Suppose that the mass on the frictionless tabletop has the value $m_1=2.45 \mathrm{~kg}$. Calculate the ratio $T / m_2 g$ and show that it is less than 1 , as expected.

Prove or disprove. Every even integer can be expressed as the sum of two even integers.

Express the required calculation in terms of

$$\pi$$

and then round to the nearest tenth. A circular rug is 6 feet in diameter. How many feet of fringe is required to edge this rug?

Complete the indirect proof of the conjecture: In a triangle the side opposite the larger of two angles has a greater measure.

Given: $\triangle A B C$ with $m \angle A>m \angle B$

Show: BC>AC

Proof: Assume $\underline{\qquad \qquad \qquad}$

Case 1: BC=AC

If BC=AC then $\triangle A B C$ is $\underline{\qquad \qquad \qquad}$ by $\underline{\qquad \qquad \qquad}$. By $\underline{\qquad \qquad \qquad}$, $\angle A \cong \angle B$, which contradicts $\underline{\qquad \qquad \qquad}$. So, $BC \neq A C$.

Case 2: BC<AC

If BC<AC, then it is possible to construct point $D$ on $\overline{C A}$ such that $\overline{C D} \equiv \overline{C B}$, by the Segment Duplication Postulate. Construct $\overline{D B}$, by the Line Postulate. $\triangle D B C$ is $\underline{\qquad \qquad \qquad}$. Complete the proof.

Rate of Change In Exercises , you are given the dollar value of a product in 1998 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value $V$ of the product in terms of the year $t$. (Let $t=8$ represent 1998. )

$\$ 2540$ $\$ 125$ increase per year

A two-stage RC circuit provides a phase shift lead of $120^{\circ}$. What is the ratio of the output-voltage amplitude to that of the input?

The following table gives data on variables $y, x_1$, and $x_2$ -

$$\begin{array}{lcc} \hline y & x_1 & x_2 \\ \hline 24 & 98 & 52 \\ 14 & 51 & 69 \\ 18 & 74 & 63 \\ 31 & 108 & 35 \\ 10 & 33 & 88 \\ 29 & 119 & 54 \\ 26 & 99 & 51 \\ 33 & 141 & 31 \\ 13 & 47 & 67 \\ 27 & 103 & 41 \\ 26 & 111 & 46 \\ \hline \end{array}$$

Using MINITAB, Identify the $y$ regression on the $x 1$ and $x 2$. Answer the following questions utilizing the provided solution. a. Write the estimated regression equation. b. Describe the significance of the computed independent variable regression coefficients. c. What are the numbers for the coefficient of multiple determination, the modified coefficient of multiple determination, and the standard deviation of errors? d. What is the expected value of $y$ for the given values of $y$ for $x 1=87$ and $x 2=54$ ? e. Given that $x 1=95$ and $x 2=49$, what is the point estimate of the expected (mean) value of $y$ for all elements? f. Construct a $99 \%$ confidence interval for the coefficient of $x_1$. g. Using the $1 \%$ significance level, test if the coefficient of $x_2$ in the population regression model is negative.

A shipping company handles containers in three different sizes: (1) $27 \mathrm{ft}^3(3 \times 3 \times 3)$, (2) $125 \mathrm{ft}^3$, and (3) $512 \mathrm{ft}^3$. Let $X_i(i=1,2,3)$ denote the number of type $i$ containers shipped during a given week. With $\mu_i=E\left(X_i\right)$ and $\sigma_i^2=V\left(X_i\right)$, suppose that the mean values and standard deviations are as follows:

$$\begin{aligned} & \mu_1=200 \quad \mu_2=250 \quad \mu_3=100 \\ & \sigma_1=10 \quad \sigma_2=12 \quad \sigma_3=8 \\ & \end{aligned}$$

a. Assuming that $X_1, X_2, X_3$ are independent, calculate the expected value and variance of the total volume shipped. b. Would your calculations necessarily be correct if the $X_i$ 's were not independent? Explain. c. Suppose that the $X_i$ 's are independent with each one having a normal distribution. What is the probability that the total volume shipped is at most $100,000 {ft}^3$ ?

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. $g(x)=f\left(\frac{1}{3} x\right)$

The perimeter of a rectangle is 40 cm. If the length was doubled and the width halved, the perimeter would be increased by 16 cm. Find the dimensions of the original rectangle

Church Company completes the following transactions during March, its first month of operations (termsfor all its credit sales are 2/10, n/30).

Mar. 2 Sold merchandise on credit to Min Cho, Invoice No. 854. for $16,800 plus sales tax of$1,176.
     3 Sold merchandise on credit to Linda Witt, Invoice No. 855, for $10,200 plus sales tax of$714.
    10 Sold merchandise on credit to Jovita Albany, Invoice No. 856, for $5,600 plus sales tax of$392.
    27 Sold merchandise on credit to Jovita Albany, Invoice No. 857, for $14,910 plus sales tax of$1,044.
    28 Sold merchandise on credit to Linda Witt, Invoice No. 858. for $4,315 plus sales tax of$302.

Required

1. Open the following general ledger accounts: Accounts Receivable (#106), Sales (#400), and SalesTax Payable (#205). Open the following accounts receivable subsidiary ledger accounts: JovitaAlbany, Min Cho, and Linda Witt.

2. Enter the transactions in a sales journal like Exhibit 11.6. Number all journal pages as page 2.

3. Post all transactions to the accounts receivable subsidiary ledger and its month-end totals to the general ledger.

4. Prove the accuracy of the subsidiary ledger by preparing a schedule of accounts receivable as of March 31.

What is the edge length (in cm) of a titanium cube that contains $2.55 \times 10^{24}$ titanium atoms? The density of titanium is 4.50 $g/cm^3$.

Write in the blank the tense of the italicized verb or verb phrase. Write past for past, past prog. for past progressive, past perf. for past perfect, pres. for present, pres. prog. for present progressive, and pres. perf. for present perfect.

I am taking out the garbage right now.

Graph the function. Compare to the parent graph. State the domain and range.

$$y = -\frac{1}{2} \sqrt x$$