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Arithmetic Reasoning

A circular logo is enlarged to fit the lid of a jar. The new diameter is 40% larger than the original. By what percentage has the area of the logo increased?

20%

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%

General Science

What part of the brain is responsible for for balance, movement, and muscle coordination?

cerebellum

The cerebellum is a large cluster of nerves at the base of the brain that's responsible for balance, movement, and muscle coordination.

Mechanical Comprehension

The advantage of using a third-class lever is that it increases:

the speed of the load

A third-class lever is used to increase distance traveled by an object in the same direction as the force applied. The fulcrum is at one end of the lever, the object at the other, and the force is applied between them. This lever does not impart a mechanical advantage as the effort force must be greater than the load but does impart extra speed to the load. Examples of third-class levers are shovels and tweezers.

General Science

Herbivores are __________ that subsist on producers like plants and fungus.

primary consumers

Primary consumers (herbivores) subsist on producers like plants and fungus. Examples are grasshoppers, cows, and plankton.

Arithmetic Reasoning

Find the average of the following numbers: 17, 13, 17, 13.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{17 + 13 + 17 + 13}{4} \) = \( \frac{60}{4} \) = 15

Electronics Information

Resistance is opposition to which of the following?

current

Resistance is opposition to the flow of current and is measured in ohms (Ω). One ohm is defined as the amount of resistance that will allow one ampere of current to flow if one volt of voltage is applied. As resistance increases, current decreases as resistance and current are inversely proportional.

Shop Information

This tool is a(n) __________.

outside micrometer

Micrometers provide accuracy to the thousandths of an inch and come in outside and inside varieties. An outside micrometer is used to measure outside thickness, such as the diameter of a bolt, while an inside micrometer is used to measure the inside dimension of an object, such as the diameter of the hole of a nut or the width of a channel.

Math Knowledge

The dimensions of this cylinder are height (h) = 5 and radius (r) = 4. What is the surface area?

72π

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(4²) + 2π(4 x 5)
sa = 2π(16) + 2π(20)
sa = (2 x 16)π + (2 x 20)π
sa = 32π + 40π
sa = 72π

General Science

A subatomic particle that orbits the nucleus of an atom. It carries a negative electric charge. This desribes which of the following?

electron

An electron is a subatomic particle that orbits the nucleus of an atom. It carries a negative electric charge. Generally, an atom has the same number of negative electrons orbiting the nucleus as it does positive protons inside.

General Science

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: \(\vec{v}\)