A company has two factories, factory A and factory B. The cost per item to produce q items in factory A is
200 + 3/q
q
. The cost per item to produce q items in factory B is
300 + q/
3q
. Find an expression for the sum of these costs per item. Then divide this expression by 2 to find an expression for the average cost per item to produce q items in each factory.

The average cost per item to produce q items in each factory is

Answer:

7/18

Step-by-step explanation:

First we need to find what values of sum we can have.

The minimum value for a cube is 1, so the minimum value for the sum is 2.

The maximum value for a cube is 6, so the maximum value for the sum is 12.

Now, we find the multiples of 6 and the multiples of 4 between 2 and 12:

4, 6, 8, 12.

To have a sum of 4, we can have the pairs:

(1,3), (2,2), (3,1)

To have a sum of 6, we can have the pairs:

(1,5), (2,4), (3,3), (4,2), (5,1)

To have a sum of 8, we can have the pairs:

(2,6), (3,5), (4,4), (5,3), (6,2)

To have a sum of 12, we can have the pairs:

(6,6)

So we have 14 pairs among the 36 (6 possibilities of each cube, so 6*6=36) total possibilities of pairs, so the probability is P = 14/36 = 7/18

The probability that the outcome of the roll is a sum that is a multiple of 6 or a sum that is a multiple of 4 is,      \(P(E)=\frac{14}{36}=\frac{7}{18}\)

The probability of any event is computed as divide number of favourable outcomes by total number of outcomes.

The sum that is a multiple of 6 or a sum that is a multiple of 4  are   4, 6, 8 and 12.

For sum of 4, we can have the pairs = (1,3), (2,2), (3,1)

For sum of 6, we can have the pairs: = (1,5), (2,4), (3,3), (4,2), (5,1)

For sum of 8, we can have the pairs = (2,6), (3,5), (4,4), (5,3), (6,2)

For sum of 12, we can have the pairs = (6,6)

Total number of favourable outcomes = 14

When two distinct number cubes are rolled. then,

Total number of outcomes  \(=6^{2}=36\)

The probability that the outcome of the roll is a sum that is a multiple of 6 or a sum that is a multiple of 4,

                  \(P(E)=\frac{14}{36}=\frac{7}{18}\)

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Answer:

F

Step-by-step explanation:I just took the test

Answer:

\(x = \sqrt{ {16}^{2} + {21}^{2} } = \sqrt{256 + 441} = \sqrt{697} = 26.4\)

Answer:

She paid tax of £18240

Step-by-step explanation:

We are told that Carys earned £45600 before tax.

Now, from the question, the tax rate that applies is 40%. This is because she earned £45600 and we are told that earnings in excess of £43000 and up to £150000 taxed at a rate of 40%.

Thus;

Tax payable = 40% × 45600

Tax payable = £18240

Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

We fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean number of days before visible results begin to show is different between the three types of facial creams.

c. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance to support the claim that the mean number of days before visible results begin to show is different between the three types of facial creams.

To test the hypothesis, we use a one-way ANOVA test since we have three independent samples. The null hypothesis is that there is no difference in the mean number of days for the three creams, and the alternative hypothesis is that at least one of the means is different. We can perform the ANOVA test and obtain an F-statistic and p-value. If the p-value is less than our significance level of 0.025, we reject the null hypothesis.

Using statistical software or a calculator, we obtain an F-statistic of 1.52 and a p-value of 0.249. Since the p-value is greater than 0.025, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean number of days before visible results begin to show is different between the three types of facial creams.

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Answer:

Discount selling price= $172.5

Step-by-step explanation:

Giving the following information:

Selling price= $230

Discount rate= 25%

To calculate the discount selling price, we need to use the following formula:

Discount selling price= selling price*(1 - discount rate)

Discount selling price= 230* (1-0.25)

Discount selling price= $172.5

Answer:

44

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, we must solve for the parenthesis so...

