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Math Knowledge

$4$ \sqrt{2} $$

If the area of this square is 16, what is the length of one of the diagonals?

4$ \sqrt{2} $

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = $ \sqrt{a} $ = $ \sqrt{16} $ = 4

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 4² + 4²
c² = 32
c = $ \sqrt{32} $ = $ \sqrt{16 x 2} $ = $ \sqrt{16} $ $ \sqrt{2} $
c = 4$ \sqrt{2} $

Electronics Information

If an electrical circuit is interrupted, which of the following will result?

open circuit

A closed circuit is a complete loop or path that electricity follows. It consists of a source of voltage, a load, and connective conductors. If the circuit is interrupted, if a wire is disconnected or cut for example, it becomes an open circuit and no electricity will flow.

Shop Information

You're constructing a cabinet in your workshop and one of the cabinet doors is slightly too big. Which of the following tools would you use to make it fit?

plane

In wooodworking, a plane is used to shave off a small amount of material to smooth a surface or make it fit properly. A jack plane is a general purpose plane that contains an adjustable depth blade set at an angle with a handle and knob to allow gripping when sliding the plane across wood.

Word Knowledge

The best–selling writer was disappointed; his new novel was only a moderate success.

medium

Tending toward the average.

Arithmetic Reasoning

A bread recipe calls for 2$\frac{1}{4}$ cups of flour. If you only have 1$\frac{5}{8}$ cups, how much more flour is needed?

$\frac{5}{8}$ cups

The amount of flour you need is (2$\frac{1}{4}$ - 1$\frac{5}{8}$) cups. Rewrite the quantities so they share a common denominator and subtract:

($ \frac{18}{8} $ - $ \frac{13}{8} $) cups
$ \frac{5}{8} $ cups
$\frac{5}{8}$ cups

General Science

During continental drift, the drifting plates move across which of the following?

liquid mantle

The crust and the rigid lithosphere (upper mantle) is made up of approximately thirty separate plates. These plates more very slowly on the slightly more liquid mantle (asthenosphere) beneath them. This movement has resulted in continental drift which is the gradual movement of land masses across Earth's surface. Continental drift is a very slow process, occurring over hundreds of millions of years.

Shop Information

Which of the following statements about an 8-point saw is not true?

an 8-point saw makes a rougher cut than a 12-point saw

Saw blades are described by the number of teeth per inch (TPI). The higher the TPI of a saw the finer the cut it will make.

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} $

Word Knowledge

Serenity most nearly means:

peace

Calmness.

Arithmetic Reasoning

Alex loaned Charlie $300 at an annual interest rate of 6%. If no payments are made, what is the interest owed on this loan at the end of the first year?

$18

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = ($ \frac{6}{100} $) x $300
i = 0.06 x $300
i = $18