Given a normal distribution with m = 70 and s = 20, what is the probability that

a. X > 110.

b. X < 10.

c. X < 70 or X > 130.

d. Between what two X values (symmetrically distributed around the mean) are 70% of the values.

When you exhale, all of the air in your lungs must exit through the trachea. If you exhale through your nose, this air subsequently leaves through your nostrils. The area of your nostrils is less than that of your trachea. How does the speed of the air in the trachea compare to that in the nostrils?

Assuming that $n$ is an even perfect number, say $n=2^{k-1}\left(2^{k}-1\right),$ prove that the product of the positive divisors of $n$ is equal to $n^{k} ;$ in symbols,

$$\prod_{d | n} d=n^{k}$$

Read each sentence. If the sentence is true, write YES. If the sentence is not true, write NO and explain why.

Ironclads were of little importance in the war at sea.

Factor the trinomial.

$$- 6 k ^ { 2 } - 13 k - 6$$

Briefly explain the importance of each of the following. culture

Infer Two astronomers with telescopes, one on Venus and one on Mars, are observing Earth. Who would have an easier time and why?

Use the Ratio Test to determine whether each series converges or diverges or state that it provides no information. $\sum_{k=1}^{\infty} \frac{(2 k) !}{5^{k} 3^{k-1}}$

Determine whether each of the statements is true or false, and explain why. In a fair game, the elements of the payoff matrix must sum to 0.

Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $\$ 14,000 /$ day to operate, and it yields $50 \mathrm{oz}$ of gold and $3000 \mathrm{oz}$ of silver per day. The Horseshoe Mine costs $\$ 16,000 /$ day to operate, and it yields $75 \mathrm{oz}$ of gold and 1000 ounces of silver per day. Company management has set a target of at least $650 \mathrm{oz}$ of gold and 18,000 oz of silver.

a. How many days should each mine be operated so that the target can be met at a minimum cost?

b. Find the range of values that the Saddle Mine's daily operating cost can assume without changing the optimal solution.

c. Find the range of values that the requirement for gold can assume.

d. Find the shadow price for the requirement for gold.

Convert each of the following binary numbers into its decimal equivalent.

(a) 101

(b) 10101

(c) 1110101

(d) 1101011011

Why is it important to only change one experimental variable at a time in an experiment?

Sketch the graph of the function. Show vertical and horizontal asymptotes and x-intercepts.

$$y=\frac{x^2-16}{x^2-6 x+8}$$

Use the concept of marginal utility to explain the following: Newspaper vending machines are designed so that once you have paid for one paper, you could take more than one paper at a time. But soda vending machines, once you have paid for one soda, dispense only one soda at a time.