Find the length of the line segment connecting each pair of points. a. (1, 3), (6, 3) b. (-4, 2), (1, 2) c. (7, -5), (7, -3) d. (-8, -4), (8, -4)

Prove the identity.

$$2sinθcos^3θ+2sin^3θcosθ=sin20$$

Independent random samples were selected from populations 1 and 2. The sample sizes, means and variances are as follows:

Sample size population 1: 64 Sample size population 2: 64 Sample mean population 1: 2.9 Sample mean population 2: 5.1 Sample variance population 1: 0.83 Sample variance population 2: 1.67

a. Find a 90% confidence interval for the difference in population means. What does the phrase "90% confident" mean? b. Find a 99% confidence interval for the difference in the population means. Can you conclude that there is a difference in the two population means? Explain.

A cable lowers a $1200-\mathrm{kg}$ elevator so that the elevator’s speed increases from zero to $4.0 \mathrm{m} / \mathrm{s}$ in a vertical distance of $6.0 \mathrm{m}$. What is the force that the cable exerts on the elevator while lowering it? Specify the system, its initial and final states, and any assumptions you made. Then change the system and solve the problem again. Do the answers match?

Perform the indicated operation. Write your answer in scientific notation. $\left( 8.9 \times 10 ^ { 7 } \right) \times \left( 9.8 \times 10 ^ { 10 } \right)$

Which of the following Period 4 elements has the most metallic characteristics? (1) Ca (2) Ge (3) As (4) Br

Use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods.

$$\lim _{x \rightarrow 0} \frac{\cos x-1}{x}$$

Consider a velocity field where the x and y components of velocity are given by $u = rac{cy}{x^2 + y^2}$ and $v = -rac{cx}{x^2 + y^2},$ where c is a constant. Obtain the equations of the streamlines.

Are people's feelings about attractiveness inborn or learned? Explain.

List several ions in body fluids.

Find the critical points of the following function. Assume a is a nonzero constant. $f(x)=\frac{x}{\sqrt{x-a}}$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Use your book or dictionary to define each term. Chromosome ____.

Determine the volume of one mole of an ideal gas at

$$25 ^ { \circ } \mathrm { C }$$

and 0.915 kPa.