The total cost of roasting 110 lb of coffee is $765.
How to solve Cost Function?Based on the given function, the marginal cost of roasting x pounds of coffee is:
C'(x) = -0.018x + 4.75 for x ≤ 200.
To find the total cost of roasting 110 lb of coffee, we need to integrate the marginal cost function to get the total cost function C(x), and then evaluate C(110).
However, since we are disregarding any fixed costs, we can assume that the total cost function is simply the integral of the marginal cost function.
Integrating C'(x) = -0.018x + 4.75 with respect to x, we get:
C(x) = -0.009x² + 4.75x + C
where C is the constant of integration. Since we are disregarding any fixed costs, we can assume that C = 0.
Therefore, the total cost of roasting 110 lb of coffee is:
C(110) = -0.009(110)² + 4.75(110) = 765
The total cost of roasting 110 lb of coffee is $765.
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Final answer:
To find the total cost of roasting 110 lb of coffee, integrate the marginal cost function C'(x) = -0.018x + 4.75 over the range of x values. Substitute 110 for x in the total cost function to find the total cost.
Explanation:
To find the total cost of roasting 110 lb of coffee, we need to integrate the marginal cost function over the desired range of x values. The marginal cost function is given by C'(x) = -0.018x + 4.75. Integrating this function will give us the total cost function C(x).
Integrating C'(x) gives C(x) = -0.009x^2 + 4.75x + C, where C is the constant of integration. Since we are disregarding any fixed costs, we can ignore the constant term C.
Now we can substitute 110 for x in the total cost function to find the total cost of roasting 110 lb of coffee: C(110) = -0.009(110)^2 + 4.75(110) = -108.9 + 522.5 = $413.6.
If Lenox has 40 shirts
If 10 cars are sold to a rental company, what is the probability that at most 3 cars have at least one surface flaw?
Given a Poisson distribution with 0.05 flaws/sq ft and 10 sq ft panels, each car has a 60.65% chance of no flaws.
The probability of at least 1 car with flaws is 99.35%.
Considering only 1 car with flaws, the final probability of at most 1 car with flaws is 90.2%.
Probability of at most 1 car with flaws: 90.2%
Here's how to calculate the probability that at most 1 car out of 10 has any surface flaws, given the Poisson distribution parameters:
1. Define parameters:
Mean flaws per square foot (λ) = 0.05
Area of plastic panel per car (A) = 10 square feet
Number of cars (N) = 10
2. Calculate probability of no flaws:
Probability of no flaws in one car (P(X=0)) = e^(-λA) = e^(-0.0510) ≈ 0.6065
3. Calculate probability of 1 car with flaws (complementary probability):
Probability of at least 1 car with flaws (1 - P(no flaws in all cars))
P(X ≥ 1) = 1 - (P(X=0))^N = 1 - (0.6065)^10 ≈ 0.9935
Probability of exactly 1 car with flaws (P(X=1)) = N * P(X=0) * (1-P(X=0))^N-1
≈ 10 * 0.6065 * (1 - 0.6065)^9 ≈ 0.3869
4. Final probability:
Probability of at most 1 car with flaws (P(X ≤ 1)) = P(X=0) + P(X=1) ≈ 0.6065 + 0.3869 ≈ 0.9934
The probability that at most 1 car out of 10 has any surface flaws is approximately 90.2%.
Therefore, Given a Poisson distribution with 0.05 flaws/sq ft and 10 sq ft panels, each car has a 60.65% chance of no flaws.
The probability of at least 1 car with flaws is 99.35%.
Considering only 1 car with flaws, the final probability of at most 1 car with flaws is 90.2%.
The probable question may be: The number of surface flaws in plastic panels used in the interior of automobile has a Poisson distribution with a man of 0.05 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel. If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?
a. The probability of no surface flaws in an auto's interior is approximately 0.7408.
b. The probability of none of the 10 cars having any surface flaws is approximately 0.0498.
c. The probability of at most 1 car having any surface flaws is approximately 0.9631.
a. Probability of no surface flaws:
Calculate the lambda parameter: The lambda parameter for the Poisson distribution represents the expected number of flaws, which is calculated as the mean flaws per square foot multiplied by the total area.
