The Shroud of Turin is a religious artifact, claimed by some to be the burial cloth of Jesus of Nazareth. The first historical references to the Turin Shroud date from the mid-1300s AD. A team of scientists was permitted to use Carbon-14 dating to estimate the date of the creation of the Turin Shroud in 1988 AD. Analyses found that the amount of Carbon-14 in the shroud was 91.88% of what would be found in a living flax plant, the plant used to make the linen for the Turin Shroud. Carbon-14 is only absorbed while a plant is living, so the linen in the Turin Shroud had 100% of its Carbon-14 at the time the shroud was made. The half-life of Carbon-14 is 5730 years.
(a)Find a model R(t) for the proportion of Carbon-14 remaining in the Turin Shroud as a function of time t in years since the Turin Shroud was created.
(b) (10 points) If the Turin Shroud dated from 33 AD1, what proportion of the initial Carbon-14 would the shroud still have in 1988 AD? You do not need to simplify your answer.
(c) (10 points) Determine an estimate for the year the Turin Shroud was created using the proportion of Carbon-14 remaining in 1988 AD. Simplify your answer and give the year in terms of the Gregorian calendar, e.g. AD or BC. 1The accepted date for the death of Jesus of Nazareth.
In: Math
1a. How has Sarbanes-Oxley of 2002 affected FASB’s jurisdiction and independence?
1b. Is it possible that the rules of internal controls in Sarbanes-Oxley of 2002 are making firms excessively risk-averse? If so, how?
In: Math
The goal is to evaluate three classifiers intending to identify gender (male/female) given the height and weight. The evaluation is to be based on the following dataset:
| Gender | Height (cm) | Weight (kg) |
| Male | 148 | 60 |
| Male | 149 | 66 |
| Female | 150 | 60 |
| Male | 151 | 62 |
| Male | 161 | 72 |
The three classifiers to be evaluated
are:
C1: Anyone with height over 150cm is male; all others are
female
C2: Everyone is male
C3: Classify using a 1-nearest neighbor classifier trained on the
following dataset:
| Male | 149 | 61 |
| Female | 149 | 61 |
| Male | 153 | 70 |
Calculate the following metrics for the
classifiers:
-Accuracy
-Error rate
-Precision of identifying males
-Recall of identifying males
-F1-score of identifying males
Complete the following table with your answers.
| Accuracy | Error Rate | Precision | Recall | F1-Score | |
| C1 | |||||
| C2 | |||||
| C3 |
In: Math
The U-Drive Rent-A-Truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25 comma 000, each small truck $30 comma 000, and each large truck $40 comma 000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy? They can buy nothing vans, nothing small trucks, and nothing large trucks.
Can you demonstrate the Guass Jordan method for solving this?
In: Math
The Candy Town Company, a competitor of the SweetTooth Candy Company, knows it will need 40,000 lbs of sugar six months from now to implement its production plans. James Taffy, Candy Town's purchasing manager, has essentially two options for acquiring the needed sugar. One option is to buy the sugar at the going market price when they need it, six months from now. Mr. Taffy has assessed the probability distribution for the possible prices of sugar six months from now (in dollars per pound) as shown below:
Price in 6-month Probability
$0.078
0.10
0.086 0.20
0.094 0.20
0.102 0.20
0.110 0.20
0.118 0.10
The second purchasing option is to buy a futures contract now. The contract guarantees delivery of the sugar in six months but the cost of purchasing it will be based on today's market price. Assume that possible sugar futures contracts available for purchase are for 10,000 lbs, 20,000 lbs or 40,000 lbs only. No futures contracts can be purchased or sold in the intervening months. The Candy Town Company will buy the total of 40,000 lbs of sugar in one way or another. The price of sugar now is $0.0851 per pound. The transaction costs for 10,000 lbs, 20,000 lbs and 40,000 lbs futures contracts are $150, $200, and $350, respectively.
(You may choose one answer more than once.)
Question 1 options:
|
|
In: Math
You begin saving for retirement at age 25, and you plan to retire at age 60. You want to deposit a certain amount each month into an account that pays an APR of 3% compounded monthly. Make a table that shows the amount you must deposit each month in terms of the nest egg you desire to have when you retire. (Round your answers to the nearest cent.)
| Nest egg size | Needed deposit |
|---|---|
| $100,000 | $ |
| $200,000 | $ |
| $300,000 | $ |
| $400,000 | $ |
| $500,000 | $ |
| $600,000 | $ |
| $700,000 | $ |
| $800,000 | $ |
| $900,000 | $ |
| $1,000,000 | $ |
In: Math
A normal distribution has a mean of 15 and a standard deviation of 4 . Use the? 68-95-99.7 rule to find the percentage of values in the distribution between 15 and 23 .
