a company is marketing an investment opportunity to four potential customers. the company believes that its probability of making a sale is 0.5 for each of the first three customers but that it is only 0.1 for the fourth customer. the customers' purchases are independent of one another. calculate the probability that at most two customers purchase the investment

Answers

Answer 1

The probability that at most two customers purchase the investment is 0.1875 or 18.75%.

To calculate the probability that at most two customers purchase the investment,  to calculate the probabilities for each possible outcome: 0, 1, and 2 customers purchasing the investment, and then sum them up.

Let's consider the customers as A, B, C, and D, with D being the fourth customer.

Probability of 0 customers purchasing:

P(0 customers) = (1 - probability of sale)²number of customers

= (1 - 0.5)²4

= 0.0625

Probability of 1 customer purchasing:

P(1 customer) = (probability of sale)²1 ×(1 - probability of sale)²3 (since 3 customers won't purchase)

= 0.5²1 ×0.5²3

= 0.5 × 0.125

= 0.0625

Probability of 2 customers purchasing:

P(2 customers) = (probability of sale)²2 × (1 - probability of sale)²2 (since 2 customers will purchase)

= 0.5²2 ×0.5²2

= 0.25 × 0.25

= 0.0625

Now  sum up these probabilities to find the probability that at most two customers purchase the investment:

P(at most 2 customers) = P(0 customers) + P(1 customer) + P(2 customers)

= 0.0625 + 0.0625 + 0.0625

= 0.1875

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Related Questions

Write an essay on Drug Addiction.

Answers

Answer:

Drug abuse and addiction are a major burden to society. Drug addiction is a pathological or abnormal condition which arises due to frequent drug use. The disorder of addiction involves the progression of acute drug use to the development of drug-seeking behavior, the vulnerability to relapse, and the decreased, slowed ability to respond to naturally rewarding stimuli. Causes Drugs known to cause addiction include illegal drugs as well as prescription or over-the-counter drugs, according to the definition of the American Society of Addiction Medicine.

One very common belief is that drug abusers should be able to just stop taking drugs if they are only willing to change their behavior. What people often underestimate is the complexity of drug addiction — that it is a disease that impacts the brain and because of that, stopping drug abuse is not simply a matter of willpower. Through scientific advances we now know much more about how exactly drugs work in the brain, and we also know that drug addiction can be successfully treated to help people stop abusing drugs and resume productive lives. People think of drug abuse and will only think of illegal drugs like marijuana or cocaine. The truth is that there are a large number of people who are abusing drugs that are legal and prescribed only by doctors. There is a study done by the United Nations that says that the number of people who are addicted to legal prescription drugs is close to the number of people who are addicted to illegal drugs. In this study the drug abuse and addiction it isn’t about consumption but more on consequences. If your drug addiction starts to affect your everyday life you most likely you’re a drug abuser or you have an addiction problem. Drug abuse and addiction can have many effects on the brain. These repeated usages of drugs can cause the way your brain’s appearance and function.

So what is drug abuse and why do we become addicted to certain drugs? Substance abuse, also known as drug abuse, is a patterned use of a substance (drug) in which the user consumes the substance in amounts or with methods neither approved nor supervised by medical professionals. Addiction is the continued use of a mood altering substance or behavior despite adverse dependency consequences, or a neurological impairment leading to such behaviors. The number in India is 3-5 million, 2 million of which are in Delhi alone. In India, there are one million heroin addicts, 2 million opium addicts and several million cannabis addicts. It may be mentioned that the ratio of drug abusers to alcoholics having serious alcohol abuse problems is 1 : 30. A Drug is any substance (other than food) that produces changes in the physical or mental functioning of an individual, and the Drug Use is taking a drug for medical purpose like treating an illness, protecting the body against the disease or to relieve pain or tension. Traditional definitions of addiction, with their criteria of physical dependence and withdrawal (and often an underlying tenor of depravity and sin) have been modified with increased understanding; with the introduction of new drugs, such as cocaine, that are psychologically or neuropsychologically addicting; and with the realization that its stereotypical application to opiate-drug users was invalid because many of them remain occasional users with no physical dependence.

To conclude, addiction is more often now defined by the continuing, compulsive nature of the drug use despite physical and/or psychological harm to the user and society and includes both licit and illicit drugs, and the term “substance abuse” is now frequently used because of the broad range of substances (including alcohol and inhalants) that can fit the addictive profile. There are many different types of drugs you should be aware of.