In this case, [tex]\lambda[/tex] = 0.03 flaws/sq ft * 10 sq ft = 0.3 flaws.
Use the Poisson probability formula: The probability of no flaws (x = 0) in a Poisson distribution is given by [tex]e^{(-\lambda)[/tex].
Plugging in lambda = 0.3, we get
P(x = 0) = [tex]e^{(-0.3)[/tex] ≈ 0.7408.
b. Probability of none of the 10 cars having flaws:
Treat each car as an independent event: Since the flaws are random and independent for each car, we can treat each car as a separate event with the same probability of no flaws (0.7408) calculated in part (a).
Calculate the combined probability: To get the probability of none of the 10 cars having flaws, we simply multiply the individual probabilities.
P(no flaws in all 10 cars) = [tex](0.7408)^{10[/tex] ≈ 0.0498.
c. Probability of at most 1 car having flaws:
Calculate probabilities for 0 and 1 flaws: We need the probabilities of 0 flaws (already calculated in part (a)) and 1 flaw (x = 1) to determine the probability of at most 1 flaw.
Probability of 1 flaw: Using the Poisson formula again,
P(x = 1) = [tex]\lambda[/tex] * [tex]e^{(-\lambda)[/tex] = 0.3 * [tex]e^{(-0.3)[/tex] ≈ 0.2222.
Probability of at most 1 flaw: This includes both scenarios with 0 and 1 flaws. P(at most 1 flaw) = P(0 flaws) + P(1 flaw) = 0.7408 + 0.2222 ≈ 0.9631.
Question:-
The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.03 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.
a. What is the probability that there are no surface flaws in an auto's interior?
b. If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?
c. If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws? Round your answers to four decimal places (e.g. 98.7654).
A machine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. The height of the pile is always twice the length of the base diameter.After 5 minutes, how fast is the area of the base increasing?
write 26/20 as a percent
Two dice are rolled one after another. Construct a sample space and determine the probability that the sum of the dots on the dice total a number greater than 4 if the second die is a 3.
Final answer:
To find the probability of the sum of two dice being greater than 4 given the second die is a 3, first identify the sample space for the first die as {1, 2, 3, 4, 5, 6}. Then, calculate the favorable outcomes where the first die, added to 3, results in a number greater than 4, which are {2, 3, 4, 5, 6}. The probability is 5/6, rounded to approximately 0.8333.
Explanation:
Sample Space and Probability Calculation
When two dice are rolled one after another, and the second die results in a 3, we consider the outcomes of the first die only. As the first die is also a fair, six-sided die with faces numbered from 1 to 6, the sample space for the first die is S = {1, 2, 3, 4, 5, 6}.
The question asks for the probability of the sum being greater than 4 given that the second die is a 3. This means we are looking for the sum to be 5 or more. We can calculate the possible outcomes where the first die, when added to 3, results in a total greater than 4.
If the first die shows 1, the sum is 4 (not greater than 4).If the first die shows 2, the sum is 5 (which is greater than 4).If the first die shows 3, 4, 5, or 6, the sum is 6, 7, 8, or 9, respectively (all greater than 4).Therefore, the outcomes in the sample space that result in a sum greater than 4 are {2, 3, 4, 5, 6}. The probability of this event, given the second die is a 3, is the number of favorable outcomes divided by the total number of possible outcomes of the first die. There are 5 favorable outcomes and 6 possible outcomes, so the probability is 5/6 or approximately 0.8333 when rounded to four decimal places.
To construct the sample space, we need to consider all possible outcomes of rolling two dice. The probability of the sum of the dots on the dice being greater than 4 given that the second die is a 3 is 5/36.
Explanation:To construct the sample space, we need to consider all possible outcomes of rolling two dice. Since each die has six sides numbered 1 to 6, the sample space will consist of 36 outcomes. We can represent the outcomes as pairs of numbers, where the first number represents the result of the first die and the second number represents the result of the second die. For example, (1, 1) represents both dice landing on 1, (1, 2) represents the first die landing on 1 and the second die landing on 2, and so on.
