Suppose you know that a(b + c) = ab + ac is true for all real numbers a, b, and c. Use the properties of real numbers to prove that (b + c)a = ba + ca is true for all real numbers a, b, and c.

What are the caveats to conducting t -tests on all of the individual

$$\beta$$

parameters in a multiple-regression model?

Perform the indicated matrix operations or solve the matrix equation for X given that A, B, and C are defined as follows. If an operation is not defined, state the reason.

$$A = \left[ \begin{array} { r r } { 0 } & { 2 } \\ { - 1 } & { 3 } \\ { 1 } & { 0 } \end{array} \right] \quad B = \left[ \begin{array} { r r } { 4 } & { 1 } \\ { - 6 } & { - 2 } \end{array} \right] \quad C = \left[ \begin{array} { r r } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right]$$

$$2 C - \frac { 1 } { 2 } B$$

Compare how the respiratory, muscular, and nervous systems interrelate to accomplish the process of breathing. If there were a disruption in any one of these systems, how would it affect homeostasis in the body?

This exercise demonstrates that, in general, the results provided by Tchebysheff’s theorem cannot be improved upon. Let Y be a random variable such that

$$p ( - 1 ) = \frac { 1 } { 18 } , \quad p ( 0 ) = \frac { 16 } { 18 } , \quad p ( 1 ) = \frac { 1 } { 18 }$$

Show that E(Y ) = 0 and V(Y ) = 1/9.

Graph the function. state the domain and range.

$$p ( x ) = \frac { 3 } { x + 1 } - 2$$

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined.

$$\cos ^ { - 1 } ( - 0.92761 )$$

Determine which are propositions. Jones is guilty of murder in the first degree.

Compute the first-order partial derivatives. z = cosh(t - cos x)

Evaluate the following definite integrals. $\int _ { 0 } ^ { \pi / 4 } \left( \sec ^ { 2 } t \mathbf { i } - 2 \cos t \mathbf { j } - \mathbf { k } \right) d t$

Evaluate the power.

$$16^2$$

Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = 4 / (x-5)

It is known that 65% of all the ZeroCal hamburger patties produced by your factory actually contain more than 1,000 calories. Compute the probability distribution for n=50 Bernoulli trials. a. What is the most likely value for the number of burgers in a sample of 50 that contain more than 1,000 calories? b. Complete the following sentence: There is an approximately 73% chance that a batch of 50 ZeroCal patties contains ____ or more patties with more than 1,000 calories. c. Compare the graphs of the distributions for n=50 trials and n=20 trials. What do you notice?