Step-by-step explanation:

The margin of error of a confidence interval is the error from biased sampling methods.a. trueb. false

Answers

Margin of error is statistical expressing the amount of a random sampling error in survay results not the error term from biased sampling method. So, correct answer is False.

What is Margin of error ?

Margin of error in statistics represents the amount of random sampling error in the survey results. The larger the margin of error, the less confident that the survey results reflect the results of the census of the entire population. It is denoted by E or MOE. It is calculated by dividing the square root of the sample size by the standard deviation of the population. 99% level is the most conservative, 90% level is the least conservative. The sampling error is a statistical error that occurs when the analyst does not select a sample that is representative of the entire data population.

False - Margin of error only account for sample variability (the fact that my sample differs from many others' samples and therefore provides different statistics.

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(b) Show that if H and K are subgroups of an abelian group G, then {hk :he Hand ke K is a subgroup of G.

Answers

To show that the set {hk : he H and ke K} forms a subgroup of an abelian group G, where H and K are subgroups of G, we need to demonstrate closure, the existence of an identity element, and the existence of inverses for every element in the set.
iden
Let's consider the set S = {hk : he H and ke K}. To show that S is a subgroup of G, we need to prove three properties: closure, existence of an identity element, and existence of inverses.Closure: For any h₁k₁, h₂k₂ ∈ S, we need to show that their product, (h₁k₁)(h₂k₂), is also in S. Since G is an abelian group, we can rearrange the product as (h₁h₂)(k₁k₂). Since H and K are subgroups, h₁h₂ ∈ H and k₁k₂ ∈ K. Therefore, (h₁k₁)(h₂k₂) = (h₁h₂)(k₁k₂) ∈ S, proving closure.
Identity element: The identity element of G is denoted as e. Since H and K are subgroups, e ∈ H and e ∈ K. Thus, e ∈ S.Inverses: For any element hk ∈ S, we need to show the existence of its inverse. Since G is an abelian group, the inverse of hk is h^(-1)k^(-1). Since H and K are subgroups, h^(-1) ∈ H and k^(-1) ∈ K. Therefore, (hk)(h^(-1)k^(-1)) = (hh^(-1))(kk^(-1)) = ee = e, demonstrating the existence of inverses.
By satisfying closure, the existence of an identity element, and the existence of inverses, we conclude that S = {hk : he H and ke K} forms a subgroup of the abelian group G.

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There are 55 hats. Each hat uses 42 beaver pelts. How many beaver pelts are you going to need to make 55 hats?

Answers

The required number of beaver pelts required for 55 hats is 2310 based on utilisation of 42 beaver pelts per hat.

The problem can be easily solved using mathematical operation multiplication. The number of beaver pelts required will be given by the formula -

Number of beaver pelts = Number of hats × number of beaver pelts required in each hat

Keep the values in formula to find the value of number of beaver pelts

Number of beaver pelts = 55 × 42

Performing multiplication on Right Hand Side of the equation

Number of beaver pelts = 2310 hats

Hence, the number of beaver pelts required is 2310 for 55 hats.

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suppose that the heights, in inches, of orangutans are normally distributed with an unknown mean and standard deviation. the orangutan heights of 27 randomly sampled orangutans are used to estimate the mean of the population. what t-score should be used to find the 99% confidence interval for the population mean?

Answers

The t-score of 2.779 is used to find the 99% confidence interval for the population mean.

Given,

Assume that orangutans' heights, measured in inches, are regularly distributed with an unidentified mean and standard deviation. The population means are calculated using the orangutan heights of 27 orangutans that were randomly selected.

What t-score should be applied to determine the population mean's 99% confidence interval?

n = 27

confidence level = 0.99

We have to find a critical value for the confidence level of 0.99.

