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Sample Practice Test Questions
Simplify (9a)(8ab) + (7a2)(8b).
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.
(9a)(8ab) + (7a2)(8b)
(9 x 8)(a x a x b) + (7 x 8)(a2 x b)
(72)(a1+1 x b) + (56)(a2b)
72a2b + 56a2b
128a2b
If the radius of the axle is 5 and the radius of the wheel is 6, what is the mechanical advantage of this wheel and axle configuration?
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 6 and the output radius (where the resistance is being applied) is 5 for a mechanical advantage of \( \frac{6}{5} \) = 1.2
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 5 = \( \frac{6 \times 5}{100} \) = \( \frac{30}{100} \) = 0.3 errors per hour
So, in an average hour, the machine will produce 5 - 0.3 = 4.7 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 4.7 = 84.6 error free parts were produced yesterday.
What is the area of a circle with a radius of 2?
The formula for area is πr2:
a = πr2
a = π(22)
a = 4π
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).
Depending on where you apply effort and resistance, the wheel and axle can multiply:
force or speed
If you apply the resistance to the axle and the effort to the wheel, the wheel and axle will multiply force and if you apply the resistance to the wheel and the effort to the axle, it will multiply speed.
If A = 9 ft. and the green box weighs 30 lbs. what is the torque acting on the A side of this lever?
The force required to initally get an object moving is __________ the force required to keep it moving.
higher than
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).
Which of the following does not represent the freezing point of water?
0°F
The Fahrenheit scale fixes the freezing point of water at 32°F, the Celsuis scale at 0°C, and the Kelvin scale at 273K.