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Arithmetic Reasoning

How many 8-passenger vans will it take to drive all 97 members of the football team to an away game?

13 vans

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = $ \frac{97}{8} $ = 12$\frac{1}{8}$

So, it will take 12 full vans and one partially full van to transport the entire team making a total of 13 vans.

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

Arithmetic Reasoning

4! = ?

4 x 3 x 2 x 1

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Word Knowledge

Diffident most nearly means:

timid

Lacking self–confidence.

General Science

Leafy vegetables, beans, potatoes, fruits, and whole grains are good sources of:

fiber

Fiber provides bulk to help the large intestine carry away waste. Good sources of fiber are leafy vegetables, beans, potatoes, fruits, and whole grains.

Math Knowledge

$2$\frac{1}{2}$$

The endpoints of this line segment are at (-2, -7) and (2, 3). What is the slope of this line?

2$\frac{1}{2}$

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -7) and (2, 3) so the slope becomes:

m = $ \frac{\Delta y}{\Delta x} $ = $ \frac{(3.0) - (-7.0)}{(2) - (-2)} $ = $ \frac{10}{4} $
m = 2$\frac{1}{2}$

General Science

The fossil record is a product of which period of Earth's history?

Cambrian

The Cambrian period is one of the most significant geological time periods. Lasting about 53 million years, it marked a dramatic burst of changes in life on Earth known as the Cambrian Explosion. It is from this period that the majority of the history of life on Earth, as documented by fossils, is found. Called the fossil record, the layering of these mineralized imprints of organisms preserved in sedementary rock have allowed geologists to build a historical record of plant and animal life on Earth.

General Science

Which of the following states of matter exists at the highest temperature?

gas

Solids exist at a lower temperature than liquids which exist at a lower temperature than gases.

Automotive Information

Which of the following is the result of the air-fuel mixture exploding instead of burning?

detonation

Normal combustion in an engine is initiated by a spark plug and results in the complete burning of the air-fuel mixture. If combustion is initiated by a source other than the spark plug, by a hot spot in the cylinder or combustion chamber for example, pre-ignition results. Detonation results if the air-fuel mixture explodes instead of burning. Detonation can cause extremes in pressure in the combustion chamber leading to engine damage.

Math Knowledge

This diagram represents two parallel lines with a transversal. If c° = 40, what is the value of x°?

140

For parallel lines with a transversal, the following relationships apply:

angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with c° = 40, the value of x° is 140.