onsider a partial output from a cost minimization problem that has been solved to optimality. Final Shadow Constraint Allowable Allowable Name Value Price R.H. Side Increase Decrease Labor Time 700 700 100 200 The Labor Time constraint is a resource availability constraint. What will happen to the dual value (shadow price) if the right-hand-side for this constraint decreases to 400? The Labor Time constraint is a resource availability constraint. What will happen to the dual value (shadow price) if the right-hand-side for this constraint decreases to 400? O It will remain at -6. It will become a less negative number, such as -4. It will become zero. O It will become a more negative number, such as -8. . It will become zero or less negative.

The speed of the current is approximately 39.05 miles per hour.

Distance equals rate times time in the equation for distance, rate, and time. This equation shows how far an item moves over a specific amount of time at a specific pace by relating the three variables in a linear equation. Any of the three variables can be solved for by rearranging the formula.

Let us suppose the speed of current = c.

Then the formula for distance is given as:

distance = rate x time

For upstream:

distance = 48 miles

rate = 20 - c miles per hour

time = distance / rate

= 48 / (20 - c) hours

For downstream:

distance = 48 miles

rate = 20 + c

time = distance / rate

= 48 / (20 + c) hours

The total time for the trip is 5 hours thus,

48 / (20 - c) + 48 / (20 + c) = 5

Taking the LCM:

48(20 + c) + 48(20 - c) = 5(20 - c)(20 + c)

1920 = 400 - c²

c² = 1520

c ≈ 39.05 miles per hour

Hence, the speed of the current is approximately 39.05 miles per hour.

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1040 - 650 = 390

By subtracting the cost from the amount she sold the stove for, we can find the profit of $390.

I hope this helps! :)

By using the concept of confidence interval, it is obtained that

We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

Second option is correct

What is Confidence interval?

Let the quantity which is to be estimated is \(\theta\).  A confidence interval for the parameter θ, with confidence level \(\alpha\) is the interval (a, b), where

P(a < \(\theta\) < b) = \(\alpha\), P is the probability

Here the  average commute time in minutes (\(\mu\)) is to be calculated

95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25)

This means that it is 95% confident that the interval (15.75, 28.25) contains the population mean commute time in minutes using public transit

So the correct interpretation is

We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

Second option is correct

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Complete Question

A researcher finds a 95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25). What is the correct interpretation of this interval?

A) There is a 95% chance commute time in minutes using public transit is between 15.75 and 28.25 minutes.

B) We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

C) We are 95% confident that all commute time in minutes for the population using public transit is between 15.75 and 28.25 minutes.

D) We are 95% confident that the interval 15.75 < μ < 28.25 contains the sample mean commute time in minutes using public transportation.

The angle of inclination or angle of incidence is 55.94 degrees.

Let the angle of incidence be θ.

Now,

cos θ = sin φ [sin δ cos β + cos δ cos γ cos ω sin β] + cos φ [cos γ cos ω cos β - sin δ cos γ sin β] + cos δ sin γ sin ω sin β

ω refers to Hour angle

γ refers to Surface Azimuth angle

δ refers to declination angle

β refers to Surface slope

φ refers to Latitude = 45.67 degree North, 118.78 degree West [For Pendleton]

So now calculating,

Declination angle (δ) = 23.45 * (sin [360(284 + n)/365])

here n = number of days out of 365 = 233 days till August 21. So,

δ = 23.45 * (sin [360(284 + 233)/365]) = 11.76 degrees

For surface inclined 35 degree from vertical, β = 35 degree

and facing south west, γ = 45 degree

ω = cos⁻¹ [- tan (φ - β) tan δ] = cos⁻¹ [- tan (45.67 - 35 ) tan 11.76] = cos⁻¹(-0.0391) = 92.24 degree

So now angle of incidence is,

cos θ = sin (45.67) [sin (11.76) cos (35) + cos (11.76) cos (45) cos ω sin (35)] + cos (45.67) [cos (45) cos ω cos (35) - sin (11.76) cos (45) sin (35)] + cos (11.76) sin (45) sin ω sin (35)

cos θ = 0.56

θ = cos⁻¹ (0.56) = 55.94 degrees

Hence the angle of inclination or angle of incidence is 55.94 degrees.

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Based on the calculations, the unit rate in feet per minute for this walking pace is equal to 250 feet per minute.

