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.

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

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

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.

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

Explain how the Mean Value Theorem is a special case of Taylor’s Theorem.

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?

Why do oceans moderate the temperatures of coastal areas? (1) Temperature of ocean water changes slowly due to water's low specific heat. (1) Temperature of ocean water changes slowly due to water's low specific heat. (2) Temperature of ocean water changes slowly due to water's high specific heat. (3) Temperature of ocean water changes rapidly due to water's low specific heat. (4) Temperature of ocean water changes rapidly due to water's high specific heat.

Evaluate the expression when x = 4 and y = 3. (x² + 9)/(y + 2)