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General Science

In cell biology, the primary difference between anaerobic and aerobic respiration is that aerobic respiration requires:

oxygen

Some plant cells produce their own energy through photosynthesis which is the process by which sunlight, carbon dioxide, and water react to make sugar and oxygen. Animal cells cannot produce their own energy and, instead, generate energy when mitochondria consume outside sugar and oxygen through aerobic respiration.

Word Knowledge

Brandish most nearly means:

flourish

To shake or wave menacingly.

Mechanical Comprehension

If you have a gear train with three gears, the first with 24 teeth, the second with 16 teeth, and the third with 4 teeth, what is its mechanical advantage?

The mechanical advantage of a gear train is its gear ratio. The gear ratio (V_r) is the product of the gear ratios between the pairs of meshed gears. Let N represent the number of teeth for each gear:

V_r = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) \( \frac{N_3}{N_4} \) ... \( \frac{N_n}{N_{n+1}} \)

In this problem, we have three gears so the equation becomes:

V_r = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) = \( \frac{24}{16} \) \( \frac{16}{4} \) = \( \frac{24}{4} \) = 6

Word Knowledge

Censure most nearly means:

blame

To find fault with.

Word Knowledge

The flighty Caroline could not be troubled with mundane tasks such as paying her bills.

commonplace

Practical, ordinary.

Arithmetic Reasoning

Find the average of the following numbers: 17, 13, 17, 13.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{17 + 13 + 17 + 13}{4} \) = \( \frac{60}{4} \) = 15

Mechanical Comprehension

Boyle's law defines the relationship between pressure and volume as:

\(\frac{P_1}{P_2} = \frac{V_2}{V_1}\)

Boyle's law states that "for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional". Expressed as a formula, that's \(\frac{P_1}{P_2} = \frac{V_2}{V_1}\)

Electronics Information

Electricity cannot flow...

through an open circuit

An electrical circuit is a path through which electricity flows. This path contains one or more components that create a load (something that is using electricity) and that load acts as resistance to the passage of electricity through the circuit. Electricity can only flow through a circuit when the path is closed and cannot flow through an open circuit.

Arithmetic Reasoning

A circular logo is enlarged to fit the lid of a jar. The new diameter is 40% larger than the original. By what percentage has the area of the logo increased?

20%

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%

Mechanical Comprehension

If the green box weighs 25 lbs. and 75 lbs. of force is applied 5 ft. from the fulcrum at the blue arrow, how far from the fulcrum would the green box need to be placed to balance the lever?

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

d_a = \( \frac{R_bd_b}{R_a} \) = \( \frac{75 lbs. \times 5 ft.}{25 lbs.} \) = \( \frac{375 ft⋅lb}{25 lbs.} \) = 15 ft.