Students carried out a pea plant experiment, where two heterozygous individuals were crossed. The predicted Mendelian ratios for the offspring were 9 : 3 : 3 : 1 for each of the four following phenotypes: round-yellow seed, round-green seed, wrinkled-yellow seed, wrinkled-green seed. The observed results were as follows: Round-yellow seed: 441, wrinkled-yellow seed: 143, Round-green seed: 159, Wrinkled-green seed: 57 Use a separate piece of paper to complete the following: (a) State the null and alternative hypotheses (

$$H_o \text{and} H_A$$

). (b) Calculate the

$$\chi^ { 2 }$$

value. (c) Calculate the degrees of freedom and state the P value corresponding to your calculated

$$\chi^ { 2}$$

value. (d) State whether or not you reject your null hypothesis: reject

$$H_o$$

/ do not reject Ho (circle one)

On January 1 of each year, you deposit $2000 in an individual retirement account (IRA) that pays 5% annual interest. You make a total of 30 deposits. How much money do you have in your IRA immediately after you make your last deposit?

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

$$^∞∑n=1(-1)^n n/√n^3+2$$

Write a recursive rule and an explicit rule for the arithmetic sequence described by these table.

$$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Month } & n & 1 & 2 & 3 & 4 & 5 \\ \hline \text{ Total deposits (\$) } & f(n) & 84 & 100 & 116 & 132 & 148 \\ \hline \end{array}$$

Determine the present worth of 5 equal annual deposits of $1,200 at the end of years 1 through 5, followed by 4 equal annual withdrawals of$700 at the end of years 4 through 7. Note that both years 4 and 5 will have a deposit and a withdrawal. Interest is 5 percent.

A volcano erupts and spreads lava in all directions. The density of the deposits at a distance t kilometers from the center is D(t) thousand tons per square kilometer, where $D(t)=11\left(t^2+10\right)^{-2}$. Find the tonnage of lava deposited between the distances of 1 and 10 kilometers from the center.

Toilet bowl cleaners often contain hydrochloric acid to dissolve the calcium carbonate deposits that accumulate within a toilet bowl. How much calcium carbonate in grams can be dissolved by $5.8 \mathrm{~g}$ of $\mathrm{HCl}$ ? (Hint: Begin by writing a balanced equation for the reaction between hydrochloric acid and calcium carbonate.)

Valentine Investigations has the following information for its cash account:

$$\begin{array}{lr} \text{Balance, 1/31}&\$~~~~7,444\\ \text{Deposits during February}&106,780\\ \text{Checks written during February}&102,341 \end{array}$$

Valentine’s bank statement for February contained the following information:

$$\begin{array}{lrr} \text{Balance per bank, 1/31}&&\$~~~~8,910\\ \text{Add: February deposits}&&\underline{~~104,950}\\ &&\$113,860\\ \text{Less:}\\ \hspace{10pt}\text{Checks paid in February}&\$(101,400)\\ \hspace{10pt}\text{Bank service charge}&(50)\\ \hspace{10pt}\text{Debit memo (electric bill)}&\underline{~~~~~~~~~~(800)}&\underline{(102,250)}\\ \text{Cash balance, 6/30}&&\underline{\underline{\$~~~11,610}} \end{array}$$

A comparison of company records with the bank statement provided the following data:

$$\begin{array}{lrr} & \text { At 1/31 } & \text { At 2/28 } \\ \hline \text { Deposits in transit } & \$ 2,750 & \$ 4,580 \\ \text { Outstanding checks } & 4,216 & 5,157 \end{array}$$

Required:

What is the amount of cash that should be reported on the February 28 balance sheet?

You are the lender of last resort and an institution approaches you for a loan. You assess that the institution has $800 million in assets, mostly in long-term loans, and$600 million in liabilities. The institution is experiencing unusually high withdrawal rates on its demand deposits and is requesting a loan to tide it over. Would you grant the loan?

Determine whether the series is absolutely convergent, conditionally convergent, or divergent. ∑∞ n=0 (-3)^n / (2n+1)!

Find the lengths of the sides of the right triangle at the left. Show that these lengths satisfy the Pythagorean Theorem.

Find the integral by using the simplest method. Not all problems require integration by parts. $\int x e ^ { 4 x } d x$

Complete and balance the following equations:
(a) A saltlike (alkaline earth metal) hydride reacting with water,

$$\mathrm{CaH}_2(s)+\mathrm{H}_2 \mathrm{O}(l) \longrightarrow$$

Determine whether the sequence is convergent or divergent. If it is convergent, find its limit.
$a_n=(\sin n) / n$