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Shop Information

Which of the following saws would you use if you're cutting wood along the grain?

ripsaw

The ripsaw delivers maximum efficiency at cutting with or along the grain (ripping).

General Science

Small rocks shed by asteroids and comets that reach the earth are called:

meteorites

Smaller rocks shed by asteroids and comets are called meteoroids. When these rocks reach Earth's atmosphere, they burn up in the mesosphere and become meteors. If a meteor manages to reach the Earth, it is called a meteorite.

Electronics Information

You would measure the amount of voltage between two points in a circuit with a(n):

voltmeter

Voltage (V) is the electrical potential difference between two points. A voltmeter is used to measure the voltage between two points in a circuit.

Arithmetic Reasoning

What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

General Science

A dominant trait will be expressed when paired with:

a recessive trait

The traits represented by genes are inherited independently of each other (one from the male and one from the female gamete) and a trait can be dominant or recessive. A dominant trait will be expressed when paired with a recessive trait while two copies of a recessive trait (one from each parent) must be present for the recessive trait to be expressed.

Arithmetic Reasoning

What is \( \frac{-7a^5}{7a^4} \)?

-a

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-7a^5}{7a^4} \)
\( \frac{-7}{7} \) a^{(5 - 4)}
-a

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.

Mechanical Comprehension

If the green box weighs 20 lbs. and is 1 ft. from the fulcrum, how far from the fulcrum would a 70 lbs. force need to be applied to balance the lever?

0.29 ft.

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 d_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{20 lbs. \times 1 ft.}{70 lbs.} \) = \( \frac{20 ft⋅lb}{70 lbs.} \) = 0.29 ft.

Electronics Information

An amplifier is most similar in function to which of the following:

step-up transformer

An amplifier is a device that takes a small input signal and creates a larger output signal. This makes it most similar to a step-up transformer which takes a smaller input voltage and creates a larger output voltage.

General Science

Which of the following substances gives up positively charged hydrogen ions (H⁺) when dissolved in water?

acid

An acid is a substance that gives up positively charged hydrogen ions (H⁺) when dissolved in water. A base (alkaline) gives up negatively charged hydroxide ions (OH^-) when dissolved in water. pH is a scale that measures of how basic or acidic a solution is. Numbered from 0 to 14, solutions with a pH of 7 are neutral, less than 7 are acidic, more than 7 are alkaline.