If 0 $\rightarrow$ L $\rightarrow$ M $\rightarrow$ N $\rightarrow$ 0 is an exact sequence of R-modules, prove that the localization $M_{P}$ is nonzero if and only if one of the localizations $N_{P}$ and $L_{P}$ is nonzero and deduce that

$$\operatorname{Supp}(M)=\operatorname{Supp}(L) \cup \operatorname{Supp}(N).$$

In particular, if

$$M=M_{1} \oplus \cdots \oplus M_{n}$$

prove that

$$\operatorname{Supp}(M)=\operatorname{Supp}\left(M_{1}\right) \cup \cdots \cup \operatorname{Supp}\left(M_{n}\right).$$

Find the cost of renting each of these cars. Use the rate charts above and on the previous page to help you.

$$\begin{aligned} \begin{array}{lllll} \textbf{Rental} && && \textbf{Time} && \textbf{Miles}\\ \textbf{Agency} && \textbf{Size of Car} && \textbf{Rented} && \textbf{Traveled}\\ \text{Bekins} && \text{Full-size} && 3\ \text{months} && 9,254 \end{array} \end{aligned}$$

For the given exrecise, determine the domain and codomain of the transformation $T_A(\mathbf{x})=A \mathbf{x}$.

(c) $A$ has size $3 \times 3$.

Determine the constant angular velocity $\dot{\theta}$ of the vertical shaft of the amusement ride if $\phi-45^{\circ}$. Neglect the mass of the cables and the size of the passengers

A convex spherical mirror with a radius of curvature of $10.0 \mathrm{~cm}$ produces a virtual image one-third the size of the real object. Where is the object?

Explain how the width of a $95 \%$ confidence interval for a mean changes as a sample's standard deviation (s) increases, considering the sample size remains the same.

List the elements of the sample space for each of the following experiment.

“red-blue-yellow” spinner is spun once. (All sectors are equal in size and shape.)

Repeat Exercise 9.50, but assume that the sample size was $n=900$ instead of $n=100$.

Assume you have two complex numbers with directions that add to more than $360^{\circ}$. Describe the process for determining the size and direction of their output.

Explain why the neutralization reaction of a strong acid and a weak base gives a weakly acidic solution.

State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.)

a. Changing from a 90 percent confidence level to a 99 percent confidence level

b. Changing from a sample size of 30 to a sample size of 200

c. Changing from a standard deviation of 20 pounds to a standard deviation of 25 pounds

Repeat previous problem with an angle $4 \times 3-1 / 2 \times 5 / 16$ and $1 / 4\ \text{in.}$ weld size.

A real process may be nearly adiabatic if it occurs over a very short time. How does the short time span help the process to be adiabatic?

What term describes a limiting factor that affects all populations in similar ways, regardless of population size?