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Word Knowledge

Precept most nearly means:

rule

A general rule of action.

General Science

Which of these is a type of Earth's crust?

oceanic

The crust is the Earth's outermost layer and is divided into oceanic and continental types. Oceanic crust is 3 miles (5 km) to 6 miles (10 km) thick and is composed primarily of denser rock. Continental crust is 20 to 30 miles (30 to 50 km) thick and composed primarily of less dense rock. The crust makes up approximately one percent of the Earth's total volume.

Mechanical Comprehension

If you lift a 30 lbs. rock 24 ft. from the ground, how much work have you done?

720 ft⋅lb

Work is force times distance. In this case, the force is the weight of the rock so:
$ W = F \times d $
$ W = 30 \times 24 $
$ W = 720 $

General Science

What type of cloud is responsible for fog?

stratus

Clouds are categorized based on their shape, size, and altitude. Stratus clouds are low-altitude clouds characterized by horizontal layering with a broad flat base. When stratus clouds occur on the ground the result is fog.

Mechanical Comprehension

If 15 lbs. of force is applied 8 ft. from the fulcrum at the blue arrow and the green box is 7 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?

17.14 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_a, our missing value, and plugging in our variables yields:

R_a = $ \frac{R_bd_b}{d_a} $ = $ \frac{15 lbs. \times 8 ft.}{7 ft.} $ = $ \frac{120 ft⋅lb}{7 ft.} $ = 17.14 lbs.

Shop Information

The __________ is an initial shallow saw cut made as a guide to prevent the saw from slipping sideways on subsequent more powerful cuts.

kerf

When you start sawing by creating a kerf it will help prevent the saw from slipping sideways when you begin the power strokes that do most of the cutting.

Word Knowledge

Gary believed the black foreboding sky was an inauspicious sign.

ominous

Not favorable.

Arithmetic Reasoning

What is -z² + 5z²?

4z²

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-1z² + 5z²
(-1 + 5)z²
4z²

Arithmetic Reasoning

Ezra loaned Monica $1,100 at an annual interest rate of 7%. If no payments are made, what is the total amount owed at the end of the first year?

$1,177

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = ($ \frac{6}{100} $) x $1,100
i = 0.07 x $1,100

No payments were made so the total amount due is the original amount + the accumulated interest:

total = $1,100 + $77
total = $1,177

General Science

The pitch of the siren of an approaching ambulance changes as it approaches you. This is an example of which of the following?

Doppler effect

The Doppler effect occurs when the source or listener (or both) of sound waves is moving. If they're moving closer together, the listener perceives the sound with a higher pitch and, when they're moving apart, the listener perceives the sound with a lower pitch.