To determine the probability of the sum of the dots on the dice being greater than 4 given that the second die is a 3, we need to identify the outcomes where the second die is 3 and the sum is greater than 4. These outcomes are (2, 3), (3, 3), (4, 3), (5, 3), and (6, 3). There are a total of 5 outcomes that satisfy these conditions. Since the sample space has 36 outcomes, the probability is 5/36. To find the probability that the sum of the dots on two dice is greater than 4 given the second die is a 3, we list the possible outcomes for the first die as {1, 2, 3, 4, 5, 6}. The favorable outcomes are those that, when added to 3, result in a number greater than 4: {2, 3, 4, 5, 6}. This results in a probability of 5/6.
Please help ASAP
Find how long it take $600 to double if it is invested at 7% interest compounded monthly.
The mathematics department of a college has 12 male professors, 7female professors, 13 male teaching assistants, and 12 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male.
[8 3 2]
What are the dimensions of the matrix?
____ * ____ * = multiplication
Answr if only know with solution..or no brainliest answer to u
Walt's monthly salary is $6,962.What would be his equivalent semimonthly salary?
An furniture salesperson sells a couch for $1,560. She receives a 2.75% commission on the sale of the couch.
How much did she earn on the sale?
Round your answer to the nearest cent.
Answer: Amount she earn on the sale is $42.9.
Step-by-step explanation:
Since we have given that
A furniture salesperson sells a couch for $1560.
Percentage of commission she receive on the sale of the couch = 2.75%
So, Amount she earn on the sale is given by
[tex]2.75\%\ of\ 1560\\\\=\frac{2.75}{100}\times 1560\\\\=0.0275\times 1560\\\\=\$42.9[/tex]
Hence, amount she earn on the sale is $42.9.
if a person puts 1 cent in a piggy bank in the first day, 2 cents on the second day, 3 cents on the third day, and so on, how much money will be in the bank after 50 days?
How do I solve this problem 16x^2 + 1 =8x Using this quadractic x=-b+ square root b-4ac /2a
show work so I can better see
Ariadne shadow is 15 feet long and Dixons shadow is 18feet long. If Ariadne is 5 feet tall how tall is dixon?
Using the concept of similar triangles, we found that Dixon's height is 6 feet, assuming that the light source causing the shadows is consistent.
Explanation:This question is about the concept of similar triangles in Mathematics. If Ariadne's shadow is 15 feet long and she is 5 feet tall, it means the ratio of her height to her shadow length is 5:15 or 1:3. If Dixon's shadow is 18 feet long, and we assume the light source creating the shadows is the same, then the same ratio can apply to him, since their shadows will be proportional to their heights. Therefore, if the ratio of Ariadne's height to her shadow length is equal to the ratio of Dixon's height to his shadow length, we can form the following equation and solve for Dixon's height: 5/15 = x/18 where 'x' is Dixon's height. Solving this equation, we find that Dixon's height is 6 feet.
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Please help with accounting. Use the following information to complete the partial worksheet for Bill’s Company. Record the appropriate adjusting entries using the data below and extend the balances over to the adjusted trial balance columns. Merchandise inventory—ending $10 Store supplies on hand 3 Depreciation on store equipment 2 Accrued salaries 1
To complete the partial worksheet for Bill's Company, you need to record the appropriate adjusting entries using the given data. Once the adjustments are recorded, you can transfer the balances to the adjusted trial balance column.
Explanation:To complete the partial worksheet for Bill's Company, we need to record the appropriate adjusting entries using the given data. Let's go step by step:
Record the ending merchandise inventory of $10 in the Adjustments column as a debit to the Merchandise Inventory account and a credit to the Adjustments account.Record the store supplies on hand of $3 in the Adjustments column as a debit to the Store Supplies account and a credit to the Adjustments account.Record the depreciation on store equipment of $2 in the Adjustments column as a debit to the Depreciation Expense account and a credit to the Accumulated Depreciation account.Record the accrued salaries of $1 in the Adjustments column as a debit to the Salaries Expense account and a credit to the Salaries Payable account.Transfer the balances from the Adjustments column to the Adjusted Trial Balance column.Once you complete these steps, you will have the adjusted trial balance with the appropriate balances extended from the adjustments.
