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Math Knowledge

A(n) __________ is to a parallelogram as a square is to a rectangle.

rhombus

A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.

Arithmetic Reasoning

23 members of a bridal party need transported to a wedding reception but there are only 4 5-passenger taxis available to take them. How many will need to find other transportation?

There are 4 5-passenger taxis available so that's 4 x 5 = 20 total seats. There are 23 people needing transportation leaving 23 - 20 = 3 who will have to find other transportation.

General Science

Saturated fats can __________ LDL ("bad") cholesterol while unsaturated fats can __________ it.

raise, decrease

Saturated fats can raise LDL ("bad") cholesterol while unsaturated fats can decrease it.

General Science

Which of the following would be found on a reflecting telescope?

concave mirror

A concave (or converging) mirror bulges inward and focuses reflected light on the mirror's focal point where the mirror's angles of incidence converge. In contrast, a convex (or diverging) mirror bulges outward and diffuses the light waves that strike it. A common use of a concave mirror is in a reflecting telescope, a common use of a convex mirror is in the side view mirror of a car.

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.

Mechanical Comprehension

If the green arrow in this diagram represents 420 ft⋅lb of work, how far will the box move if it weighs 140 pounds?

3 ft.

The Law of Work states that the work put into a machine is equal to the work received from the machine under ideal conditions. In equation form, that's:

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 420 ft⋅lb and the resistance force is 140 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
420 ft⋅lb = 140 lbs. x d_resistance
d_resistance = \( \frac{420ft⋅lb}{140 lbs.} \) = 3 ft.

Arithmetic Reasoning

A triathlon course includes a 500m swim, a 30.8km bike ride, and a 8.100000000000001km run. What is the total length of the race course?

39.4km

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.5km + 30.8km + 8.100000000000001km
total distance = 39.4km

Arithmetic Reasoning

What is c⁵ x 4c⁷?

4c¹²

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

c⁵ x 4c⁷
(1 x 4)c^{(5 + 7)}
4c¹²

Shop Information

Screwdrivers are most broadly classified by their:

tip

Screwdrivers come in many different handle, shaft, and tip configurations for use in a wide variety of applications. Screwdrivers are classified by their tip which is shaped to fit a corresponding screw head. Common tips are slotted (flat) and Phillips (x-shaped).

General Science

Which of the following would be used in eye glasses to correct farsightedness?

convex lens

Unlike curved mirrors that operate on the principle of reflection, lenses utilize refraction. A convex lens is thicker in the middle than on the edges and converges light while a concave lens is thicker on the edges than in the middle and diffuses light. A common use for curved lenses is in eye glasses where a convex lens is used to correct farsightedness and a concave lens is used to correct nearsightedness.