Find the exact interest, to the nearest cent. $(P=$ principal, $R=$ rate, $T=$ time $)$

$$\begin{array}{lllllllll} \boldsymbol{P} & \boldsymbol{R} & \boldsymbol{T} & \text { Interest }\\ \$ 22,500 & 9 \% & 90\ \text{days} \end{array}$$

Draw two vector field diagrams, one for a particle carrying charge +q and located at the origin of a rectangular coordinate system and one for a particle carrying charge -2q and located at the origin. Describe the principal differences between the two diagrams.

Vasectomy is a procedure for birth control in which the principal ducts carrying sperm out of the testes are tied off. Basing your answer on the cellular structure of the human testis, explain why a man’s testosterone level is not affected by vasectomy.

Which gases are the principal contributors to the natural greenhouse effect? (a) carbon dioxide, methane, water vapour (b) carbon dioxide, methane, oxygen (c) carbon dioxide, water vapour, oxygen (d) argon, carbon dioxide, methane

Let $X=\operatorname{Spec} R$ and let $X_{f}$ be the principal open set corresponding to f $\in$ R. Prove that $X_{f} \cap X_{g}=X_{f g}$. Prove that $X_{f}=X$ if and only if f is a unit in R, and that $X_{f}=\emptyset$ if and only if f is nilpotent.

The future value of a simple interest investment is given by S=P(1+r t). What principal P must be invested for t=5 years at the simple interest rate r=10% so that the future value grows to $9000?

If $X_{f}$ and $X_{g}$ are principal open sets in X = Spec R, prove that the open set $X_{f} \cup X_{g}$ is the complement of the closed set $\mathcal{Z}(I)$ where I = (f, g) is the ideal in R generated by f and g.

Find the interest in each exercise below. $(P=$ principal, $R=$ rate, $T=$ time $)$

$$\begin{array}{lllllllll} \boldsymbol{P} & \boldsymbol{R} & \boldsymbol{T} & \text { Interest }\\ \$ 6,270 & 6.5 \% & 5\ \mathrm{yr} \end{array}$$

Find the interest in each exercise below. $(P=$ principal, $R=$ rate, $T=$ time $)$

$$\begin{array}{lllllllll} \boldsymbol{P} & \boldsymbol{R} & \boldsymbol{T} & \text { Interest }\\ \$ 4,250 & 7.5 \% & 6\ \mathrm{mo}\end{array}$$

Find the interest in each exercise below. $(P=$ principal, $R=$ rate, $T=$ time $)$

$$\begin{array}{lllllllll} \boldsymbol{P} & \boldsymbol{R} & \boldsymbol{T} & \text { Interest }\\ \$ 3,000 & 13 \% & 3\ \mathrm{yr} \end{array}$$

The scatterplot shows the batting average (BA) during April and the batting average during May-September for 66 Major League Baseball players who played regularly throughout the 2010 season. Also included on the scatterplot are the line $y=x$ and a vertical line showing the average batting average in April 2010.

a) Of the 36 hitters who were better than average in April, what percentage of these players had worse PERFORMANCES in May-September?

b) Of the 30 hitters who were worse than average in April, what percentage of these players had better PERFORMANCES in May-September?

c) Explain how your answers to parts (a) and (b) illustrate regression to the mean.

Find the unit tangent and principal unit normal vectors at the given points. $\mathbf{r}(t)=\langle\cos 2 t, t, \sin 2 t\rangle$ at t=0, $t=\frac{\pi}{2}$

Solve each problem The amount of simple interest on a deposit varies jointly with the principal and the time in days. If $\$ 20.80$ is earned on a deposit of $\$ 4000$ for $16$ days, how much interest world be earned on a deposit of $\$ 6500$ for $24$ days?

The 2-in.-diameter drive shaft AB on the helicopter is subjected to an axial tension of 10 000 lb and a torque of 300 lb · ft. Determine the principal stresses and the maximum in-plane shear stress that act at a point on the surface of the shaft.