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Arithmetic Reasoning

If a car travels 45 miles in 3 hours, what is the average speed?

15 mph

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

speed = $ \frac{\text{distance}}{\text{time}} $
speed = $ \frac{45mi}{3h} $
15 mph

Mechanical Comprehension

A 290 lb. barrel is rolled up a 14 ft. ramp to a platform that's 2 ft. tall. What effort is required to move the barrel?

41.4 lbs.

This problem describes an inclined plane and, for an inclined plane, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance:

F_ed_e = F_rd_r

Plugging in the variables from this problem yields:

F_e x 14 ft. = 290 lbs. x 2 ft.
F_e = $ \frac{580 ft⋅lb}{14 ft.} $ = 41.4 lbs.

Mechanical Comprehension

If this lever is in equilibrium with an effort force of 10.0 ft. lb. at the blue arrow and a resistance force of 3 ft. lb. at the green box, what is its mechanical advantage?

0.3

Mechanical advantage (MA) is the ratio by which effort force relates to resistance force. If both forces are known, calculating MA is simply a matter of dividing resistance force by effort force:

MA = $ \frac{F_r}{F_e} $ = $ \frac{3 ft.}{10.0 ft.} $ = 0.3

In this case, the mechanical advantage is less than one meaning that each unit of effort force results in just 0.3 units of resistance force. However, a third class lever like this isn't designed to multiply force like a first class lever. A third class lever is designed to multiply distance and speed at the resistance by sacrificing force at the resistance. Different lever styles have different purposes and multiply forces in different ways.

Electronics Information

Resistance is measured in:

ohms

Resistance is opposition to the flow of current and is measured in ohms (Ω). One ohm is defined as the amount of resistance that will allow one ampere of current to flow if one volt of voltage is applied. As resistance increases, current decreases as resistance and current are inversely proportional.

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

212°F is how many °C?

100

The formula to convert from F° to C° is:

$C° = {5 \over 9} (F° - 32)$

plugging in our values gives:

$C° = {5 \over 9} (212 - 32)$

$C° = {5 \over 9} (180) = {{180 \times 5} \over 9}$

$C° = {900 \over 9}$

$C° = 100$

Mechanical Comprehension

If the handles of a wheelbarrow are 1.5 ft. from the wheel axle, how many pounds of force must you exert to lift the handles if it's carrying a 130 lbs. load concentrated at a point 0.5 ft. from the axle?

43.3

This problem describes a second-class lever and, for a second class lever, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance: F_ed_e = F_rd_r. In this problem we're looking for effort force:
$ F_e = \frac{F_r d_r}{d_e} $
$ F_e = \frac{130 \times 0.5}{1.5} $
$ F_e = \frac{65.0}{1.5} $
$ F_e = 43.3 $

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.

General Science

Earth's history is divided into time periods, which of these is the longest time period?

eon

The Earth is approximately 4.6 billion years old and its history is divided into time periods based on the events that took place and the forms of life that were dominant during those periods. The largest graduation of time is the eon and each eon is subdivided into eras, eras into periods, periods into epochs, and epochs into ages.

Mechanical Comprehension

A box is resting on a smooth floor. Static friction is present:

when an attempt is made to move the box

For any given surface, the coefficient of static friction is higher than the coefficient of kinetic friction. More force is required to initally get an object moving than is required to keep it moving. Additionally, static friction only arises in response to an attempt to move an object (overcome the normal force between it and the surface).