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Arithmetic Reasoning

What is \( 5 \)\( \sqrt{20} \) - \( 2 \)\( \sqrt{5} \)

8\( \sqrt{5} \)

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

5\( \sqrt{20} \) - 2\( \sqrt{5} \)
5\( \sqrt{4 \times 5} \) - 2\( \sqrt{5} \)
5\( \sqrt{2^2 \times 5} \) - 2\( \sqrt{5} \)
(5)(2)\( \sqrt{5} \) - 2\( \sqrt{5} \)
10\( \sqrt{5} \) - 2\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

10\( \sqrt{5} \) - 2\( \sqrt{5} \)
(10 - 2)\( \sqrt{5} \)
8\( \sqrt{5} \)

General Science

Which of the following would you find in the side view mirror of a car?

convex mirror

A concave (or converging) mirror bulges inward and focuses reflected light on the mirror's focal point where the mirror's angles of incidence converge. In contrast, a convex (or diverging) mirror bulges outward and diffuses the light waves that strike it. A common use of a concave mirror is in a reflecting telescope, a common use of a convex mirror is in the side view mirror of a car.

Word Knowledge

Opportune most nearly means:

propitious

Suitable or convenient.

General Science

An element in the physical state of __________ maintains neither a constant volume nor a constant shape.

gas

The gaseous state occurs at a higher temperature range than the solid and liquid states of the same substance. In this state, molecules flow very freely around each other and will spread out as far as they're able. Gases maintain neither a constant volume nor a constant shape.

Word Knowledge

Simone, an expert in African sculpture, was asked to appraise the ambassador's collection of masks.

assess

To evaluate the worth of.

Electronics Information

This circuit component symbol represents a(n):

DC source

Direct current flows in only one direction in a circuit, from the negative terminal of the voltage source to the positive. A common source of direct current (DC) is a battery.

Mechanical Comprehension

If A = 10 ft., B = 1 ft., C = 9 ft., the green box weighs 50 lbs. and the blue box weighs 60 lbs., what does the orange box have to weigh for this lever to balance?

48.89 lbs.

In order for this lever to balance, the torque acting on each side of the fulrum must be equal. So, the torque produced by A must equal the torque produced by B and C. Torque is weight x distance from the fulcrum which means that the following must be true for the lever to balance:

f_Ad_A = f_Bd_B + f_Cd_C

For this problem, this equation becomes:

50 lbs. x 10 ft. = 60 lbs. x 1 ft. + f_C x 9 ft.

500 ft. lbs. = 60 ft. lbs. + f_C x 9 ft.

f_C = \( \frac{500 ft. lbs. - 60 ft. lbs.}{9 ft.} \) = \( \frac{440 ft. lbs.}{9 ft.} \) = 48.89 lbs.

General Science

Tertiary consumers eat which of the following?

primary and secondary consumers

Tertiary consumers eat primary consumers and secondary consumers and are typically carnivorous predators. Tertiary consumers may also be omnivores. Examples include wolves, sharks, and human beings.

Word Knowledge

The meticulous detective found every shred of evidence at the crime scene.

fastidious

Extrememly careful regarding details.

General Science

The crust and lithosphere of the Earth is made up of which of the following?

plates

The crust and the rigid lithosphere (upper mantle) is made up approximately thirty separate plates. These plates more very slowly on the slightly more liquid mantle (asthenosphere) beneath them. This movement has resulted in continental drift which is the gradual movement of land masses across Earth's surface. Continental drift is a very slow process, occurring over hundreds of millions of years.