In: Math
45. If the area model for a triangle is A = 1/2 bh, find the area of a triangle with a height of 16 in. and a base of 11 in.? the answer should be A=88 in.squier
43. Using the formula in the previous exercise, find the distance that Susan travels if she is moving at a rate of 60 mi/h for 6.75 h.? the answer should be 405 mi
47. Use the formula from the previous question to find the height to the nearest tenth of a triangle with a base of 15 and an area of 215.? the answer should be 28.7
53. The formula for the circumference of a circle is C = 2πr. Find the circumference of a circle with a diameter of 12 in. (diameter = 2r). Use the symbol π in your final answer.? the answer should be C=12π
In: Math
find the difference between the sum of the first 900 multiples of three and the sum pf the first 900 multiples of four
In: Math
Find a matrix P that diagonalizes the matrix A = [ 2 0 ?2 / 0 3 0 / 0 0 3 ] and compute P ?1AP.
In: Math
Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two? blends, robust and mild. A pound of the robust blend requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans. A pound of the mild blend requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans. Coffee is shipped in 138pound burlap bags. The company has 65 bags of Colombian beans and 30 bags of Brazilian beans on hand. How many pounds of each blend should they produce in order to use all the available? beans?
|
Robustequals= |
nothing lbs |
|
Mildequals= |
nothing lbs |
In: Math
1. A living room is 15 ft x 19 ft. The walls of the room are 8.5 ft tall.
Calculate the total area of the West wall?
How many rolls of wallpaper will you need to cover the wall. One roll will cover 44 square feet
What will be the cost of the wallpaper? ($14.99 for a pack of 2 rolls)
2. Calculate the following for the remaining walls
Calculate the total area of the North Wall. (Note: You are not painting the Kitchen door.) Kitchen door is 3.5 ft wide by 7 ft tall
Calculate the total area of the East Wall.
Calculate the total area of the South Wall. (Note: You are not painting the Front Door or the Window.) Front door is 3.5 ft wide by 7 ft tall and the window is 8 ft by 4 ft tall
Calculate the total area of the North, East, and South Walls combined.
How many cans of paint do you need? Why? (Remember, you are doing a double coating.) one can of paint will cover 400 square feet and is $17.99 per can
Calculate the total cost of paint.
3.When looking at your dingy carpet, you noticed the dirt trail leading from the Front Door to the Kitchen Door. In order to negate this problem you decided to create a 4 ft laminate tile walkway from the Front Door to the Kitchen Door. Then the rest of the room would be re-carpeted.
Calculate the following for the new walkway.
What are the dimensions of the new walkway?
Calculate the total area of the new walkway.
Calculate how many boxes of laminate tiles you need. Laminate tiles one box will cover 12 square feet and is $24.99 per sq yd
Calculate the total cost of creating the new walkway.
4. Calculate the following for the recarpeted area.
What is the dimension of the area that will be recarpeted?
Calculate the total area that will be recarpeted in sq ft.
Calculate the total area that will be recarpeted in sq yd.
Calculate the total cost of the recarpeted area.Carpet is sold by the square yard and is $29.99 per sq yd
4. Calculate the total cost of the recarpeted floor and making a new walkway.
5.Next, it is time to fix the ceiling. After all the other work you have done, you decided it was best to keep the ceiling uniform with a single type of tile.
Calculate the total area of the ceiling.
Calculate the total amount of boxes of ceiling tiles you need. One box of tile will cover 20 square ft and it is $19.99 per box
Calculate the total cost of the ceiling tiles.
6. Finally, you are finished! All that is left is to calculate how much money you spent on your wonderful renovations.
What was the total cost of fixing the entire living room? Give an itemized list.
In: Math
How many methods are there for solving quadratic equations? And which is a preferred method?
In: Math
the number of bacteria in millions in a petri dish t seconds after an antibiotic is added is given by the function b(t) Assume b(t) is an exponential function first point (1,12) second point (2,2) What is the 1 unit growth factor? what is the 1 unit percent change? How many bacteria in millions are there in the petri dish at the moment the antibiotic is added? Find the function of B(t) How long does it take the number of bacteria to decrease by 50%? include units
In: Math