The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light. a) What is the radius of a black hole with a mass twice that of the Sun? b) At what radius from the center of the black hole in part (a) would the orbital speed be equal to the speed of light? c) What is the radius of a black hole with the same mass as that of the Earth?

Four of the 33 possible patterns use up the raw roll with no waste, that is, the widths add up to exactly 100 in. Find these four patterns.

A normal population has a mean of 75 and a standard deviation of 5. You choose a 40-person sample. Calculate the likelihood that the sample mean is less than 74.

Lincoln Company owns no plant assets and reported the following income statement for the current year:

$$\begin{array}{lrr} \text{ Sales} & \hspace{100pt}\\ \text{ Cost of goods sold }& \$470,000 & \$750,000\\ \text{ Wages expense }& 110,000 \\ \text{ Rent expense }& 42,000 \\ \text{ Insurance expense }& 15,000 & 637,000\\ \text{ Net income }& & \$113,000 \end{array}$$

Additional balance sheet information about the company follows:

Use the information to calculate its operating cash flow to current liabilities (OCFCL) ratio. (Assume current liabilities consist of accounts payable and wages payable.)

What is the work $W$ done by the applied force of magnitude $F$?

Mike Greenberg opened Clean Window Washing Inc. on July 1, 2014. During July, the following transactions were completed.

July 1 Issued 12,000 shares of common stock for $12,000 cash. 
     1  Purchased used truck for$8,000, paying $2,000 cash and the balance on account. 
     3 Purchased cleaning supplies for$900 on account. 
     5 Paid $1,800 cash on a 1-year insurance policy effective July 1. 
     12 Billed customers$3,700 for cleaning services. 
     18  Paid $1,000 cash on amount owed on truck and$500 on amount owed on cleaning supplies. 
     20 Paid $2,000 cash for employee salaries.
     21 Collected$1,600 cash from customers billed on July 12. 
     25 Billed customers $2,500 for cleaning services. 
     31 Paid$290 for maintenance of the truck during month. 
     31 Declared and paid $600 cash dividend. 

The chart of accounts for Clean Window Washing contains the following accounts: Cash, Accounts Receivable, Supplies, Prepaid Insurance, Equipment, Accumulated Depreciation—Equipment, Accounts Payable, Salaries and Wages Payable, Common Stock, Retained Earnings, Dividends, Income Summary, Service Revenue, Maintenance and Repairs Expense, Supplies Expense, Depreciation Expense, Insurance Expense, Salaries and Wages Expense.

Instructions

(g) Prepare the income statement and a retained earnings statement for July and a classified balance sheet at July 31.

On the basis of the following data, determine the value of the inventory at the lower of cost or market. Apply lower of cost or market to each inventory item as shown previously.

$$\begin{array}{lccc} & \textbf{Inventory} & \textbf{Unit} & \textbf{Unit}\\ \textbf{Item} & \textbf{Quantity} & \textbf{Cost Price} & \textbf{Market Price}\\ \hline \text{Widget} & 100 & \$30 & \$27\\ \text{Gidget} & \hspace{4pt}75 & \hspace{4pt}24 & \hspace{4pt}25 \end{array}$$

Why did the British initially exercise restraint in their efforts to defeat the rebellious colonies?

The masses of the person and the diving board are $54 \mathrm{~kg}$ and $36 \mathrm{~kg}$, respectively. Assume that they are in equilibrium. (a) Draw the free-body diagram of the diving board. (b) Determine the reactions at the supports $A$ and $B$.

A normal population has a mean of 75 and a standard deviation of 5. You choose a 40-person sample. Calculate the likelihood that the sample mean is between 76 and 77.

Find the magnitude of v. $\mathbf{v}=\langle-24,7\rangle$

Specify the mathematical symbol used for each of the following descriptive measures. a. Sample mean, b. Sample standard deviation, c. Population mean, d. Population standard deviation.

What happens to disaccharides and polysaccharides during digestion?

Suppose that the radius r changes by a very small amount, $\Delta r$, due to some internal cause, such as thermal expansion. Show that the fractional change in the period $\Delta T$ is given approximately by $\Delta T / T=2 \Delta r / r$.