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Arithmetic Reasoning

How many hours does it take a car to travel 75 miles at an average speed of 25 miles per hour?

3 hours

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

speed = \( \frac{\text{distance}}{\text{time}} \)

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{75mi}{25mph} \)
3 hours

Mechanical Comprehension

If the green box weighs 55 lbs. and is 3 ft. from the fulcrum, how far from the fulcrum would a 70 lbs. weight need to be placed to balance the lever?

2.36 ft.

To balance this lever the torques on each side of the fulcrum 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 left side of the fulcrum and b the right, R is resistance (weight) and d is the distance from the fulcrum.

Solving for d_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{55 lbs. \times 3 ft.}{70 lbs.} \) = \( \frac{165 ft⋅lb}{70 lbs.} \) = 2.36 ft.

Electronics Information

How would you connect 4 [15V 15A] batteries to achieve a combined power output of 60V 15A?

series

Connecting the 4 batteries in series multiplies their voltage while keeping their current the same yielding a 60V 15A configuration. Connecting the 4 batteries in parallel multiplies their current while keeping their voltage the same yieleding a 15V 60A configuration. Using a series-parallel connection, 2 batteries can be connected in series and 2 can be connected in parallel resulting in a 30V 30A configuration.

Word Knowledge

Gary believed the black foreboding sky was an inauspicious sign.

ominous

Not favorable.

Math Knowledge

Find the value of a:
5a + z = -1
-2a - 3z = -3

-\(\frac{6}{13}\)

You need to find the value of a so solve the first equation in terms of z:

5a + z = -1
z = -1 - 5a

then substitute the result (-1 - 5a) into the second equation:

-2a - 3(-1 - 5a) = -3
-2a + (-3 x -1) + (-3 x -5a) = -3
-2a + 3 + 15a = -3
-2a + 15a = -3 - 3
13a = -6
a = \( \frac{-6}{13} \)
a = -\(\frac{6}{13}\)

Arithmetic Reasoning

What is c⁵ x 4c⁷?

4c¹²

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

c⁵ x 4c⁷
(1 x 4)c^{(5 + 7)}
4c¹²

Mechanical Comprehension

If the radius of the axle is 5 and the radius of the wheel is 8, what is the mechanical advantage of this wheel and axle configuration?

0.63

The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 5 and the output radius (where the resistance is being applied) is 8 for a mechanical advantage of \( \frac{5}{8} \) = 0.63

Word Knowledge

Demeanor most nearly means:

disposition

Behavior towards others.

General Science

Within DNA, a variety of a particular gene is called a(n):

allele

The gene is the base unit of inheritance and is contained within DNA. A gene may come in several varieties (alleles) and there are a pair of alleles for every gene. If the alleles are alike, a person is homozygous for that gene. If the alleles are different, heterozygous.

Electronics Information

Voltage and current are __________ proportional.

directly

Voltage (V) is the electrical potential difference between two points. Electrons will flow as current from areas of high potential (concentration of electrons) to areas of low potential. Voltage and current are directly proportional in that the higher the voltage applied to a conductor the higher the current that will result.