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Math Knowledge

Simplify (9a)(8ab) + (7a²)(8b).

128a²b

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(9a)(8ab) + (7a²)(8b)
(9 x 8)(a x a x b) + (7 x 8)(a² x b)
(72)(a¹⁺¹ x b) + (56)(a²b)
72a²b + 56a²b
128a²b

General Science

Meteoroids, meteors and meteorites are categorized based on which of the following?

their location

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.

Mechanical Comprehension

A wedge is most similar to what other type of simple machine?

inclined plane

The wedge is a moving inclined plane that is used to lift, hold, or break apart an object. A wedge converts force applied to its blunt end into force perpendicular to its inclined surface. In contrast to a stationary plane where force is applied to the object being moved, with a wedge the object is stationary and the force is being applied to the plane. Examples of a wedge include knives and chisels.

General Science

Which of the following is the correct order for types of radiation from longest to shortest wavelength?

radio waves → visible light → gamma rays

The electromagnetic spectrum covers all possible wavelengths and frequencies of radiation. From lowest frequency (longest wavelength) to highest frequency (shortest wavelength) radiation: radio waves → microwaves → infrared waves → visible light → ultraviolet light → X-rays → gamma rays.

Math Knowledge

A right angle measures:

90°

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

General Science

Which of Earth's layers has weather?

troposphere

The Earth's atmosphere has several layers starting with the troposphere which is closest in proximity to the surface. Containing most of the Earth's breathable air (oxygen and nitrogen), it's a region with warmer temperatures closer to the surface and cooler temperatures farther away which results in the rising and falling air that generates weather.

Mechanical Comprehension

If the radius of the axle is 5 and the radius of the wheel is 6, what is the mechanical advantage of this wheel and axle configuration?

The mechanical advantage of a wheel and axle lies in the difference in radius between the inner (axle) wheel and the outer wheel. But, this mechanical advantage is only realized when the input effort and load are applied to different wheels. Applying both input effort and load to the same wheel results in a mechanical advantage of 1.

Word Knowledge

The drab winter scene made Keisha long for the vibrant colors of spring.

dreary

Dull, monotonous.

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

Shop Information

Which of the following is not an advantage of using a tape measure over using a ruler?

measure with more accuracy

Rulers are used to both measure distance and to draw straight lines. Tape measures are flexible rulers useful for measuring longer distances and in tighter spaces. Rulers and tape measures provide similarly accurate measurements.