A unit rate refers to a measurement of a quantity which is calculated as a ratio of one parameter to another.

This ultimately implies that, we would divide the distance covered in feet by the time taken to cover this distance as follows:

Unit rate = distance/time

Unit rate = 3750/15

Unit rate = 250 feet per minute.

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The error for the 3rd week, using SES forecast with α=0.3, is -0.1.

To calculate the error for the 3rd week using SES (Simple Exponential Smoothing) forecast, we first need to calculate the forecasted value for the 3rd week. The forecasted value is calculated using the formula:

\(F_t = α * A_{t-1 }+ (1 - α) * F_{t-1}\)

Where:

\(F_t\) is the forecasted value for week t

\(A_{t-1}\) is the actual value for the previous week (week t-1)

\(F_{t-1}\) is the forecasted value for the previous week (week t-1)

α is the smoothing factor

Given the time series values for weeks 1, 2, 3, and 4 as 22.00, 7.00, 10.00, and 13.00 respectively, and α=0.3, we can calculate the forecasted value for the 3rd week as follows:

F₃ = 0.3 * 7.00 + (1 - 0.3) * 10.00

= 2.1 + 7

= 9.1

The error for the 3rd week is then calculated as the difference between the actual value and the forecasted value:

Error₃ = Actual Value₃ - Forecasted Value₃

= 10.00 - 9.10

= -0.1

Therefore, the error for the 3rd week, using SES forecast with α=0.3, is -0.1.

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Answer:

-2

Step-by-step explanation:

5 to the 2nd power is 25 and a number to a negative power is 1/number^power

Answer:

A: b^3. B. X^3

Step-by-step explanation:

When dividing subtract the exponents is the property.

Answer:

A: \(b^3\) B: \(X^3\)

Step-by-step explanation:

\(A: b^7 - 4\\= b^3\)

B: \(X^5 - 2 \\=X^3\)

Answer:

the second choice or B would be the answer

The function that has a domain where x ≠ 3 and a range where y ≠ 2  are:

f(x) = 2 (x + 5) / (x - 3)

f(x) = 2 (x + 5) / (x - 3)

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The domain of a function consists of all the possible values of x for which the function is defined, and the range of a function consists of all the possible values of y that the function can take.

Now,

f(x) = 2 (x + 5) / (x - 3)

The denominator x - 3 cannot be equal to zero, so x cannot be equal to 3.

Therefore,

The domain of the function is all real numbers except x = 3,

or (-∞, 3) U (3, ∞).

To find the range, we need to consider what values of y the function can take for different values of x.

As x approaches 3 from either side, the value of the function becomes increasingly large (positive infinity for x approaching 3 from the right, and negative infinity for x approaching 3 from the left).

This means that the function has a vertical asymptote at x = 3, and the range of the function is all real numbers except y = 2, or (-∞, 2) U (2, ∞).

And,

f(x) = 2 (x + 5) / (x - 3)

The only value of x that makes the denominator x - 3 equal to zero is x = 3. Therefore,

The domain of the function is all real numbers except x = 3, or

(-∞, 3) U (3, ∞).

To find the range, we again consider what values of y the function can take for different values of x.

As x approaches 3 from either side, the value of the function approaches positive or negative infinity (depending on the sign of x - 3).

This means that the function has a vertical asymptote at x = 3, and the range of the function is all real numbers except y = 2, or (-∞, 2) U (2, ∞).

Therefore,

Both functions have the same domain and range, and both satisfy the conditions of having a domain where x is not equal to 3 and a range where y is not equal to 2.

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The probability of Laura missing 3 free throws before making 12 is approximately 0.0037 or 0.37%.
The basketball free throw.

A success would be considered when Laura makes a free throw.

A failure would be when Laura misses a free throw.
The negative binomial distribution is a probability distribution that calculates the probability of obtaining a certain number of failures before a specified number of successes occur.

The specified number of successes is 12, and the number of failures is represented by the variable x.
To calculate the probability of x failures, we need to know the probability of a single failure.

Since Laura is an 82% free throw shooter, the probability of her missing a free throw is 18%.
We can use the formula for negative binomial distribution to determine how many failures are required before 12 successes are achieved.