Caleb works on commission as a car salesman. Today he sold a car that cost $12,000 and received a $240 commission. What percent of his sale is Caleb's commission?
write the complex number -12+16i in trigonometric form r(cos theta+i sin theta), with theta in the interval
Ava's game piece is on 36. She wants to capture a chip that is on 72. Can she do it with these change cards?if so, how? If not,explain why not. -10 +30 -1 +1-2
Final answer:
Ava can capture the chip on square 72 by using the +30 change card once to reach 66, and then the +1 change card six times to reach the final value of 72.
Explanation:
Ava's game piece is on square number 36, and she wants to capture a chip on square number 72. By using the change cards, Ava needs to adjust her position from 36 to 72 with the change cards provided. The change cards are: -10, +30, -1, +1, and -2. To determine if Ava can capture the chip, we need to see if we can use the cards to add up to a net change of +36 (since 72 - 36 = 36).
By analyzing the cards, we can use the +30 card once, which would take Ava's position from 36 to 66. Next, she can use the +1 card six times to go from 66 to 72. Ava does not need to utilize the -10, -1, or -2 cards as they would move her backwards. Therefore, Ava can indeed capture the chip using the change cards provided.
The steps Ava should follow are:
Use the +1 card six times to move from 66 to 72.
17 is what percent of 340
Answer:
5%
Step-by-step explanation:
to work out what percent 17 is out of 340 we can formulate an equation
so 340(x%)=17
when we solve for x we get 5
find tan x/2, given that tan x=3 and x terminates in pi < x < ((3)pi/2)
To find tan x/2, given that tan x=3 and x terminates in π < x < (3π/2), we can use the half-angle formula for tangent. The value of tan (x/2) is ±1/√2.
Explanation:To find tan x/2, given that tan x=3 and x terminates in π < x < (3π/2), we can use the half-angle formula for tangent. The half-angle formula for tangent is tan(x/2) = ±√((1-cosx) / (1+cosx)). Since tan x=3, we need to find the value of cos x first.
Given that tan x = 3, we can use the fact that tan x = sin x / cos x to find the value of cos x. Rearranging the equation, we have cos x = sin x / tan x = 1 / 3. Now, we can substitute this value of cos x into the half-angle formula to find tan (x/2).
tan (x/2) = ±√((1-cos x) / (1+cos x))
tan (x/2) = ±√((1-1/3) / (1+1/3))
tan (x/2) = ±√((2/3) / (4/3))
tan (x/2) = ±√(2/4)
tan (x/2) = ±√(1/2)
tan (x/2) = ±1/√2
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Without random assignment, which of the following can happen?
1.
Naturally occurring confounding variables can result in an apparent relationship between the explanatory and response variables.
2.
The results may not be able to be extended to a larger population.
3.
Many people in the study will drop out because they aren’t happy with the treatment they were assigned to. This will cause bias in the results.
4.
None of the above
All tickets for a concert are the same price. the ticket agency adds a fixed fee to every order. a person who orders 5 tickets pays $93. a person who orders 3 tickets pays $57. write an equation relating the total cost to the number of tickets purchased
To write an equation relating the total cost to the number of tickets purchased with a fixed fee, set up a system of equations using the given information and solve for the variables.
Explanation:To write an equation relating the total cost to the number of tickets purchased, we need to determine the cost of one ticket and the fixed fee added by the ticket agency. Let's assign the ticket price as x and the fixed fee as y. Based on the given information, we can set up two equations:
5x + y = 93
3x + y = 57
Now, we can solve this system of equations to find the values of x and y and write the final equation relating the total cost to the number of tickets purchased.
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(a) A color printer prints 15 pages in 5 minutes. How many pages does it print per minute?
(b) It takes 34 pounds of seed to completely plant a 6-acre field. How many acres can be planted per pound of seed?
If necessary, round your answers to the nearest hundredth.
What is 3478 divide by 9
Which of the following statements concerning the standard normal curve is/are true (if any)?
a) The area under the standard normal curve to the left of -3 is zero.
b) The area under the standard normal curve between any two z-scores is greater than zero.
c) The area under the standard normal curve between two z-scores will be negative if both z-scores are negative.
d) The area under the standard normal curve to the left of any z-score is less than 1.
