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Math Knowledge

This diagram represents two parallel lines with a transversal. If z° = 40, what is the value of a°?

For parallel lines with a transversal, the following relationships apply:

angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with z° = 40, the value of a° is 40.

Mechanical Comprehension

What type of load is sudden and for a relatively short duration?

impact load

A concentrated load acts on a relatively small area of a structure, a static uniformly distributed load doesn't create specific stress points or vary with time, a dynamic load varies with time or affects a structure that experiences a high degree of movement, an impact load is sudden and for a relatively short duration and a non-uniformly distributed load creates different stresses at different locations on a structure.

Arithmetic Reasoning

Convert 0.0006095 to scientific notation.

6.095 x 10^-4

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0006095 in scientific notation is 6.095 x 10^-4

Word Knowledge

Onset most nearly means:

start

Beginning.

Mechanical Comprehension

A block and tackle with four pulleys would have a mechanical advantage of:

Two or more pulleys used together constitute a block and tackle which, unlike a fixed pulley, does impart mechanical advantage as a function of the number of pulleys that make up the arrangement. So, for example, a block and tackle with three pulleys would have a mechanical advantage of three.

Arithmetic Reasoning

What is the next number in this sequence: 1, 7, 13, 19, 25, __________ ?

The equation for this sequence is:

a_n = a_n-1 + 6

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 6
a₆ = 25 + 6
a₆ = 31

General Science

Food is mixed with gastric acid and pepsin in the __________ to help break down protein.

stomach

Food is mixed with gastric acid and pepsin in the stomach to help break down protein.

Mechanical Comprehension

A screw is most like which of the following other simple machines?

inclined plane

A screw is an inclined plane wrapped in ridges (threads) around a cylinder. The distance between these ridges defines the pitch of the screw and this distance is how far the screw advances when it is turned once. The mechanical advantage of a screw is its circumference divided by the pitch.

Mechanical Comprehension

The radius of the axle is 3, the radius of the wheel is 4, and the blue box weighs 35 lbs. What is the effort force necessary to balance the load?

26.32 lbs.

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 4 and the output radius (where the resistance is being applied) is 3 for a mechanical advantage of \( \frac{4}{3} \) = 1.33

MA = \( \frac{load}{effort} \) so effort = \( \frac{load}{MA} \) = \( \frac{35 lbs.}{1.33} \) = 26.32 lbs.

Word Knowledge

Punctual most nearly means:

prompt

On time.