The formula is:
\(P(X = x) = (r+x-1)C(x) \times p^r \times (1-p)^x\)
Where:
P(X = x) is the probability of having x failures before achieving 12 successes
r is the number of successes required (in this case, 12)
p is the probability of a single success (in this case, 0.82)

\((r+x-1)C(x)\)is the combination of r+x-1 choose x

For example, if we want to find the probability of Laura missing 3 free throws before making 12, we will plug in x = 3, r = 12, p = 0.82 into the formula:

\(P(X = 3) = (12+3-1)C(3) \times 0.82^1^2\times (1-0.82)^3\)
\(P(X = 3) = 14C3 \times 0.082^1^2 \times 0.18^3\)
\(P(X = 3) = 364 \times 0.000018 \times 0.005832\)
P(X = 3) = 0.000037
Overall, the trial in this scenario is each individual attempt at a free throw, the success is making a free throw, and 12 successes are required before the shooting session is considered complete.

The negative binomial distribution is used to calculate the probability of obtaining a certain number of failures before achieving the specified number of successes.

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'x' follows a negative binomial distribution with 'r' being 12 successes.

In this scenario, a trial refers to each individual attempt at shooting a free throw. A success is when Laura successfully makes a free throw. To achieve her goal of making 12 free throws, she needs to have 11 successes (since she will miss on the final attempt). Therefore, r = 11.

In this context, a "trial" refers to each individual attempt Laura makes to shoot a basketball free throw. A "success" is when Laura makes a free throw (hits the basket), while a "failure" (not mentioned in the question) would be when Laura misses a free throw. Since Laura keeps shooting free throws until she makes 12, the number of successes required, denoted as 'r', is 12.

Therefore, 'x' follows a negative binomial distribution with 'r' being 12 successes.

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The mean (μx) of the sampling distribution of sample means is 78, and the standard deviation (σx) is 1. This means that on average, the sample means will be centered around the population mean of 78, and the spread of the sample means will be relatively small with a standard deviation of 1.

In statistics, the sampling distribution of sample means refers to the distribution of means obtained from all possible samples of a given size taken from a population. The mean of this sampling distribution is equal to the population mean, while the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size.

In this case, we are given that the population mean (μ) is 78 and the population standard deviation (σ) is 7. We are interested in finding the mean (μx) and standard deviation (σx) of the sampling distribution of sample means when the sample size (n) is 49.

Since the mean of the sampling distribution is equal to the population mean, μx = 78.

To find the standard deviation of the sampling distribution (σx), we divide the population standard deviation by the square root of the sample size:

σx = σ / √n.

In this case, σx = 7 / √49

= 7 / 7

= 1.

Therefore, the mean (μx) of the sampling distribution of sample means is 78, and the standard deviation (σx) is 1. This means that on average, the sample means will be centered around the population mean of 78, and the spread of the sample means will be relatively small with a standard deviation of 1.

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The total Amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.

a) The down payment of Jason is 10% of $430,000 =$43,000b) The amount of the mortgage is the difference between the home value and the down payment.

Mathematically, $430,000 - $43,000 = $387,000.c) The closing costs are 3.5% of the mortgage. So, 3.5% of $387,000 is: 0.035 × $387,000 = $13,545.

Hence, the closing costs are $13,545. d) The total amount of the mortgage if they finance the closing costs with the mortgage is the sum of the amount of mortgage and the closing cost.

So, the total amount of the mortgage is: $387,000 + $13,545 = $400,545.Solution:a) Jason's down payment is 10% of the cost of the house, which is given as $430,000.

To calculate the down payment, multiply the cost of the house by 10%.Down payment = $430,000 x 10% = $43,000

Therefore, Jason's down payment is $43,000.b)

The amount of the mortgage is the difference between the total cost of the house and the down payment. The cost of the house is given as $430,000.

Thus, we have:Mortgage amount = Total cost - Down paymentMortgage amount = $430,000 - $43,000Mortgage amount = $387,000

Therefore, the amount of the mortgage is $387,000.c) The closing costs are 3.5% of the mortgage.

Using the mortgage amount calculated in part b), we can compute the closing costs as follows:Closing costs = 3.5% x Mortgage amountClosing costs = 3.5% x $387,000

Closing costs = $13,545

Therefore, the closing costs are $13,545.

d) If the closing costs are financed with the mortgage, we simply need to add the closing costs to the mortgage amount calculated in part b):Total amount of the mortgage = Mortgage amount + Closing costsTotal amount of the mortgage = $387,000 + $13,545

Total amount of the mortgage = $400,545

Therefore, the total amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.

