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Question 998396: Alexander's car has a 16-gallon gas tank. Before filling his tank with gas, the gas gauge of his car indicates that g gallons of gas are in the tank. If gas costs $p per gallon and Alexander fills the tank to capacity, write an expression that represents how much Alexander paid for the gas.
Click here to see answer by Theo(13342)   |
Question 998418: A store advertises that during Labor Day sale $15 will be deducted from every purchase over $100. Furthermore, after the deduction is taken, the store offers and early-bird discount of 20% to any person who makes the purchase before 10:00 am. If Rifah makes a purchase of x dollars where x > 100, at 8 am ,what is the cost of Rifah's purchase?
Click here to see answer by addingup(3677)  |
Question 998712: a grocer wants to mix nuts which sells for Rs 14.4 per kilo which nuts selling for Rs 22.8 per kilo in order to make a mixture which would sell for Rs 19 per kilo how many kilos of Rs 14.4 per kilo nuts should be mixed with 30 kilos of Rs 22.8 per kilo nuts?
Click here to see answer by josgarithmetic(39617) |
Question 998712: a grocer wants to mix nuts which sells for Rs 14.4 per kilo which nuts selling for Rs 22.8 per kilo in order to make a mixture which would sell for Rs 19 per kilo how many kilos of Rs 14.4 per kilo nuts should be mixed with 30 kilos of Rs 22.8 per kilo nuts?
Click here to see answer by ikleyn(52781)  |
Question 760644: What is the value of a $1,000 par value bond with annual payments of an
a. 10% coupon with a maturity of 10 years and a 15% required return?
b. 8% coupon with a maturity of 10 years and a 8% required return?
c. 11% semiannual coupon with a maturity of 20 years and a 11% required return?
d. 8% semiannual coupon with a maturity of 20 years and a 9% required return?
Click here to see answer by mpare(1) |
Question 999039: Suppose that $2600 is initially invested in an account with an APR of 3.3% compounded continuously.
I created this function, I don't know if it helps:
f(t)=2600e^(.033t)
And I calculated that the annual percent change (APY) of the account is 3.36%
What is the percent change over 10 years for this account?
Please help!!!!
Click here to see answer by fractalier(6550)  |
Question 999106: You decide to work part time at a local super market. The job pays $8.00 per hour and your work 21 hours a week. Your employed withholds 10 percent of your gross pay for federal taxes,5.65 percent for FICA taxes and 3 percent for state taxes.
What percentage of your gross pay is withheld for taxes?
Click here to see answer by stanbon(75887) |
Question 999327: If you use the Mean Value Theorem with f(x) = √(x), What can you say that the expression: √(256) - √(250) equals?
NOTE: Use your answer and the fact that √(256) = 16 to answer: Is it true or false that √(256) = √(250) < 6/32?
Please explain
Thank you
Click here to see answer by ikleyn(52781) |
Question 999361: Very confused on taking antiderivatives. In my class I am not allowed to use integrals, just math logical to solve this problem: e^(x/5) + sin(3x). I know it's sort of like figuring out what the function must have been before the derivative was taken but this keeps giving me trouble. I have to reverse the derivative and get it back to its original state. sin(3x) is simple enough for it to be +sin(3x) it must be a negative cosine and something for which cancels the 3 out so 1/3 therefore, -1/3cos(3x) would be the original. But the original of e^(x/5) this one baffles me. It's really the (x/5) that I don't get. How does undoing that work exactly? what must I do/understand first before getting its antiderivative/
Thank you!
Click here to see answer by Alan3354(69443)  |
Question 999361: Very confused on taking antiderivatives. In my class I am not allowed to use integrals, just math logical to solve this problem: e^(x/5) + sin(3x). I know it's sort of like figuring out what the function must have been before the derivative was taken but this keeps giving me trouble. I have to reverse the derivative and get it back to its original state. sin(3x) is simple enough for it to be +sin(3x) it must be a negative cosine and something for which cancels the 3 out so 1/3 therefore, -1/3cos(3x) would be the original. But the original of e^(x/5) this one baffles me. It's really the (x/5) that I don't get. How does undoing that work exactly? what must I do/understand first before getting its antiderivative/
Thank you!
Click here to see answer by stanbon(75887) |
Question 999360: What is the process for finding max/min for functions?
I have this function: f(x) = 2x^3 - 3x^2 + 6. Find the max/min values of f on [-1,1]
I know that I must find all the critical points for and that is when f'=0 and the bounded pts, so, x=-1,1.
Work:
f'(x) = 6x^2 - 6x = 0
f'(x) = 6x(x-1) = 0
//6x = 0
//x=0
f'(x) = x-1 = 0
f'(x) = x = -1
Hence, x = -1,1,0,-1
So, these are all my critical values
Then I take the second derivative:
f"(x) = 12x - 6
then I plug the critical values into the second derivative, then thing that bothers me is I don't understand is why this produces a relevant result.
