Find the coordinates of the points one-third and two-thirds of the way from a=2 to b= 8 on a number line.

Solve the equation in two ways. Then explain which way is easier.

$$\frac{3}{4}(z-4)=6$$

Given the following information obtained from four normally distributed populations, construct an ANOVA table and perform an ANOVA test of mean differences at the 5% significance level.

$$S S T=70.47 ; \text { SSTR }=11.34 ; c=4 ; n_1=n_2=n_3=n_4=15$$

Fill in the blank so that the resulting statement is true.

We begin the process of factoring a polynomial by first factoring out the $\rule{1cm}{1pt}$ , assuming that there is one other than 1.

The sum of an infinite geometric series is twice its first term. A student says the common ratio of the series is $\frac{3}{2}.$ What is the student's error?

One cell phone plan costs $29.94 per month plus$ .10 for each text message sent. Another plan costs $32.99 per month plus$ .05 for each text message sent. State for what number of text messages the monthly bill for both plans will be the same.

Write an equation to represent the situation and then solve it to answer the equation. A situation may require more than one equation. There are two routes Jasmine can take when she bikes home from school-the long way and the short way. The long way is $1 \frac{1}{2}$ times as far as the short way. During one week, she biked a total of 30 miles from school to home. She took the short way three times. a. What is the distance of the short way? b. What is the distance of the long way?

Who was Prince Shotoku, and how did he contribute to early Japanese history?

Which statement is incorrect? Explain.

a. We need a Tukey test because ANOVA doesn’t tell which group means differ.

b. Hartley’s Fmax test is needed to determine whether the means of the groups differ.

c. ANOVA assumes equal variances in the k groups being compared.

Suppose that 1 is substituted for x in the Maclaurin series for $e^x$. The result is the series of reciprocals of factorials.

$$\sum_{n=0}^{=} \frac{1}{n !}=\frac{1}{0 !}+\frac{1}{1 !}+\frac{1}{2 !}+\frac{1}{3 !}+\frac{1}{4 !}+\frac{1}{5 !}+\frac{1}{6 !}+\cdots$$

a) Explain why it would be difficult to find an upper bound for the tail of the series using an improper integral.

b) Comparing the given series with the geometric series with first term 1 and ratio $\frac{1}{2}$ shows Given: $\quad 1+1+\frac{1}{2}+\frac{1}{6}+\frac{1}{24}+\frac{1}{120}+\frac{1}{720}+\cdots$ Geometric: $\quad 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{61}+\cdots$

From term $t_4$ on, the geometric series terms are upper bounds for the terms of the given series. To what number does the tail of the geometric series converge?

c) Find an upper bound for the remainder of the given series after $S_3$, the fourth partial sum.

d) Find an upper bound for the entire given series.

e) Explain how the reasoning in part a allows you to conclude that the given series converges.

Given the following information obtained from three normally distributed populations, construct an ANOVA table and perform an ANOVA test of mean differences at the 1% significance level.

$$S S T R=220.7 ; S S E=2252.2 ; c=3 ; n_1=n_2=n_3=8$$

Find the first four nonzero terms of the Maclaurin series of the function by multiplying or dividing the appropriate power series in the table of power series for elementary functions on the said page. Use a graphing utility to obtain a graph of the function and its corresponding polynomial approximation.

$$f(x)=\dfrac{e^x}{1+x}$$

Find the sum of the given series, or show that the series diverges (possibly to infinity or negative infinity.) $\sum_{n=1}^{\infty} \frac{3+2^{n}}{2^{n+2}}$

Give the common ratio of each geometric series and tell whether the series has a sum.

$$\frac { 9 } { 4 } + \frac { 3 } { 2 } + 1 + \cdots$$