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Answer:

1/2 or 0.5

Step-by-step explanation:

since there are two options, heads and tails, the probability of not flipping tails is 1/2, since the probability of flipping heads is 1/2

Answer:

1/2

Step-by-step explanation:

There are 2 sides of a coin.

Heads or Tails.

That means you have a 1/2 chance of getting tails. This also means you have 1/2 chance of not getting tails, in other words, getting heads.

Answer: 18

Do Keep Change Flip (KCF)

Keep: 9/2

Change: ÷ into ×

Flip: 1/4 into 4/1

Your new problem should be 9/2×4/1

Multiply

9/2×4/1=36/2

36/2=18

Final Answer: 18

Answer:

\( \frac{ - 4}{29} = \\ = { \boxed{ \boxed{- \frac{4}{29}}}}\)

Answer: $32.39

Step-by-step explanation:

The car's tank has a capacity of 15 gallons and has only 1/5 of a tank left which means that the quantity left is:

= 1/5 * 15

= 3 gallons

If Ayssa is going to fill up the tank, the number of gallons needed is:

= 15 - 3

= 12 gallons

Gas is $2.699 per gallon so cost is:

= 12 * 2.699

= $32.39

Answer:

0.012

Step-by-step explanation:

Answer:

0.012km is the correct answer

Step-by-step explanation:

m ( < E ) = m ( < N )

m ( < H ) = m ( < J )

m ( < A ) = m ( < O )

NH = EJ

NA = EO

AH = JO

The surface area of that part of the plane 6x+10y+z=9 that lies inside the elliptic cylinder \(x^{2}/49 + y^{2}/9 =1\\\) is 21 \(\pi\) \(\sqrt{137\\\).

Given:

6x + 10y + z = 9  ..... (1)

\(x^{2}/49 + y^{2}/9 =1\\\) ..... (2)

Equation (1) can also be written as:

z = 9 - 6x - 10y ...... (3)

The surface area is given by the equation:

SA = ∫∫\(\sqrt{((df/dx)^2) + (df/dy)^2 + 1} )dA\)

\(\sqrt{df}/dx = -6\)

\(\sqrt{df}/dy = -10\)

Now, substitute the known values in equation (4).

SA = ∫∫\(\sqrt{(-6)^2 + (-10)^2 + 1} dA\)

SA =\(\sqrt{137}\)  ∫∫dA

Now the area enclosed by an ellipse is given by:

\(x^{2}/49 + y^{2}/9 =1\\x^{2}/a^2 + y^2/b^2=1\\\)

By comparing the above equation:

a = 7

b = 3

The area is given by:

SA = \(\sqrt{137}\) \(\pi\) (7 x 3)

SA = 21 \(\pi\) \(\sqrt{137\\\)

The surface area of an elliptic cylinder is 21 \(\pi\) \(\sqrt{137\\\).

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a)The value of X determines the value of Y and vice versa, so they are dependent variables.

b), X and Y are uncorrelated.

c) X and Y are not orthogonal.  

(a) X and Y are independent if the joint probability distribution of X and Y is equal to the product of their marginal probability distributions. In this case, X = cos(ø) and Y = sin(ø), where ø is uniformly distributed in the interval (0, π).

Since the values of cos(ø) and sin(ø) are related by the trigonometric identity \(cos^2(ø) + sin^2(ø) = 1,\)

we can see that X and Y are not independent. The value of X determines the value of Y and vice versa, so they are dependent variables.

(b) Yes, X and Y are uncorrelated. The covariance of two random variables is a measure of the linear relationship between the variables. Since the variables X and Y are both uniformly distributed over the interval [-1, 1], their covariance is 0.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. The correlation coefficient between X and Y is the covariance of X and Y divided by the product of their standard deviations.

Since the standard deviation of X is 1 and the standard deviation of Y is 1, the correlation coefficient between X and Y is also 0. Therefore, X and Y are uncorrelated.

(c) No, X and Y are not orthogonal. Orthogonal variables are two variables whose product is zero. In this case, X = cos(ø) and Y = sin(ø), and their product is XY = sin(ø)cos(ø) = -cos(ø)sin(ø). Therefore, X and Y are not orthogonal.  

