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Arithmetic Reasoning

Which of the following is not an integer?

\({1 \over 2}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

General Science

During digestion, where is digested food absorbed into the blood stream?

small intestine

The small intestine is where most digestion takes place. As food travels along the small intestine it gets broken down completely by enzymes secreted from the walls. These enzymes are produced in the small intestine as well as in the pancreas and liver. After the enzymes break down the food, the resulting substances are then absorbed into the blood via capillaries in the small intestine walls.

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.

Word Knowledge

Solace most nearly means:

comfort

Source of consolation.

Arithmetic Reasoning

What is \( 5 \)\( \sqrt{28} \) + \( 7 \)\( \sqrt{7} \)

17\( \sqrt{7} \)

To add these radicals together their radicands must be the same:

5\( \sqrt{28} \) + 7\( \sqrt{7} \)
5\( \sqrt{4 \times 7} \) + 7\( \sqrt{7} \)
5\( \sqrt{2^2 \times 7} \) + 7\( \sqrt{7} \)
(5)(2)\( \sqrt{7} \) + 7\( \sqrt{7} \)
10\( \sqrt{7} \) + 7\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

10\( \sqrt{7} \) + 7\( \sqrt{7} \)
(10 + 7)\( \sqrt{7} \)
17\( \sqrt{7} \)

Word Knowledge

Clarence, an irrepressible comic, was held after cass for his buffoonery.

jocularity

Foolish behavior.

General Science

Which of the following describes the Earth's mantle?

all of these

Mantle makes up 84% of the Earth's volume and has an average thickness of approximately 1,800 miles (2,900 km). It is dense, hot, and primarily solid although in places it behaves more like a viscous fluid as the plates of the upper mantle and crust gradually "float" along its circumference.

Math Knowledge

What is 7a³ + 7a³?

14a³

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a³ + 7a³ = 14a³

Mechanical Comprehension

Which of the following will increase the mechanical advantage of this inclined plane?

lengthen the ramp

The mechanical advantage (MA) of an inclined plane is the effort distance divided by the resistance distance. In order to increase mechanical advantage, this ratio must increase which means making the effort distance longer and this can be accomplished by lengthening the length of the ramp.

Mechanical Comprehension

Which of the following surfaces would have the highest coefficient of friction?

concrete

Coefficient of friction (μ) represents how much two materials resist sliding across each other. Smooth surfaces like ice have low coefficients of friction while rough surfaces like concrete have high μ.