A certain type of stainless steel powder is supposed to have a mean particle diameter of $\mu=15 \mu \mathrm{m}.$ A random sample of 87 particles had a mean diameter of $15.2 \mu \mathrm{m},$ with a standard deviation of $1.8 \mu \mathrm{m}.$ A test is made of $H_{0}: \mu=15 \text { versus } H_{1}: \mu \neq 15.$ a. Find the P-value. b. Do you believe it is plausible that the mean diameter is $15 \mu \mathrm{m},$ or are you convinced that it differs from $15 \mu \mathrm{m} ?$ Explain your reasoning.

Find all solutions of the equation

$$y y^{\prime \prime}-2\left(y^{\prime}\right)^{2}=0$$

that pass through the point x=1, y=1.

Suppose that you are raising Mongolian gerbils. You notice that some of your gerbils have white spots, whereas others have solid coats. What type of crosses could you carry out to determine whether white spots are due to a recessive or a dominant allele?

a. List and briefly describe three major parts of the lithosphere.
b. Which layer serves as the main storehouse of chemical resources used in manufacturing consumer products ?

Evaluate (a) $\operatorname{Re}(\exp 2 i z)$, (b) $\operatorname{Im}\left(\cosh ^2 z\right)$, (c) $(-1+\sqrt{3} i)^{1 / 2}$, (d) $\left|\exp \left(i^{1 / 2}\right)\right|$, (e) $\exp \left(i^3\right)$, (f) $\operatorname{Im}\left(2^{i+3}\right)$, (g) $i^i$, (h) $\ln \left[(\sqrt{3}+i)^3\right]$.

Repeating a pair of ice tongs is shown in the figure. The ice weighs $50 \mathrm{~lb}$ and is $10 \mathrm{~in}$ wide across the tongs. The distance between the handles is $4 \mathrm{~in}$, and the mean radius $r$ of a tong is $6 \mathrm{~in}$. The rectangular cross-sectional dimensions are $0.750 \mathrm{~in}$ deep $\times 0.312 \mathrm{~in}$ wide. Determine the safety factor for the tongs if their $S_{y}=30 \mathrm{~kpsi}$.with the tongs made of Class 20 gray cast iron.

Do you think one person tan make a difference when it comes to saving earth's resources? Explain.

Predict how the relative volumes of the large intestines of herbivores and carnivores would compare, and explain your reasoning.

The equation for the reaction of iron and oxygen gas to form rust $\left(\mathrm{Fe}_2 \mathrm{O}_3\right)$ is written as

$$4 \mathrm{Fe}(s)+3 \mathrm{O}_2(g) \longrightarrow 2 \mathrm{Fe}_2 \mathrm{O}_3(s) \quad \Delta H=-1.7 \times 10^3 \mathrm{~kJ}$$

How many grams of rust form when 150 kJ are released?

Billions of neutrinos continually pass through each square centimeter of your body each second. Why don’t you notice them?

Perform the indicated operation. Simplify the answer when possible.

$$\sqrt { 2 } \cdot \sqrt { 26 }$$

Prove Formula (21) for the given linear transformations. $T_1\left(x_1, x_2\right)=\left(x_1+x_2, x_1-x_2\right)$ and $T_2\left(x_1, x_2\right)=\left(3 x_1, 2 x_1+4 x_2\right)$

Calcium sulfate, $\mathrm{CaSO}_4$, is a white, crystalline powder. Gypsum is a mineral, or natural substance, that is a hydrate of calcium sulfate. A 1.000-g sample of gypsum contains $0.791 \mathrm{~g} \mathrm{CaSO}_4$. How many moles of $\mathrm{CaSO}_4$ are there in this sample? Assuming that the rest of the sample is water, how many moles of $\mathrm{H}_2 \mathrm{O}$ are there in the sample? Show that the result is consistent with the formula $\mathrm{CaSO}_4 \cdot 2 \mathrm{H}_2 \mathrm{O}$.

For the given problem, determine the equations of the polynomials of degree two whose graphs pass through the given points.

$$(-1,-1),(0,1),(1,-3)$$

Determine the value of $y$ when $x=3.$