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Sample Practice Test Questions
What is \( \frac{28\sqrt{35}}{4\sqrt{5}} \)?
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{28\sqrt{35}}{4\sqrt{5}} \)
\( \frac{28}{4} \) \( \sqrt{\frac{35}{5}} \)
7 \( \sqrt{7} \)
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.
Connecting the 8 batteries in series multiplies their voltage while keeping their current the same yielding a 72V 15A configuration. Connecting the 8 batteries in parallel multiplies their current while keeping their voltage the same yieleding a 9V 120A configuration. Using a series-parallel connection, 4 batteries can be connected in series and 4 can be connected in parallel resulting in a 36V 60A configuration.
Which of the following is not an advantage of using a tape measure over using a ruler?
measure with more accuracy
Rulers are used to both measure distance and to draw straight lines. Tape measures are flexible rulers useful for measuring longer distances and in tighter spaces. Rulers and tape measures provide similarly accurate measurements.
The voltage output of a transformer primarily depends on which of the following?
the number of turns in the wire of the coils
A transformer utilizes an inductor to increase or decrease the voltage in a circuit. AC flowing in a coil wrapped around an iron core magnetizes the core causing it to produce a magnetic field. This magnetic field generates a voltage in a nearby coil of wire and, depending on the number of turns in the wire of the primary (source) and secondary coils and their proximity, voltage is induced in the secondary coil.
Concurrent forces:
pass through a common point
Collinear forces act along the same line of action, concurrent forces pass through a common point and coplanar forces act in a common plane.
What is \( 5 \)\( \sqrt{28} \) + \( 7 \)\( \sqrt{7} \)
To add these radicals together their radicands must be the same:
5\( \sqrt{28} \) + 7\( \sqrt{7} \)
5\( \sqrt{4 \times 7} \) + 7\( \sqrt{7} \)
5\( \sqrt{2^2 \times 7} \) + 7\( \sqrt{7} \)
(5)(2)\( \sqrt{7} \) + 7\( \sqrt{7} \)
10\( \sqrt{7} \) + 7\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
10\( \sqrt{7} \) + 7\( \sqrt{7} \)Scalar quantities are fully described by which of the following?
a magnitude only
Velocity and displacement are vector quantities which means each is fully described by both a magnitude and a direction. In contrast, scalar quantities are quantities that are fully described by a magnitude only. A variable indicating a vector quantity will often be shown with an arrow symbol: \(\vec{v}\)