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Mechanical Comprehension

The steering wheel of a car is an example of which type of simple machine?

wheel and axle

A wheel and axle uses two different diameter wheels mounted to a connecting axle. Force is applied to the larger wheel and large movements of this wheel result in small movements in the smaller wheel. Because a larger movement distance is being translated to a smaller distance, force is increased with a mechanical advantage equal to the ratio of the diameters of the wheels. An example of a wheel and axle is the steering wheel of a car.

Shop Information

Which of the following saws is not good for cutting wood?

hacksaw

A hacksaw has replaceable blades and is used to cut metal. The blade type is chosen based on the material that is to be cut. Blades with larger numbers of teeth per inch are more appropriate for cutting thinner materials.

Mechanical Comprehension

A screw is most like which of the following other simple machines?

inclined plane

A screw is an inclined plane wrapped in ridges (threads) around a cylinder. The distance between these ridges defines the pitch of the screw and this distance is how far the screw advances when it is turned once. The mechanical advantage of a screw is its circumference divided by the pitch.

General Science

The coldest point in the Earth's atmosphere is reached in which atmospheric layer?

mesosphere

In the mesosphere, temperature again drops as altitude increases until the coldest point in the Earth's atmosphere, the mesopause, is reached where temperatures fall to −225 °F (−143 °C).

Arithmetic Reasoning

If a rectangle is twice as long as it is wide and has a perimeter of 12 meters, what is the area of the rectangle?

8 m²

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 12 meters so the equation becomes: 2w + 2h = 12.

Putting these two equations together and solving for width (w):

2w + 2h = 12
w + h = $ \frac{12}{2} $
w + h = 6
w = 6 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 6 - 2w
3w = 6
w = $ \frac{6}{3} $
w = 2

Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m²

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$\frac{1}{2}$

Word Knowledge

Clarity most nearly means:

lucidity

Clearness.

General Science

In the classification of life, which of the following is not a domain?

animalia

The broadest classification of life splits all organisms into three groups called domains. The three domains of life are bacteria, archaea and eukaryota.

Mechanical Comprehension

What is the power output of a 9 hp engine that's 85% efficient?

4207.5 $ \frac{ft⋅lb}{s} $

$ Efficiency = \frac{Power_{out}}{Power_{in}} \times 100 $
Solving for power out: $ P_{o} = \frac{E \times P_{i}}{100} $
Knowing that 1 hp = 550 $ \frac{ft⋅lb}{s} $, P_i becomes 9 hp x 550 $ \frac{ft⋅lb}{s} $ = 4950 $ \frac{ft⋅lb}{s} $
$ P_{o} = \frac{E \times P_{i}}{100} = \frac{85 \times 4950 \frac{ft⋅lb}{s}}{100} $ $ = \frac{420750 \frac{ft⋅lb}{s}}{100} $ = 4207.5 $ \frac{ft⋅lb}{s} $

Math Knowledge

Which of the following statements about a parallelogram is not true?

opposite sides and adjacent angles are equal

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).