An open cardboard box (with no top) is to be constructed so that the width of the box is four times its length. The length of the box is labeled x in the picture. You have 100 in2 of cardboard to use. Find the length x and the height y that maximize the volume of the box.
(a.) Find a formula for the volume V in terms of x and y.
(b) Use the constraint given by the amount of cardboard available to rewrite your formula for V above in terms of a function of x alone.
(c) Find the dimensions, x and y, that result in the maximum volume.
(d) Justify that the values x and y given in (c) yield a maximum using either the First or Second Derivative Test.

In: Advanced Math
Sweet Company’s outstanding stock consists of 2,000 shares of
cumulative 4% preferred stock with a $100 par value and 12,000
shares of common stock with a $10 par value. During the first three
years of operation, the corporation declared and paid the following
total cash dividends.
| Dividends Declared & Paid | ||
| Year 1 | $ | 4,000 |
| Year 2 | $ | 8,000 |
| Year 3 | $ | 42,000 |
The total amount of dividends paid to preferred and common
shareholders over the three-year period is:
Multiple Choice
$24,000 preferred; $30,000 common.
$16,000 preferred; $38,000 common.
$8,000 preferred; $46,000 common.
$20,000 preferred; $34,000 common.
$16,000 preferred; $38,000 common.
In: Accounting
Sweet Company’s outstanding stock consists of 1,900 shares of
cumulative 5% preferred stock with a $100 par value and 10,900
shares of common stock with a $10 par value. During the first three
years of operation, the corporation declared and paid the following
total cash dividends.
| Dividends Declared & Paid | ||
| Year 1 | $ | 2,900 |
| Year 2 | $ | 6,900 |
| Year 3 | $ | 36,500 |
The total amount of dividends paid to preferred and common
shareholders over the three-year period is:
Multiple Choice
$16,400 preferred; $29,900 common.
$28,500 preferred; $17,800 common.
$21,900 preferred; $24,400 common.
$9,500 preferred; $36,800 common.
$19,000 preferred; $27,300 common.
In: Accounting
. An automobile company is ready to introduce a new line of hybrid cars through a national sales campaign. After test marketing the line in a carefully selected city, the marketing research department estimates that sales (in millions of Ghana Cedis) will increase at the monthly rate of S'(t) = 20t − 15e−0.15t 0 ≤ t ≤ 36 t months after the campaign has started. (a) What will be the total sales S(t) in t months after the beginning of the national campaign if we assume no sales at the beginning of the campaign? (b) What are the estimated total sales for the first 12 months of the campaign? (c) When will the estimated total sales reach 100 million Cedis?
In: Advanced Math
An instructor would like to know about the difference in test averages between the first and second exams of the school year. To that end, we sample 100 of each test and find Test 1 has sample average 85 and Test 2 has sample average 79. From past experience we know Test 1 grades have a standard deviation of 3 and Test 2 grades have a standard deviation for 4.If μ1 is the population mean for Test 1 and μ2 is the population mean for Test 2, find the margin of error for a 99% confidence interval for the true difference μ1-μ2. Round your answer to three decimal places.
In: Statistics and Probability
The introductory biology class at a large university is taught to hundreds of students each semester. For planning purposes, the instructor wants to find out the average amount of time that students would use to take the first quiz if they could have as long as necessary to take it. She takes a random sample of 100 students from this population and finds that their average time for taking the quiz is 20 minutes, and the standard deviation is 10 minutes.
a). Compute the standard error of the mean (SEM) for the average time to take this quiz in a minute.
b). the lower limit of 95% confidence interval for the average time to take this quiz is?
c). the upper limit of 95% confidence interval for the average time to take this quiz is?
In: Statistics and Probability
1.)An annuity pays $7800 each year. It cost $58200 today. The interest rate is 4 percent. How many years is the annuity?
2.)An annuity pays $100 each year. It is worth $507.57 today. The annual interest rate is 5 percent. How many years is the annuity?
3.)
|
Corp has a new manager. The compensation agreement calls for a single payment of $25,200,000 be paid after the first 9 years of work. Corp wants to invest an equal amount each year to pay for this future obligation. The interest rate on investment is 8 %. How much must be invested each year? |
$2,221,566.51
$1,949,396.38
$2,018,008.67
$1,954,643.20
$2,016,000.00
In: Finance
Sales on account for the first two months of the current year are budgeted as follows.
| January | $ | 374,000 |
| February | 580,000 | |
|
|
||
All sales are made on terms of 2/10, n/30 (2 percent discount if paid in 10 days, full amount by 30 days); collections on accounts receivable are typically made as follows.
| Collections within the month of sale: | ||
| Within discount period | 60 | % |
| After discount period | 15 | |
| Collections within the month following sale: | ||
| Within discount period | 15 | |
| After discount period | 7 | |
| Returns, allowances, and uncollectibles | 3 | |
| Total | 100 | % |
|
|
||
Compute the estimated cash collections on accounts receivable for the month of February.
In: Accounting
Which of the following statements below are TRUE regarding why
an LBO works conceptually?
a. By using debt, the PE firm reduces up-front cash required,
thereby boosting returns
b. Using cash flows produced by the company to pay down debt and
make interest payments produces a better return for the PE firm
than simply keeping the cash flows
c. Since the PE firm sells the entire company in the future, it's
guaranteed to at least get back 100% of its original capital
d. The PE firm sells the company in the future, which allows it to
get back (at least some of) the funds that it used to acquire the
company in the first place.
In: Finance
| The null and alternate hypotheses are: | |||||||||
| H0: μ1 ≤ μ2 | |||||||||
| H1: μ1 > μ2 | |||||||||
| A random sample of 20 items from the first population showed a mean of 100 and | |||||||||
| a standard deviation of 15. A sample of 16 items for the second population showed | |||||||||
| a mean of 94 and a standard deviation of 8. Use the .05 significant level. | |||||||||
| Assume the sample populations do not have equal standard | |||||||||
| deviations and use the .05 significance level: (a) determine the number of degrees of | |||||||||
| freedom, (b) state the decision rule, (c) compute the value of the test statistic, and (d) | |||||||||
|
state your decision about the null hypothesis. Need to show all work and formulas. Thank you |
|||||||||
In: Statistics and Probability