How do mucus and cilia work together to remove dust that enters your nose? How do they differ?

Suppose you are a doctor with patients who are mountain climbers. Write a letter to these patients that explains how gas exchange is affected at the top of a mountain, where air pressure is lower and there is less oxygen than at lower elevations.

a. What three substances are exchanged in the alveoli? b. What happens to the carbon dioxide in the blood when it flows through the capillaries in the alveoli? c. How would gas exchange be affected at the top of a tall mountain, where air pressure is lower and there is less oxygen than at lower elevations? Explain.

Plot the graphs of the given functions. Check these graphs by using a calculator.

$$y=x^2-8x-5$$

The probabilities that students A, B, and C can solve a particular problem are $\frac{3}{5}, \frac{2}{3}$, and $\frac{1}{2}$ respectively. If they all try, determine the probability that at least one of the group solves the problem.

Let

$$A = \left[ \begin{array} { r r r } { 1 } & { - 4 } & { 0 } \\ { - 4 } & { 7 } & { 0 } \\ { 0 } & { 0 } & { 5 } \end{array} \right],$$

and let S be the matrix with column vectors

$$\mathbf { s } _ { 1 } = \left[ \begin{array} { l } { 0 } \\ { 0 } \\ { z } \end{array} \right] , \mathbf { s } _ { 2 } = \left[ \begin{array} { c } { 2 x } \\ { x } \\ { 0 } \end{array} \right] , \text { and } \mathbf { s } _ { 3 } = \left[ \begin{array} { r } { y } \\ { - 2 y } \\ { 0 } \end{array} \right],$$

where x, y, z are constants. (a) Show that

$$A S = \left[ 5 \mathbf { s } _ { 1 } , - \mathbf { s } _ { 2 } , 9 \mathbf { s } _ { 3 } \right].$$

(b) Find all values of x, y, z such that

$$S ^ { T } A S =\operatorname { diag } ( 5 , - 1,9 ).$$

If $x \equiv a($ mod $n),$ prove that either $x \equiv a(\bmod 2 n)$ or $x \equiv a+n(\bmod 2 n)$.

Simplify the given expression. $j^{15}-j^{13}$

Find each product. $3 y\left(5 y^{3}+2\right)\left(5 y^{3}-2\right)$

A manufacturing process produces, on average, 3% defective items. The company ships 10 items in each box and wants to guarantee no more than 1 defective item per box. If this guarantee applies to each box, what is the probability that the box will fail to meet the guarantee?

Find the indicated maximum and minimum values by the linear programming method of this section.The constraints are shown below the objective function.

$$\begin{array}{l}{\text { Minimum } C :} \\ {C=5 x+6 y} \\ {x \geq 0, y \geq 0} \\ {x+y \geq 5} \\ {x+2 y \geq 7}\end{array}$$

Calculate the requested term for the arithmetic sequence. A sequence starts -4, -9, -14, -19. What is the 8th term?

Can you catch_ a cold by sitting in a chilly draft? Explain.

Find the area of the surface generated when the given curve is revolved about the given axis.

$$y=x^{3}, \text { for } 0 \leq x \leq 1 ; \text { about the } x$$