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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°

Mechanical Comprehension

Boyle's law defines the relationship between pressure and volume as:

\(\frac{P_1}{P_2} = \frac{V_2}{V_1}\)

Boyle's law states that "for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional". Expressed as a formula, that's \(\frac{P_1}{P_2} = \frac{V_2}{V_1}\)

Arithmetic Reasoning

What is \( \sqrt{\frac{16}{4}} \)?

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{4}} \)
\( \frac{\sqrt{16}}{\sqrt{4}} \)
\( \frac{\sqrt{4^2}}{\sqrt{2^2}} \)
\( \frac{4}{2} \)
2

Word Knowledge

Beneficial most nearly means:

advantageous

Helpful.

General Science

In the foood chain, producers serve as a food source for other organisms. Typical producers are plants that can make their own food through photosynthesis and certain bacteria that are capable of converting inorganic substances into food through:

chemosynthesis

Producers (autotrophs) serve as a food source for other organisms. Typical producers are plants that can make their own food through photosynthesis and certain bacteria that are capable of converting inorganic substances into food through chemosynthesis

General Science

Which of these is matter than cannot be separated into different types of matter by ordinary chemical methods?

element

An element is matter than cannot be separated into different types of matter by ordinary chemical methods.

Automotive Information

Which of the following receive signals from the powertrain control module (PCM) and carry out its instructions?

actuators

Actuators receive signals from the PCM and carry out adjustments needed based on the data the PCM received from the sensors.

Electronics Information

Capacitors store:

electricity

Capacitors store electricity and are used in circuits as temporary batteries. Capacitors are charged by DC current (AC current passes through a capacitor) and that stored charge can later be dissipated into the circuit as needed. Capacitors are often used to maintain power within a system when it is disconnected from its primary power source or to smooth out or filter voltage within a circuit.

Electronics Information

Which of the following is not a characteristic of a step-up transformer?

the primary voltage is higher than the secondary voltage

As their names indicate, a step-up transformer is used to step up or increase voltage and a step-down transformer is used to step down or decrease voltage. In a step-up transformer, the secondary voltage is higher than the primary voltage and it has more turns in the secondary winding than in the primary winding.

Mechanical Comprehension

Force of friction due to kinetic friction is __________ the force of friction due to static friction.

the same as

The formula for force of friction (F_f) is the same whether kinetic or static friction applies: F_{f =}μF_N. To distinguish between kinetic and static friction, μ_k and μ_s are often used in place of μ.