Work:
f"(x) = 12x - 6
f"(0) = 12(0) - 6 = -6 <0, MIN
f"(-1) = 12(-1) - 6 = -18 <0, MIN
f"(1) = 12(1) - 6 = +6 >0, MAX
At this point I hit a wall. Am I suppose to plug these output values of the 2nd derivative back into the original function. Or am I completely missing steps?
Also, another confusion I have is do the critical values represent x coordinates and the max and min represent the y coordinate and together they give (x,y)?
Thank you for any and all help!
Click here to see answer by ikleyn(52781) |
Question 999534: Case 52
Aunt Allee’s Jams and Jellies
Coauthored by
Neal Lewis
University of Bridgeport
Aunt Allee’s Jams and Jellies was founded by Allee Glover and her husband Mangrum in the kitchen of their modest farm in 1958. The original products that were produced by the company were cherry jam and cherry jelly using an old family recipe and fruit grown on the family farm. As demand grew cherries were bought from local farms (all within 50 miles of the factory).
By 2002 the business had grown to occupy a modest 20,000 square foot factory/office building on the site of the old farm. In 2002 the company was still family owned and was operated by four of the founder’s grandchildren. Hobb Glover was the company’s president. He manages the business and generally helps out in the office as needed. His sister, Alice Smith, does the marketing and selling of the product. Their cousin, Conrad Glover, is the business’s accountant and materials manager. Another cousin, Edith Woods, is the production and maintenance and engineering manager.
By 1995 demand for the cherry jam and jelly had outstripped the company’s ability to produce enough jam and jelly from fresh fruit in season. Production was converted to using concentrates and frozen cherries – but all from locally grown fruit. In 2000 the current plant was built with the idea that the company would diversify its product line by introducing two new jams, white grape and blueberry, and a new jelly, white grape, using other fruits available in the state. Test marketing had shown all three products to be popular and each could command a premium price with higher markups than the current cherry products.
The new products were introduced in late 2000 and were in full production throughout 2001. The family was pleased that the new jams and jellies performed as well as forecast. They were also pleased that the sales of the cherry jelly and jam were not depressed by the sales of the new products. Unfortunately, the financial results (Table 52-1) were disappointing since traditionally the company has achieved an average of 43% return on sales.
Table 52-1 Financial Results
Cherry Grape Blueberry
Jelly Jam Jelly Jam Jam Total
Sales $576,000 $432,000 $145,455 $72,730 $36,669 $1,262,854
Materials 230,400 172,800 43,637 21,819 12,101 480,756
Direct Labor 30,789 23,092 16,986 8,493 4,057 83,418
Overhead @ 13.6% of sales 78,522 58,892 19,829 9,915 4,998 172,120
Total Operating Income 236,288 177,216 65,004 32,503 15,513 526,560
Return on Sales 41.0% 41.0% 44.7% 44.7% 42.3% 41.7%
The factory is operating near capacity so some decisions need to be made on next year’s production. In January 2002, Hobb called a meeting with Alice, Conrad, and Edith to discuss the financial results and decide on what needed to be done.
Hobb opened the meeting with a review of the company’s current financial situation. While return on sales are only slightly lower than before plant expansion, the increased profit from the new products was being counted on to pay the loan on the new building. Hobb and Conrad do not believe that the company can afford to expand again for at least three more years.
Alice reported that she had been looking at extensions to the product line. The current products are meeting demand and she does not believe that demand will increase substantially. She has identified two additional jams which can be sold in quantities similar to blueberry and which should return similar margins. She recommends cutting back on cherry jelly production, if necessary, in order to fill all the orders she can generate for the higher margin items.
Edith reports that the new products cause several problems in production. The main problem is in the set-up of the production run. In the past, setups were relatively painless. Since both products were the same color and flavor, changing over to run a different product was just a matter of emptying and flushing the lines with water. With the current products, when flavors are changed, an extensive changeover is required. Where in the past setups took less than 30 minutes, they now take over an hour depending on the product to be produced, because some changeovers require the equipment be cleaned and sanitized between products. Before, negligible amounts of product were scrapped as a result of changing from jelly to jam. Now, about $100 of product is lost when the lines are cleaned out and production re-started. She has had to increase hours worked per day to 10 to offset the setups. Edith has so far kept the workweek to four days with no overtime but warns that the limit has been reached with the current crew size. Another shift will be necessary if demand increases.
