back to life.

Shop Information

You're replacing the hubcaps on a car. Which of the following are you most likely to use?

rubber mallet

A mallet is a hammer with a relatively large head, often made of rubber or wood. Both the size and material of the mallet head help prevent damage when striking more delicate surfaces.

Math Knowledge

If angle a = 53° and angle b = 27° what is the length of angle d?

127°

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 53° - 27° = 100°

So, d° = 27° + 100° = 127°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 53° = 127°