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Sample Practice Test Questions
The mechanical advantage of a gear train is its gear ratio. The gear ratio (Vr) is the product of the gear ratios between the pairs of meshed gears. Let N represent the number of teeth for each gear:
Vr = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) \( \frac{N_3}{N_4} \) ... \( \frac{N_n}{N_{n+1}} \)
In this problem, we have three gears so the equation becomes:
Vr = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) = \( \frac{24}{16} \) \( \frac{16}{4} \) = \( \frac{24}{4} \) = 6
A ramp is an example of which kind of simple machine?
inclined plane
An inclined plane is a simple machine that reduces the force needed to raise an object to a certain height. Work equals force x distance and, by increasing the distance that the object travels, an inclined plane reduces the force necessary to raise it to a particular height. In this case, the mechanical advantage is to make the task easier. An example of an inclined plane is a ramp.
Which of the following is the result of the air-fuel mixture exploding instead of burning?
detonation
Normal combustion in an engine is initiated by a spark plug and results in the complete burning of the air-fuel mixture. If combustion is initiated by a source other than the spark plug, by a hot spot in the cylinder or combustion chamber for example, pre-ignition results. Detonation results if the air-fuel mixture explodes instead of burning. Detonation can cause extremes in pressure in the combustion chamber leading to engine damage.
Simplify (5a)(2ab) - (9a2)(3b).
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
(5a)(2ab) - (9a2)(3b)
(5 x 2)(a x a x b) - (9 x 3)(a2 x b)
(10)(a1+1 x b) - (27)(a2b)
10a2b - 27a2b
-17a2b
Convert 0.0006095 to scientific notation.
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0006095 in scientific notation is 6.095 x 10-4
If there were a total of 350 raffle tickets sold and you bought 24 tickets, what's the probability that you'll win the raffle?
You have 24 out of the total of 350 raffle tickets sold so you have a (\( \frac{24}{350} \)) x 100 = \( \frac{24 \times 100}{350} \) = \( \frac{2400}{350} \) = 7% chance to win the raffle.
Solve for \( \frac{5!}{6!} \)
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)
The biosphere consists of which of the following?
all of these
The biosphere is the global ecological system integrating all living beings and their relationships. This includes their interactions with the lithosphere (the rigid outer part of the earth, consisting of the crust and upper mantle), hydrosphere (all surface water), and atmosphere (the envelope of gases surrounding the planet).