Identify the following term or individuals and explain their significance. John C. Calhoun

Construct a stem and leaf plot for these 50 measurements: 3.1 4.9 2.8 3.6 2.5 4.5 3.5 3.7 4.1 4.9 2.9 2.1 3.5 4.0 3.7 2.7 4.0 4.4 3.7 4.2 3.8 6.2 2.5 2.9 2.8 5.1 1.8 5.6 2.2 3.4 2.5 3.6 5.1 4.8 1.6 3.6 6.1 4.7 3.9 3.9 4.3 5.7 3.7 4.6 4.0 5.6 4.9 4.2 3.1 3.9 a. Describe the shape of the data distribution. Do you see any outliers? b. Use the stem and leaf plot to find the smallest observation. c. Find the eighth and ninth largest observation.

Estimate the limit numerically to two decimal places or state that the limit does not exist.

$$\lim _ { x \rightarrow 2 } \frac { x - 2 } { \ln ( 3 x - 5 ) }$$

A manufacturer produces three different models of a product and ships them to two warehouses. In the matrix

$$A=\begin{bmatrix} 200 & 300\\ 600& 350\\250&400 \end{bmatrix}$$

$a_{ij}$ represents the number of units of model $i$ that the manufacturer ships to warehouse $j$. The matrix

$$B = \begin{bmatrix} 12.50& 9.00&21.50 \end{bmatrix}$$

represents the prices of the three models in dollars per unit. Find the product $BA$ and state what each entry of the matrix represents.

Each of the eight possible blood types is listed in the table below along with the percent of the U.S. population having that type.

$$\begin{array}{l|l} \hline \text{ O Positive - } 39\% & \text{ A Negative - } 6\% \\ \hline \text{ A Positive - } 31\% & \text{ AB Positive - } 3\% \\ \hline \text{ B Positive - } 9\% & \text{ B Negative - } 2\% \\ \hline \text{ O Negative - } 9\% & \text{ AB Negative - } 1\% \\ \hline \end{array}$$

What is the probability a randomly selected person has a blood type that is type O or Rh-positive?

For a hydrogen atom in its ground state, calculate the relative probability of finding the electron in the area described. a. in a sphere of volume $1.0 \times 10 ^ { -3 }\ \mathrm { pm } ^ { 3 }$ centered at the nucleus b. in a sphere of volume $1.0 \times 10 ^ { - 3 }\ \mathrm { pm } ^ { 3 }$ centered on a point $1.0 \times 10 ^ { - 11 }\ \mathrm { m }$ from the nucleus c. in a sphere of volume $1.0 \times 10 ^ { - 3 }\ \mathrm { pm } ^ { 3 }$ centered on a point 53 pm from the nucleus d. in a shell between two concentric spheres, one with radius 9.95 pm and the other with radius 10.05 pm e. in a shell between two concentric spheres, one with radius 52.85 pm and one with radius 52.95 pm

Solve the initial value problem, and graph the solution function $x(t)$.

$$x ^ { \prime \prime } + 9 x = \delta ( t - 3 \pi ) + \cos 3 t ; x ( 0 ) = x ^ { \prime } ( 0 ) = 0$$

Solve the system of equations, and graph the lines.

$$\left\{\begin{aligned} 6 x - 8 y & = 15 \\ - \frac { 3 } { 2 } x + 2 y & = - 4 \end{aligned} \right.$$

Describe the data on first ladies' ages at death. Compute whatever numerical summaries you think are appropriate, and then write a narrative summary based on the computed information. Include graphical displays if appropriate.

A fair die is rolled three times and the random variable X records the number of different outcomes that result. For example, if two 5’s and one 4 are rolled, then X records two different outcomes. Determine (a) the probability distribution for X; (b) E(X); and (c) Var(X).

Use inductive reasoning to decide whether each statement is correct. Note: The numbers 1, 2, 3, 4, 5, ... are called counting numbers or natural numbers. Any counting number n divided by 2 produces a remainder of 0 or 1. If

$$n \div 21$$

has a remainder of 0, then n is an even counting number. If

$$n \div 2$$

has a remainder of 1, then n is an odd counting number. Even counting numbers: 2, 4, 6, 8, 10, ... Odd counting numbers: 1, 3, 5, 7, 9, ... The sum of any two even counting numbers is always an even counting number.

A king’s crown, presumed to be pure gold, has a mass of 1.00 kg. When submerged in water its apparent mass in measured to be 0.92 kg. What volume of water (in liters) is displaced?

Terry and Tony had 50 balloons to use for decorations. They put 30 on the tables and 4 at each end of the refreshment table. Their advisor thought they needed balloons at the entrance and brought 10 more. The expression 50 − 30 − 4 × 2 + 10 shows the number of balloons they have for the entrance. Tony thinks they will have 42 balloons for the entrance but Terry says there will only be 22. Who is correct? Explain the reasoning

(a) Describe the primary function of a flower. (b) Describe two ways in which different plants carry out this function,