Conrad reports similar problems in the production control and the accounts payable functions. He reminds the management team that they have had to add one person to the office to support the additional support work required by the diversification in the product line. The additional workload is being caused by more items needing to be tracked such as labels, fruit, additional ingredients, and more payments to be processed to the fruit growers and more invoices to check. While Conrad is happy with the sales and apparent markups achieve by the new products, he openly wonders if the current costing system (where overhead allocations are based on dollar sales) is misrepresenting the true costs and thus the true returns on the new items. Conrad suggests reanalyzing the costs based on activity based costing.
The management team agrees that it is difficult to make decisions if there is concern about the cost system, especially from the head of accounting,. Conrad and Edith are tasked with looking into what the five products are really costing Aunt Allee’s Jams and Jellies.
As a first step, Conrad and Edith, tabulate production requirements and production rates (see Table 52-2). Edith notes that the batch size differences were caused by the size of the different kettles used for each product. Edith also notes that the reason for the different setup times was caused by the product color . During setup, three people of the four-person crew work on setup while the fourth attends to preventive maintenance and other indirect labor activities. During processing, four members of the crew are needed.
Table 52-2 Production Data
Cherry Grape Blueberry
Jelly Jam Jelly Jam Jam
Units Produced 128,000 96,000 29,091 14,546 6,667
Price per Unit $4.50 4.50 $5.00 $5.00 $5.50
Batch size, gallons 200 200 50 50 50
Batches produced 42 32 38 19 9
Direct Material per Unit $1.80 $1.80 $1.50 $1.50 $1.82
Direct Labor Hours per 100 Units 1.92 1.92 4.67 4.67 4.87
Direct Labor Hours 2463 1847 1359 679 325
Direct Labor $ $30,789 $23,092 $16,986 $8,493 $4,057
Units per Batch @ 95% yield 3040 3040 760 760 760
Setup Time per Batch 0.5 0.5 1.5 1.5 1
Administration 1 1 1 1 1.25
As a second step, Conrad and Edith look at the overhead dollars. Conrad notes that the overhead rate was just over 11% of sales two years earlier. The overhead was broken down into five categories (see Table 52-3). The remaining expenses (the salaries of the cousins, the depreciation of the building and equipment, etc.) are considered period costs in Aunt Allee’s Jams and Jellies accounting system.
Conrad explains that the indirect labor includes all the hours of the four-person production crew not charged as direct labor. They are all paid $12.50 per hour and work 2000 hours per year. Conrad and Edith agree that the indirect labor hours of the four-person crew is either setup labor or maintenance. The indirect labor is largely driven by the hours that the machines are in use, which is equivalent to the direct labor hours.
Table 52-3 Overhead
Indirect Labor $16,582
Fringe benefits $50,000
Machine Maintenance
Cleaning & Disposables $20,000
$20,000
Energy $12,000
Indirect Materials $ 4,500
Scrap
Office Worker
Total $24,038
$25,000
$172,120
Fringe benefits are based on wages and amount to an additional 40% (insurance, FICA, benefits, etc). They can be allocated among the products based on direct labor hours.
Machine maintenance costs are directly related to machine use, which can be tracked by the number of units produced. Cleaning supplies and disposable parts are used during the setup of the processing line. Usage is reasonably proportional to the number of setups (which is equal to the number of batches produced).
Energy costs are most directly related to the number of units produced. The scrap costs are directly related to setup, and usually amounts to 5% of the value of materials.
Indirect materials are mainly shipping supplies. Their consumption is a based on orders shipped. As an order can be a mix of products and can be of varying quantities of product, Conrad does not see an easy cost driver. Since it is a relatively minor sum, he figures that sales volume is as good a method of allocation as any other.
Conrad estimates that the office workload is the same for cherry jelly, cherry jam, white grape jelly and white grape jam. The workload (parts administration) caused by blueberry jam is 1.25 time as high for any of the other products due to supplier issues. The office worker makes the same pay rate as the production workers.
Based on the above activity based costs, what margin is each product achieving? Should Aunt Allee’s Jams and Jellies expand their product line to include more low volume specialty jams and jellies?
Click here to see answer by solver91311(24713)  |
Question 999624: Hey guys I asked two question earlier. But I didn't get a response. Now I don't want to sound disrespectful because I know you all have many questions to answer but I would really appreciate it if you answered my question it is for my studies and it is very important. Thank you for understanding and please do not take this in any way offensive.
Have a wonderful day :)
Click here to see answer by fractalier(6550) |
Question 999394: Good evening
Before I ask my question I would like to know what |-x| or |x| means in math. I need to know this before I could answer any question with that symbol in it.
Mow here is my real question:
solve
|x - 4| = 2
I know this has nothing to do with math but I would like to know how to ask a question directly from this site.
I normally would have to go to google first and type in "how to ask a question on algebra.com" then click on ask a question on algebra.com but I would like to be able to this directly from the site. Thank you for your help.
Click here to see answer by Fombitz(32388)  |
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