Free ASVAB Practice Tests

Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:

MA = \( \frac{E_d}{R_d} \)

where E_d is the effort distance and R_d is the resistance distance. For this problem, the equation becomes:

MA = \( \frac{5 ft.}{2.5 ft.} \) = 2

You might be wondering how having an effort distance of 2 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 2 times the resistance distance, the effort force must be \( \frac{1}{2} \) the resistance force. You're trading moving 2 times the distance for only having to use \( \frac{1}{2} \) the force.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

Like decomposers, scavengers also break down the dead bodies of plants and animals into simple nutrients. The difference is that scavengers operate on much larger refuse and dead animals (carrion). Decomposers then consume the much smaller particles left over by the scavengers.

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -32 as well and sum (Inside, Outside) to equal -4. For this problem, those two numbers are -8 and 4. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 4y - 32
y² + (-8 + 4)y + (-8 x 4)
(y - 8)(y + 4)

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

Solving for R_a, our missing value, and plugging in our variables yields:

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{15 lbs. \times 8 ft.}{7 ft.} \) = \( \frac{120 ft⋅lb}{7 ft.} \) = 17.14 lbs.

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 26 large cakes are needed for the party so \( \frac{26}{10} \) = 2\(\frac{3}{5}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 20 x 2 = 40 small cakes during that time. 480 small cakes are needed for the party so \( \frac{480}{40} \) = 12 cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 12 = 15 cooks.

The number of students taking German or Spanish is 14 + 6 = 20. Of that group of 20, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 20 - 3 = 17 who are taking at least one language. 24 - 17 = 7 students who are not taking either language.

Part of the brainstem, the medulla is the connection between the brain and the spinal cord. It controls involuntary actions like breathing, swallowing, and heartbeat.

The more mass a substance has the more force is required to move it or to change its direction. This resistance to changes in direction is known as inertia.