An observed frequency distribution is as follows:

$$\begin{matrix} \text{Number of successes} & \text{0} & \text{1} & \text{2} & \text{3}\\ \text{Frequency} & \text{89} & \text{133} & \text{52} & \text{26}\\ \end{matrix}$$

Use a 0.05 significance level to test the claim that the observed frequencies fit a binomial distribution for which n=3 and p=1/3.

Determine the critical value of $\chi^2$ with 1 degree of freedom in each of the following circumstances:

$$\alpha=0.005$$

For each sentence below, underline the correct word in parentheses.

It will take a (weak, week) to get my watch repaired.

State whether each function has a maximum or minimum point.

$$y=\frac{1}{2} x^2+9$$

Solve following problem for x.

$$\log _5 x+\log _5(x+20)=3$$

Prove that a BIBD with parameters b, v, k, r, $\lambda$ has a complementary design il and only if $2 \leq k \leq v-2$

Simplify.

$$2 \log _ { 10 } 5 + \log _ { 10 } 4$$

Find the length and width of a rectangle that has the given area and a minimum perimeter.
Area: $64$ square feet

Write a conversation in which you greet your French teacher, ask how he or she is, and then introduce your best friend to him or her.

Underline the interjections in the following sentences.

Example 1. $\underline{\text{Goodness}}$! You startled me!

Oh, I think it will be fun.

Show that B={0, 1, 3, 9} is a difference set in $Z_{13}$, and use this difference set as a starter block to construct an SBIBD. Identify the parameters of the block design.

Reread all or part of the text to help you answer the following questions.

What does Antigone ask Ismene to do?

Prove that M = 0 if and only if $\operatorname{Supp}(M)=\emptyset$. [Use Proposition 47.]

Use the graph of each function to help you identify its maximum and minimum values, if they exist.

$$f(x) = -2^x$$