Identify the following term or individuals and explain their significance. Robert M. Lafollette

Antibiotics are drugs that selectively kill bacteria without harming animals. Many antibiotics act by selectively binding to certain proteins that are critical for bacterial function. Explain why some of the most successful antibiotics target bacterial RNA polymerase.

State the cardinality of each set. a. The set of whole numbers less than 4, b. The set of integers

State whether the domain of the function must be restricted to ensure that its inverse is a function. Give an appropriate restriction where needed.

$$g(x) = \sqrt{2x + 4}$$

Fill in each blank so that the resulting statement is true. If the occurrence of one event has an effect on the probability of another event, the events are said to be _______ For such events, P(A and B) = _______.

Compare. Use > , < , or = to complete each statement.

$$\frac { 8 } { 8 } \ ? \ \frac { 3 } { 3 }$$

Which of the following is not a parallelogram? A. square B. rectangle C. trapezoid D. rhombus

A city is planning to build a new park in a shape of a square in the business district. It has a side length of 2 x + 6 feet. Find the area of this park.

A small block of wood of inertia $m _ { \text { block } }$ is released from rest a distance h above the ground, directly above your head. You decide to shoot it with your pellet gun, which fires a pellet of inertia $m _ { \text { pellet } }$. After the block has fallen a distance d, the pellet hits it and becomes embedded in it, kicking it upward. At the instant of impact, the pellet is moving at speed $v _ { \text { pellet } }$. (a) To what maximum height $h _ { \max }$ does the pellet-block system rise above the ground? Express your answer in terms of the given variables and known values, such as g. (b) How much energy is dissipated in the collision?

Position function s(t) = -4.9t² + 250, which gives the height (in meters) of an object that has fallen for t seconds from a height of 250 meters. The velocity at time t=a seconds is given by lim_(t→a) s(a) - s(t) / a-t. -At what velocity will the object impact the ground?

(a) If A is a 3 x 5 matrix, then the number of leading 1's in the reduced row echelon form of A is at most _____.Why? (b) If A is a 3 x 5 matrix, then the number of parameters in the general solution of Ax = 0 is at most _____. Why? (c) If A is a 5 x 3 matrix, then the number of leading 1's in the reduced row echelon form of A is at most ____. Why? (d) If A is a 5 x 3 matrix, then the number of parameters in the general solution of Ax = 0 is at most _____. Why?

Factor and simplify each algebraic expression.

$$( x + 5 ) ^ { - \frac { 1 } { 2 } } - ( x + 5 ) ^ { - \frac { 3 } { 2 } }$$

What is the excluded value for

$$\frac { x - 4 } { x ^ { 2 } - 8 x + 16 }$$

?

The body of a 90.0 kg person contains 0.020

$$m^3$$

of body fat. If the density of fat is 890

$$\mathrm { kg } / \mathrm { m } ^ { 3 }$$

, what percentage of the person's body weight is composed of fat?