To find the critical value we need degrees of freedom and significance level.

df = n-1 = 27 - 1 = 26

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

For α/2 = 0.005 and df = 26, the critical value using the above table is,

t-critical value = 2.779

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Find the percent of sugar in the concentration:

A syrup made of 10kg of water and 2kg of sugar

Answers

Answer: 2/12= 16.67% four sig fig

Step-by-step explanation:

Using (mass of sugar)/(total mass)

and total mass equals (mass of sugar) + (mass of water)


get a total mass of 12kg

Therefore percentage is 2/12=1/6=16.666666%

Answer:

The percentage of sugar in the syrup is 16.66...%

Step-by-step explanation:

lmk

which ordered pair makes both of these equations true?
A. (-9,25)
B. (-3,-13)
C. (2,-3)
D. (3,-1)
E. (9,11)

which ordered pair makes both of these equations true?A. (-9,25)B. (-3,-13)C. (2,-3)D. (3,-1)E. (9,11)

Answers

D is the answer im sure

Answer:

D. (3, -1)

Step-by-step explanation:

y = 2x - 7 and 4x + y = 11 are two given equation

Now, Name the equation

y = 2x - 7 ...(1)

4x + y = 11 ...(2)

Then, Put the value of y in equation (2)

4x + y = 11

4x + (2x - 7) = 11

4x + 2x - 7 = 11

6x - 7 = 11

6x = 11 + 7

6x = 18

x = 18/6

x = 3

Here, put the value of x in equation (1)

y = 2x - 7

y = 2(3) - 7

y = 6 - 7

y = - 1

Thus, (3, - 1) pair makes both of these equations true

-TheUnknownScientist

6. If WXYZ is a square with WZ = 27, find each measure.

X

a) ZY =

b) WY =

c) RX =

d) m2 WRZ

e) mZXYZ -

f) mZZWY =

z

Answers

a) ZY= 27b

b) WY= diagonal = 27 × sqrt2

c) RX= half of diagonal = (27 × sqrt2) divided by 2

d) m2 WRZ = 90 degrees

e) mZXYZ = 90 degrees

f) mZZWY = 45 degrees

Hope this helps!

PLEASE HELP!!! WILL GIVE BRAINLIEST

PLEASE HELP!!! WILL GIVE BRAINLIEST

Answers

so
y=-10x-29 and y=-59

substitute the y in the equation for -59:
-59=-10x-29
add 29 on both sides
-30=-10x
divide both sides by -10
3=x

so,
x=3

need help i can’t remember this !

need help i cant remember this !

Answers

i think the answer is d but i’m not sure

the average quarterly percentage change of gasoline is 2.84% and the quarterly volatility of gasoline is 8.22%. Over the next quarter, what is the probability of a percentage increase in gasoline that is 4% or larger?

Answers

The probability of a percentage increase in gasoline that is 4% or larger over the next quarter is approximately 25%.

Gasoline exhibits an average quarterly percentage change of 2.84% and a quarterly volatility of 8.22%. To determine the probability of a percentage increase in gasoline that is 4% or larger over the next quarter, we need to consider the distribution of the data.

The average quarterly percentage change of 2.84% provides us with a baseline expectation of how gasoline prices may change over time. However, the quarterly volatility of 8.22% indicates that there is significant variability in these price changes. This volatility suggests that gasoline prices can deviate considerably from the average.

To calculate the probability, we can use the concept of standard deviations. A 4% increase in gasoline prices is equivalent to a change of (4 - 2.84) / 8.22 standard deviations from the mean. By referring to a standard normal distribution table or using statistical software, we can determine the proportion of the distribution that falls above this threshold.

Based on the available information, the probability of a percentage increase in gasoline that is 4% or larger can be estimated to be approximately 25%.

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8/12 = y/30 using proportion how can I solve this?

Answers

Answer:

y = 20

Step-by-step explanation:

\(\frac{8}{12}\) = \(\frac{y}{30}\) ( cross- multiply )

12y = 8 × 30 = 240 ( divide both sides by 12 )

y = 20

Which expression is represented by the diagram?

Which expression is represented by the diagram?

Answers

The expression shown by the model is (a) -6 - (-1)

How to determine the expression shown by the model?

From the question, we have the following parameters that can be used in our computation:

The model

Where, we have

Total shaded boxes = -1 in 6 places

Total canceled boxes = -1

Using the above as a guide, we have the following:

Equation = -1 * 6 - (-1)

Evaluate

Equation = -6 - (-1)

Hence, the expression shown by the model is (a) -6 - (-1)

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a study of data compiled from emergency departments reveals that the number of hospital visits for cooking-related knife injuries significantly increases around major holidays. what do the variables examined in the study show?

Answers

The variables examined in the study show the number of hospital visits for cooking-related knife injuries and their frequency during major holidays. The data compiled from emergency departments shows that there is a significant increase in the number of hospital visits for such injuries around major holidays.