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Answer:

the answer is -18

Step-by-step explanation:

Put 6 in for x and 3 in for y 3 times 6 is 18 and since there is a negative in front then it is a negative answer

Answer:

Heya your answer is - 18 (minus 18)

Answer:

-100 (10*10)- (-10*-10) - (10*10)

Step-by-step explanation:

The samples of size n = 2 that can be drawn from this population is 28

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

Population, N = 8

Sample, n = 2

The samples of size n = 2 that can be drawn from this population is calculated as

Sample = N!/(n! * (N - n)!)

substitute the known values in the above equation, so, we have the following representation

Sample = 8!/(2! * 6!)

Evaluate

Sample = 28

Hence, the number of samples is 28

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Complete question

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

How many samples of size n = 2 can be drawn this population?

Answer:144

Step-by-step explanation:

First find the area of that shape

24x48=1152

then reduce

1152/8=144

Winona's average cost per visit C as a function of the number of visits x is given by:

C(x) = (135 + 1.25x)/x

To find her average cost per visit when she has visited the zoo 135 times, we substitute x = 135 in the above expression:

C(135) = (135 + 1.25(135))/135 = 2.083

Therefore, her average cost per visit when she has visited the zoo 135 times is $2.083.

When Winona starts visiting the zoo every day, the number of visits x will be very large. As x approaches infinity, her average cost per visit will approach the admission fee of $1.25, since the fixed cost of $135 becomes negligible compared to the large number of visits. In other words, the average cost per visit will approach the marginal cost per visit, which is constant at $1.25.

To graph the function C(x) for x > 0, we can use any graphing tool, such as Desmos or Wolfram Alpha. The graph shows that the average cost per visit decreases as the number of visits increases, but approaches a horizontal asymptote of $1.25 as x approaches infinity.

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Answer:

16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

0-4 Go no more

5-9 move up the line

7 is in between 5 and 9 so round 15.74 to 16

Hope this helped.

Answer:

(4x^2-5) x (2x^2-9)

Step-by-step explanation:

01.) Write -46x^2 as a difference

8x^4-10x^2-36x^2+45

02.) Factor out 2x^2 from the expression

8x^4-10x^2 -36x^2+45

2x^2 * (4x^2-5) - 36x^2+45

03.) Factor out -9 from the expression

2x^2 * (4x^2-5) - 9(4x^2-5)

2x^2 *(4x^2-5)-9(4x^2-5)

04. Factor out 4x^2-5 from the expression

(4x^2-5) *(2x^2-9)

The total cost of the guitar including sales tax is $85.31

A sales tax is a tax levied on the sale of certain goods and services and paid to the government. In general, rules compel the seller to collect tax money from the buyer at the time of purchase.

The tax is added on the sale price and it is not apart of the profit.

Cost of the guitar = $131.25

Sales tax = 6.5%

Total cost of guitar = 6.5% of 131.25 = 0.65 × 131.25 = $85.31

A use tax is a levy on services or goods that a client pays directly to a governing body. Food, education, and medications are usually exempt from sales and use tax under state law.

Hence the total cost of the guitar is $85.31

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a. Using intersection of events probability of FUA is 0.0165

b. Using complement rule, the probability of F'UA is 0.9835

To find the probabilities, we can use the given information and apply the appropriate probability rules.

(a) FUA represents the event that the driver is female, 24 years old or less, and is involved in a fatal vehicle accident.

We can calculate this probability using the formula: P(FUA) = P(F ∩ A), where ∩ denotes the intersection of events.

P(FUA) = P(F) * P(A|F)

Given information:

P(F) = 0.2868 (probability that the driver is female)

P(A) = 0.1828 (probability that the driver is 24 years old or less)

P(A|F) = 0.0576 (probability that the driver is 24 years old or less given that the driver is female)

P(FUA) = 0.2868 * 0.0576 ≈ 0.0165

Therefore, the probability of FUA is approximately 0.0165.

(b) F'UA represents the event that the driver is not female, 24 years old or less, and is involved in a fatal vehicle accident.

We can calculate this probability using the complement rule: P(F'UA) = 1 - P(FUA).

P(F'UA) = 1 - P(FUA) ≈ 1 - 0.0165 ≈ 0.9835

Therefore, the probability of F'UA is approximately 0.9835.

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