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Math Knowledge

The dimensions of this cube are height (h) = 5, length (l) = 1, and width (w) = 4. What is the volume?

The volume of a cube is height x length x width:

v = h x l x w
v = 5 x 1 x 4
v = 20

General Science

Generally, an atom has __________ negative electrons orbiting the nucleus as it does positive protons inside.

equal numbers of

An electron is a subatomic particle that orbits the nucleus of an atom. It carries a negative electric charge. Generally, an atom has the same number of negative electrons orbiting the nucleus as it does positive protons inside.

Mechanical Comprehension

A fixed pulley has a mechanical advantage of:

A fixed pulley is used to change the direction of a force and does not multiply the force applied. As such, it has a mechanical advantage of one. The benefit of a fixed pulley is that it can allow the force to be applied at a more convenient angle, for example, pulling downward or horizontally to lift an object instead of upward.

Mechanical Comprehension

The mechanical advantage of a block and tackle is equal to which of the following?

the number of pulleys

Two or more pulleys used together constitute a block and tackle which, unlike a fixed pulley, does impart mechanical advantage as a function of the number of pulleys that make up the arrangement. So, for example, a block and tackle with three pulleys would have a mechanical advantage of three.

Word Knowledge

Sari embellished the plain curtains with satin ribbons and tassels.

adorn

To decorate.

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

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.

Electronics Information

The diameter of a number 12 wire is __________ the diameter of a number 6 wire?

less than

The larger the number the smaller the diameter of the wire. So, the diameter of a number 12 wire is less than the diameter of a number 6 wire.

General Science

212°F is how many °C?

100

The formula to convert from F° to C° is:

\(C° = {5 \over 9} (F° - 32)\)

plugging in our values gives:

\(C° = {5 \over 9} (212 - 32)\)

\(C° = {5 \over 9} (180) = {{180 \times 5} \over 9}\)

\(C° = {900 \over 9}\)

\(C° = 100\)

General Science

Which of the following describes the Earth's mantle?

primarily solid

Mantle makes up 84% of the Earth's volume and has an average thickness of approximately 1,800 miles (2,900 km). It is dense, hot, and primarily solid although in places it behaves more like a viscous fluid as the plates of the upper mantle and crust gradually "float" along its circumference.