This suggests that there may be a correlation between the holidays and the use of knives in cooking, possibly due to increased meal preparation and cooking during these times. Other variables that could be examined in further studies include the types of knives and cooking equipment used, the types of foods being prepared, and the demographics of those who sustain these injuries.

Variables refer to any characteristic, quantity, or attribute that can be measured and that can fluctuate or vary. Variables are of two types:

Dependent variablesIndependent variables

An independent variable is one that is thought to influence the dependent variable, which is the characteristic or response that is being measured.

The variables examined in the study indicate that the number of hospital visits for cooking-related knife injuries increases around major holidays. This implies that there is a direct relationship between cooking and knife injuries on major holidays. As a result, measures must be put in place to reduce the risk of knife injuries during the holidays. This includes the creation of awareness campaigns and the promotion of safety in the kitchen.

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Compute the second-order partial derivative of the function ℎ(u,v)= u/u+16v

Answers

The second-order partial derivative of the function ℎ(u,v) = u/(u + 16v) is: ∂²ℎ/∂u² = -32v / (u + 16v)²

How to find second-order partial derivative?

To compute the second-order partial derivative, we first differentiate ℎ(u,v) with respect to u to obtain the first derivative (∂ℎ/∂u). Then we differentiate (∂ℎ/∂u) with respect to u again to obtain the second derivative (∂²ℎ/∂u²).

To find ∂ℎ/∂u, we use the quotient rule:

∂ℎ/∂u = [(1)(u + 16v) - (u)(1)] / (u + 16v)²

       = (u + 16v - u) / (u + 16v)²

       = 16v / (u + 16v)²

Now, to find ∂²ℎ/∂u², we differentiate ∂ℎ/∂u with respect to u:

∂²ℎ/∂u² = d/du (16v / (u + 16v)²)

        = -32v / (u + 16v)²

Therefore, the second-order partial derivative of ℎ(u,v) with respect to u is -32v / (u + 16v)².

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Please express each of the following formula in big-O notation. (A) n
3
+10

2
n
(B) n
2
+3log
2

n (C) 5n

log
2

n+2n
2
(D) 1+2+3+…+(n−1)+n (E) What is the worst-case big-O complexity of the following code fragment? int ans =0; for(int i=0;i

Answers

(A) n3+10*2n expressed in big-O notation is O(n3).

(B) n2+3log2⁡n expressed in big-O notation is O(n2).

(C) 5nlog2⁡n+2n2 expressed in big-O notation is O(n2).

(D) 1+2+3+…+(n−1)+n can be simplified as 1+2+3+…+n and using the formula for the sum of an arithmetic series, we have n(n+1)/2. Therefore, its big-O notation is O(n2).

(E) The code fragment can be written as:

                               for(int i=0;i< n;i++){for(int j=0;j< n;j++){ans++;}}

This code fragment has two nested loops.

The outer loop executes n times, while the inner loop also executes n times for each iteration of the outer loop.

Therefore, the code fragment has a time complexity of O(n2) in the Worst case.

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Define: stratified random sample a) population is divided into similar groups and a SRS is chosen from each group. b) gives each member of the population a known chance to be selected. c) people who choose themselves for a sample by responding to a general appeal. d) the explanatory variable(s) in an experiment. e) directly holding extraneous factors constant. f) every possible sample of a given size has the same chance to be selected. g) using extraneous factors to create similar groups. h) successively smaller groups are selected within the population in stages. i) choosing the individuals easiest to reach.

Answers

Answer:

d) population is divided into similar groups and a SRS is chosen from each group.

Step-by-step explanation:

Stratified random sampling

can be regarded as "proportional random sampling" and is method of sampling which entails division of a population to more simpler sub- groups, this sub- groups are regarded as " strata". This strata are been formed on the basis of shared attributes of the members. This attribute could be educational attainment as well as income. It should be noted that stratified random sample is population is divided into similar groups and a SRS is chosen from each group.

Fast Food At a local fast food restaurant 70% of customers buy a burger, 55% buy fries, and 45% buy both.
What is the probability that a customer at the restaurant buys a burger or fries? What is the probability that a customer at the restaurant buysa burger but does not buy fries? 25

Answers

To calculate the probability that a customer at the restaurant buys a burger or fries, we can add the probabilities of buying a burger and buying fries, and then subtract the probability of buying both (to avoid double-counting):

P(burger or fries) = P(burger) + P(fries) - P(burger and fries)

P(burger or fries) = 70% + 55% - 45%

P(burger or fries) = 70% + 55% - 45% = 80%

Therefore, the probability that a customer at the restaurant buys a burger or fries is 80%.

