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Math Knowledge

If side x = 12cm, side y = 9cm, and side z = 9cm what is the perimeter of this triangle?

30cm

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 12cm + 9cm + 9cm = 30cm

General Science

Absolute zero is which of the following?

the coldest temperature possible in the universe

In contrast to the Celsius scale (measured in degrees centigrade) that fixes 0° at the freezing point of water and the Fahrenheit scale that uses 32°, the Kelvin scale fixes 0 at absolute zero (-273°C) which is the lowest temperature possible in the universe.

Automotive Information

Spark plugs receive current from the:

distributor

Spark plugs receive current from the distributor and use it to spark combustion in the combustion chamber of a cylinder.

Mechanical Comprehension

Which class of lever is used to increase force on an object in the same direction as the force is applied?

second

A second-class lever is used to increase force on an object in the same direction as the force is applied. This lever requires a smaller force to lift a larger load but the force must be applied over a greater distance. The fulcrum is placed at one end of the lever and mechanical advantage increases as the object being lifted is moved closer to the fulcrum or the length of the lever is increased. An example of a second-class lever is a wheelbarrow.

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

Which of the following is not true about simple magnets?

opposite poles repel each other

Simple magnets have two poles, north and south, and opposite poles attract each other (N attracts S, S attracts N). Likewise, the same pole of two magnets repel (N repels N, S repels S). The Earth has a magnetic field and North and South Poles which enables the use of a magnetic compass to determine direction.

General Science

Poor balance could indicate an issue with which part of the nervous system?

cerebellum

The cerebellum is a large cluster of nerves at the base of the brain that's responsible for balance, movement, and muscle coordination.

General Science

Leafy vegetables, beans, potatoes, fruits, and whole grains are good sources of:

fiber

Fiber provides bulk to help the large intestine carry away waste. Good sources of fiber are leafy vegetables, beans, potatoes, fruits, and whole grains.

General Science

Examples of tertiary consumers include:

sharks

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.

Arithmetic Reasoning

Solve 2 + (5 + 2) ÷ 5 x 3 - 4²

-9\(\frac{4}{5}\)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (5 + 2) ÷ 5 x 3 - 4²
P: 2 + (7) ÷ 5 x 3 - 4²
E: 2 + 7 ÷ 5 x 3 - 16
MD: 2 + \( \frac{7}{5} \) x 3 - 16
MD: 2 + \( \frac{21}{5} \) - 16
AS: \( \frac{10}{5} \) + \( \frac{21}{5} \) - 16
AS: \( \frac{31}{5} \) - 16
AS: \( \frac{31 - 80}{5} \)
\( \frac{-49}{5} \)
-9\(\frac{4}{5}\)