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Word Knowledge

The school decided to take corrective measures to prevent truancy.

remedial

Intended to correct.

Word Knowledge

Prune most nearly means:

trim

To reduce by removing excess.

Math Knowledge

$\sqrt{80}$

If side a = 8, side b = 4, what is the length of the hypotenuse of this right triangle?

$ \sqrt{80} $

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = $ \sqrt{80} $

General Science

In which type of compound are electrons shared between atoms?

covalent

A compound is a substance containing two or more different chemical elements bound together by a chemical bond. In covalent compounds, electrons are shared between atoms. In ionic compounds, one atom borrows an electron from another atom resulting in two ions (electrically charged atoms) of opposite polarities that then become bonded electrostatically.

Automotive Information

The combustion chamber is enclosed by the:

cylinder head

Cylinders act as a guide for the pistons that translate the heat energy of combustion into the mechanical energy necessary to move a vehicle. Piston rings seal the piston to the cylinder to contain combustion gases and also regulate the oil distribution between the piston and cylinder wall. A cylinder head closes in the top of the cylinder forming the combustion chamber which is sealed by a head gasket (head). The head provides space for air and fuel intake valves, exhaust valves, and mounts for spark plugs and fuel injectors.

Arithmetic Reasoning

Simplify $ \sqrt{8} $

2$ \sqrt{2} $

To simplify a radical, factor out the perfect squares:

$ \sqrt{8} $
$ \sqrt{4 \times 2} $
$ \sqrt{2^2 \times 2} $
2$ \sqrt{2} $

General Science

pH is a scale that measures of how basic or acidic a solution is. A solution with a pH of 4 is:

acidic

An acid is a substance that gives up positively charged hydrogen ions (H⁺) when dissolved in water. A base (alkaline) gives up negatively charged hydroxide ions (OH^-) when dissolved in water. pH is a scale that measures of how basic or acidic a solution is. Numbered from 0 to 14, solutions with a pH of 7 are neutral, less than 7 are acidic, more than 7 are alkaline.

Word Knowledge

Mediate most nearly means:

arbitrate

To come between parties in order to reconcile.

Arithmetic Reasoning

What is $ \frac{4}{6} $ + $ \frac{4}{14} $?

$\frac{20}{21}$

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

$ \frac{4 x 7}{6 x 7} $ + $ \frac{4 x 3}{14 x 3} $

$ \frac{28}{42} $ + $ \frac{12}{42} $

Now, because the fractions share a common denominator, you can add them:

$ \frac{28 + 12}{42} $ = $ \frac{40}{42} $ = $\frac{20}{21}$

Automotive Information

The fuel injectors are fed fuel by the:

electric fuel pump

The electric fuel pump feeds pressurized fuel through a fuel filter to the fuel injectors via the fuel rail manifold. The fuel rail contains the fuel pressure regulator which ensures that the fuel injectors receive fuel at a consistent and known rate. Excess fuel bled off by the pressure regulator returns to the fuel tank through the fuel return line.