To calculate the probability that a customer at the restaurant buys a burger but does not buy fries, we can subtract the probability of buying both from the probability of buying a burger:

P(burger but not fries) = P(burger) - P(burger and fries)

P(burger but not fries) = 70% - 45%

P(burger but not fries) = 25%

Therefore, the probability that a customer at the restaurant buys a burger but does not buy fries is 25%.

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Find the least common denominator (LCD) of
1/20 and 11/8

Answers

Answer:

The leastcommon denominator is 40.

What is the answer to this question −11+4x≤ 17

Answers

You move the 11 to the right and switch the sign

4x ≤ 17 + 11

Add the numbers

4x ≤ 28

Divide both sides by 4

The answer is

x ≤ 7

Linear inquality : −11+4x≤ 17

Adding 11 on both sides

=> -11 + 4x + 11 < 17 + 11

=> 4x < 28

Dividing both sides by 4

=> 4x/4 < 28/4

=> x < 7

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The length of the rectangular field is 18cm, and the width is 24cm,
find perimeter and area of the field.

Answers

Step-by-step explanation:

Just do this

2(L+B)

2(18+24)

2×42

84 Ans.

perimeter is the sum of every side of the shape. in this case you have two sides that are 18 and two that are 24 (since a rectangle has two congruent sides). so when you add 18+18+24+24 together you get 84 which is your answer

I need help with this question... I suck very much at mathematics. CAN SOMEONE HELP ME???

I need help with this question... I suck very much at mathematics. CAN SOMEONE HELP ME???

Answers

Answer:

Jeana has to spend less

Step-by-step explanation:

I did the math and 17.95+27=44.95 and

                                 18.95+18=36.95

An avid gardener wants to know which of two brands of fertilizer is best for her tomatoes. The two brands of fertilizer are A and B. She plants five pairs of tomato plants in two rectangular planters and places them beside one another. She gives each set of tomato plants the same amount of water each day, only she gives one set of plants fertilizer A and the other set of plants fertilizer B. At the end of the growing season, she counts the number of tomatoes each plant has yielded. Assume that all conditions for inference have been met. The rectangular planters are lined up so that plant 1 is beside plant 6, and plant 2 is beside plant 7, and so on. The yield for the five pairs of tomato plants are given. Plant 1 2 3 4 5 Yield with Fertilizer A 7 6 5 8 10 Plant 6 7 8 9 10 Yield with Fertilizer B 4 7 6 5 3 The gardener believes that fertilizer A enhances the yield of her tomatoes more than fertilizer B. She uses the following order of subtraction when determining the difference in the yields for the two brands: A- B (a) We would like to carry out a t test for the population mean difference. Calculate the point estimate. (b) Calculate the standard deviation of the differences. (Round your answer to three decimal places.) (c) Calculate the test statistic. (Round your answer to two decimal places.)

Answers

(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.

To perform a t-test for the population mean difference, follow these steps:

(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.

Mean difference = (Sum of differences) / Number of pairs

Using the given data gives:

Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5

Subtracting gives:

Mean difference = (3 - 1 - 1 + 3 + 7) / 5

Solving gives:

Mean difference = 11 / 5

Dividing gives:

Mean difference = 2.2

(b) Calculate the standard deviation of the differences:

To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.

Squared differences:\((3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2\)

Solving gives:

Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)

Solving gives:

The sum of squared differences = 48.36

The standard deviation of the differences \(= \sqrt{48.36 / 4}\)

Solving gives:

The standard deviation of the differences \(= \sqrt{2.09}\)

Rounded to three decimal places

The standard deviation of the differences ≈ 3.47

c) Calculate the test statistic:

The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))

Let's assume the null hypothesis is that there is no difference between the two fertilizers

(i.e., mean difference = 0).

\(t = (2.2 - 0) / (3.47 / \sqrt5)\)

Substituting \(\sqrt 5 = 2.236\)

t = 2.2 / (3.47 / 2.236)

Rounded to two decimal places

t ≈ 1.378

So, the test statistic is approximately 1.378.