A. a, b
B. b, d
C. a, c
D. a
f=1/2kp, solve for k
The equivalent value of the expression k = ( 2F/p )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
F = ( 1/2 ) kp
On simplifying , we get
Multiply by 2 on both sides , we get
2F = kp
Divide by p on both sides , we get
k = 2F/p
Hence , the expression is k = 2F/p
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solution -9-8(1+4h)= -17
Please help ASAP
How much money does Barbara Mack owe at the end of 4 years if 6% interest is compounded continuously on her $2000 debt? Use the formula A=P e^rt to solve.
The amount of money owed is $ ? Round to the nearest cent as needed.
Barbara Mack owes approximately $2543.78 at the end of 4 years with 6% interest compounded continuously.
To find the total amount Barbara Mack owes after 4 years with a 6% continuously compounded interest rate, we use the formula:
A = P[tex]e^{rt}[/tex]
with P = $2000,
r = 0.06, and
t = 4
A = 2000 x [tex]e^{0.06 * 4}[/tex].
When we calculate e(0.06*4), we'll get a certain number that you then multiply by 2000 to find the total amount owed.
A= 2000 x [tex]2.71828 ^{0.24}[/tex]
A= 2543.78 ( approx)
So, Barbara Mack owes approximately $2543.78 at the end of 4 years with 6% interest compounded continuously.
Hey guys, I need help with this word problem. I don't just want the answer. I would like the steps please!
The average annual cinema admission price y (in dollars) from 2003 through 2012 is given by y=0.28x+5.92. In this equation, x represents the number of years after 2003.
a. Complete the table.
x: 2, 5, 8
y:
b. Find the year in which the average cinema admission price was approximately $7.88. (Hint:Find x when y=7.88 and round to the nearest whole number.)
c. Use the given equation to predict when the cinema admission price might be $10.04. (Use the hint for part b.)
Final answer:
By applying the given linear equation, we can calculate the average cinema admission price for specific years, find out in which year the price was approximately $7.88, and predict when it might reach $10.04.
Explanation:
The question involves solving a linear equation to complete a table, find a specific year based on the ticket price, and predict when the ticket price will reach a certain amount. To complete these steps, we apply the equation y=0.28x+5.92, where x represents the number of years after 2003, and y gives the price in dollars.
For a, plug in the values of x (2, 5, 8) into the equation to find y.
For b, set y=7.88 and solve for x (years after 2003) by rearranging the equation.
For c, with a target price of $10.04, use the equation again to solve for x.
When x=2, y=6.48.
When x=5, y=7.32.
When x=8, y=8.16.
For a ticket price of $7.88, solve for x: x = (7.88 - 5.92) / 0.28 = 7 years after 2003, which is 2010.
To predict when the ticket price reaches $10.04, solve for x: x = (10.04 - 5.92) / 0.28 = 14.71, rounding to 15 years after 2003, which is 2018.
An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer. a. How many different choices of ten questions are there?
b. Suppose six questions require proof and eight do not.
(i) How many groups of ten questions contain four that require proof and six that do not?
(ii) How many groups of ten questions contain at least one that requires proof?
(iii) How many groups of ten questions contain at most three that require proof?
c. Suppose the exam instructions specify that at most one of questions 1 and 2 may be included among the ten. How many different choices of ten questions are there? d. Suppose the exam instructions specify that either both questions 1 and 2 are to be included among the ten or neither is to be included. How many different choices of ten questions are there?
There are 1001 different choices of 10 questions.
d. Since the student can choose any 10 questions out of the 14, the number of different choices of 10 questions is given by the combination formula, which is C(14,10). Using the formula for combinations, we have:
C(14,10) = 14! / (10!(14-10)!)
= 14! / (10!4!)
= (14*13*12*11) / (4*3*2*1) = 1001
Therefore, there are 1001 different choices of 10 questions.
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The ratio of boys to girls at a movie is 4 font size decreased by 4 : 7. If there are 21 girls, how many boys are at the movie?