An inheritance of $20,000 is divided among three investments yielding a total of$1780 in interest per year. The interest rates for the three investments are 7%, 9%, and 11%. The amounts invested at 9% and 11% are $3000 and$1000 less than the amount invested at 7%, respectively. Find the amount invested at each rate.

Let $P(n): n^{2}-n+5$ is a prime. be an open sentence over a domain S. (a) Determine the truth values of the quantified statements $\forall n \in S, P(n)$ and $\exists n \in S, \sim P(n)$ for S = {1, 2, 3, 4}. (b) Determine the truth values of the quantified statements $\forall n \in S, P(n)$ and $\exists n \in S, \sim P(n)$ for S = {1, 2, 3, 4, 5}. (c) How are the statements in (a) and (b) related?

A total of $25,000 is invested in two funds paying 8% and 8.5% simple interest. The annual interest is$2060. How much is invested in each fund?

Describe the neural mechanisms responsible for controlling blood pressure

The sum of three positive numbers is 24. The second number is 4 greater than the first, and the third is three times the first. Find the three numbers.

Suppose the weight of an animal is normally distributed with mean 3720 g and standard deviation 527 g. What percentage of the population has a weight that exceeds 5000 g?

Give an example of a set A = {1, 2, . . . , k} for a smallest $k \in \mathbf{N}$ containing subsets $A_{1}, A_{2}, A_{3}$ such that $\left|A_{i}-A_{j}\right|=\left|A_{j}-A_{i}\right|=|i-j|$ for every two integers i and j with $1 \leq i<j \leq 3.$

Let X and Y be two random variables with the following joint distribution:

$$\begin{array}{lcc} \hline & X=0 & X=1 \\ \hline Y=0 & 0.2 & 0.0 \\ Y=1 & 0.3 & 0.5 \\ \hline \end{array}$$

(a) Find P(X = 0, Y = 1). (b) Find P(X = 0). (c) Find P(Y = 1). (d) Find P(X = 0|Y = 0).

(Some questions have more than one correct answer. Select the best answer or answers from the choices given.) Which statement does not accurately describe veins? (a) Have less elastic tissue and smooth muscle than arteries, (b) contain more fibrous tissue than arteries, (c) most veins in the extremities have valves, (d) always carry deoxygenated blood.

Prove the following statement using more than one method of proof. For every three integers a, b and c, exactly two of the integers ab, ac and bc cannot be odd.

Let $a, b, x, y \in \mathbf{R}$ and $r \in \mathbf{R}^{+}.$ Prove that if |x − a| < r/2 and |y − b| < r/2, then |(x + y) − (a + b)| < r.

A grocer wishes to mix three kinds of nuts to obtain 50 pounds of a mixture priced at $4.10 per pound. Peanuts cost$3.00 per pound, pecans cost $4.00 per pound, and cashews cost$6.00 per pound. Three-quarters of the mixture is composed of peanuts and pecans. How many pounds of each variety should the grocer use?

Use Lagrange multipliers to find the maxima and minima of the functions under the given constraints. $f(x, y)=2 x-y ; x^{2}+y^{2}=5$

We consider differential equations of the form $\frac{d \mathbf{x}}{d t}=A \mathbf{x}(t)$ where

$$A=\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right]$$

The eigenvalues of A will be real, distinct, and nonzero. Analyze the stability of the equilibrium (0, 0), and classify the equilibrium according to whether it is a sink, a source, or a saddle point.

$$A=\left[\begin{array}{ll} -4 & 2 \\ -5 & 3 \end{array}\right]$$