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Arithmetic Reasoning

Convert x^-3 to remove the negative exponent.

\( \frac{1}{x^3} \)

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

Word Knowledge

Mandate most nearly means:

command

An official order or commission to do something.

General Science

Convert -20C° to F°.

-4

To convert from C° to F° use:

\(F° = {9 \over 5}C° + 32\)

\(F° = {9 \over 5}(-20) + 32\)

\(F° = {-180 \over 5} + 32\)

\(F° = -36 + 32 = -4\)

General Science

In which type of compound are electrons shared between atoms?

covalent

A compound is a substance containing two or more different chemical elements bound together by a chemical bond. In covalent compounds, electrons are shared between atoms. In ionic compounds, one atom borrows an electron from another atom resulting in two ions (electrically charged atoms) of opposite polarities that then become bonded electrostatically.

General Science

In cell biology, where does DNA replication take place?

nucleus

The cell nucleus contains the genetic material of the cell and is where DNA replication takes place.

Mechanical Comprehension

The mechanical advantage of a wheel and axle is equal to the:

ratio of the diameters of the wheels

A wheel and axle uses two different diameter wheels mounted to a connecting axle. Force is applied to the larger wheel and large movements of this wheel result in small movements in the smaller wheel. Because a larger movement distance is being translated to a smaller distance, force is increased with a mechanical advantage equal to the ratio of the diameters of the wheels. An example of a wheel and axle is the steering wheel of a car.

Math Knowledge

Solve for b:
b² - 5b - 6 = 0

-1 or 6

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

b² - 5b - 6 = 0
(b + 1)(b - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 1) or (b - 6) must equal zero:

If (b + 1) = 0, b must equal -1
If (b - 6) = 0, b must equal 6

So the solution is that b = -1 or 6

General Science

Earth's history is divided into time periods, which of these is the longest time period?

eon

The Earth is approximately 4.6 billion years old and its history is divided into time periods based on the events that took place and the forms of life that were dominant during those periods. The largest graduation of time is the eon and each eon is subdivided into eras, eras into periods, periods into epochs, and epochs into ages.

Mechanical Comprehension

If the green box weighs 30 lbs. and is 8 ft. from the fulcrum, how much force would need to be applied at the blue arrow to balance the lever if the arrow's distance from the fulcrum is 9 ft.?

26.67 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_b, our missing value, and plugging in our variables yields:

R_b = \( \frac{R_ad_a}{d_b} \) = \( \frac{30 lbs. \times 8 ft.}{9 ft.} \) = \( \frac{240 ft⋅lb}{9 ft.} \) = 26.67 lbs.

Automotive Information

Another name for the powertrain control module is the __________ control unit.

engine

The main computer or powertrain control module (PCM) uses pre-programmed software to analyze the input received from sensors and produce output signals to adjust vehicle performance and operation. (Engine control unit (ECU) is another name for the PCM.)