The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma

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consider y=1/2x+1 complete the table for x and y

Answers

Answer:

y=-1.5

x=-2

Step-by-step explanation:

I hope this answer can help

A firm uses two inputs x and y, and their profit function is P(x,y)=2xy-3x+y. Input x costs $2 each and y costs $3 each and they are constrained to spend a total of $100 on inputs. If the firm wants to maximise profit, they should use of input x, of input y. In addition, the shadow price will be Round your answer to two decimal places.

Answers

The optimal allocation is x = -1/2, y = 3/2, with a shadow price of 1.50.

What is Supply and demand equilibrium factors?

To maximize profit, the firm needs to determine the optimal allocation of inputs x and y within the budget constraint of $100.

Let's assume the firm uses 'a' units of input x and 'b' units of input y. Since each unit of x costs $2 and each unit of y costs $3, the total cost constraint can be expressed as:

2a + 3b ≤ 100

To maximize profit, we need to differentiate the profit function P(x, y) with respect to both inputs and set the derivatives equal to zero:

∂P/∂x = 2y - 3 = 0 ---> y = 3/2

∂P/∂y = 2x + 1 = 0 ---> x = -1/2

However, x and y cannot have negative values, so these values are not feasible. To find the feasible values, we can substitute the values of x and y into the cost constraint:

2(-1/2) + 3(3/2) = 0 + 9/2 = 9/2 ≤ 100

This constraint is satisfied, so the feasible allocation is x = -1/2 and y = 3/2.

To find the shadow price, we need to determine the rate at which the maximum profit would change with respect to a one-unit increase in the budget constraint. We can do this by finding the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = λ

Where λ represents the shadow price or the marginal value of an additional dollar in the budget. In this case, λ is the shadow price.

Taking the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = ∂(2xy - 3x + y)/∂(2a + 3b) = 0

2y - 3 = 0 ---> y = 3/2

Thus, the shadow price (λ) is 3/2 or 1.50 when rounded to two decimal places.

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5. lan is 5 years older than Craig. If the sum of their ages is 45, find both
their ages. Be sure to create an equation then solve. *

Answers

Answer: Ian is 25 and craig is 20

Step-by-step explanation:

(45 - 5) /2 +5 to one of them

Answer:

Craig is 20 and Ian is 25 years old.

Step-by-step explanation:

I = Ian

C = Craig

I = C + 5

45 = C + I

45 = C + C + 5

45 - 5 = C + C

40 = 2C

C = 20

I = 20 + 5

Craig is 20 and Ian is 25.

how to add the integers -7 and -5 plzzz help

Answers

Answer:

oh its really easy

so for -7 you would just count up but negatives so -7 and -5= -13 :)

Step-by-step explanation:

Step-by step

-13 I think

2x+4=12 Y=4x+12
Solve using substitution

Answers

Answer:

X=4 Y=28

Step-by-step explanation:

We have our two equations, 2x+4=12 and Y=4x+12
Solve for x of one of the equations so that the repeating (common) variable can be cancelled out.

Using 2x+4=12, we can solve for the x-value and replace it back into y.

2x+4=12
2x=8
x=4

We can replace our new x-value into the other equation, y=4x+12

y=4(4)+12
y=16+12
y=28

So x=4, and y=28

What Is The Slope Of the Line

What Is The Slope Of the Line

Answers

Answer:

2/2.5 or 3/4 I pretty sure that's right

Unit Test Unit Test Active 1 2 3 4 5 6 7 CO Given fix) = 17- x2, what is the average rate of change in f(x) over the interval [1, 5]? -6, -1/2, 1/4, 1​

Answers

Answer:

Step-by-step explanation:

Average rate of change is the same thing as the slope. This is a quadratic so the slope is not something that is constant like it is in a line. Here you have the x coordinates of 1 and 5; each one of these x coordinates has a y coordinate that goes with it. If we draw a line from one of these coordinates to another,  that line will have a slope. That is the slope we are trying to find. Thus, we need the y coordinates that go with each of these x coordinates. To do that, plug x into the equation and do the math to find y:

Let's start with x = 1.

f(1) = \(17-(1)^2\) so

f(1) = 16 and the coordinate is (1, 16).

f(5) = \(17-(5)^2\) so

f(5) = -8 and the coordinate is (5, -8). Now we apply the slope formula:

\(m=\frac{-8-16}{5-1}=\frac{-24}{4}=-6\) So the answer is -6.

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