-2x-8=4x+16

Then we must simplify this even more so lets add the 8 to 16

-2x=4x+24

Then we must subtract 4x from -2x

-6x=24

we must now divide 24 by -6 so we can isolate the x

x=-4

I hope this helped :)

Answer:

the successful candidate won the election with a 24% margin.

Step-by-step explanation:

With the infomation provided, first you need to find the total amount of votes by adding the number of votes that the successful candidate registered plus the number of votes that his nearest rival secured:

577,500+ 348,700=926,200

Next, you need to find the percentage of votes that the successful candidate registered and that the nearest rival secured by dividing the number of votes by the total amount of votes and multiplying the result for 100:

577,500/925,200=0.62*100=62%

348,700/926,200=38%

Now, you need to find the difference between both percentages to get the margin:

62%-38%=24%

According to this, the answer is that the successful candidate won the election with a 24% margin.

Answer:

The second choice is correct.

Step-by-step explanation:

As we go right on the number line, we are getting to larger and larger values.

D is greater than C because it is to the right of C, so the first choice is not correct.

The third choice is showing absolute value.  This is saying that the letters C and D are both the same distance from zero. They are not.

The last choice says that A is to the right of B and it is not.

The second choice that is B≥ C is correct.

The basics of this question requires us to read the number line perfectly

As we go right on the number line, we are getting to larger and larger values.

D is greater than C because it is to the right of C, so the first choice is not correct.

The third choice is showing absolute value.  This is saying that the letters C and D are both the same distance from zero. They are not.

The last choice says that A is to the right of B and it is not.

Thus option 2) is correct

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Answer:

0.533

Step-by-step explanation:

2/5

3/4

=2/15 4 simplify this and you get:

1/30

Decimal: 0.033333

The standard deviation of a beta distribution is calculated using the formula \(\(\sigma = \sqrt{\frac{\alpha \cdot \beta}{(\alpha + \beta)^2 \cdot (\alpha + \beta + 1)}}\),\) where \(\(\alpha\)\) and \(\(\beta\)\) are the parameters defining the shape of the distribution. It does not involve multiplying the sigma value by any fixed factor.

When calculating the standard deviation of a beta distribution, the denominator of the formula is not directly related to the sigma (standard deviation) parameter.

The standard deviation of a beta distribution depends on the alpha and beta parameters, which define the shape of the distribution.

The formula for the standard deviation of a beta distribution is:

\(\[ \sigma = \sqrt{\frac{\alpha \cdot \beta}{(\alpha + \beta)^2 \cdot (\alpha + \beta + 1)}} \]\)

Here, the standard deviation \((\(\sigma\))\) is calculated using the alpha and beta parameters of the beta distribution. It does not involve multiplying the sigma value by any particular factor or using a fixed denominator.

The denominator in the formula for the standard deviation of a beta distribution involves the alpha and beta parameters, which determine the shape and spread of the distribution.

It does not directly relate to the sigma value or involve multiplying sigma by a fixed factor.

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Answer: A=48 squared centimeters

Step-by-step explanation: First you need to find the area of the whole rectangle. Area equals length times width (9*8), which is 72. Next you find the area of the white region: 4*6=24. Finally, you subtract the smaller region from the whole: 72-24=48. BOOM: you got the exact right answer :)

Answer:

\( - 3 - 9 = - 3y \\ - 12 = - 3y \\ y = ( - 12) \div ( - 3) \\ y = 4\)

Answer:

k=3

Step-by-step explanation

1.)Group like terms 2+6k-18= -3k+11

2.)Add/Subtract the numbers 2-18=-16 6k-16= -3k+11

3.)Add 16 to both sides

4.)Simplify 6k=-3k+27

5.)Add 3k to both sides

6.)Simplify 9k=27

7.)Divide both sides by 9

8.)Simplify k=3

Answer: 215,820 ways

Step-by-step explanation:

There are 110 applicants for three cosmetology positions. How many different ways can the three positions be filled?

Number of positions = 110

Number of applicants = 3

Number of way in which the positions can be filled ;

This is a combination problem

nCr = n! ÷ (n-r)! r!

110C3 = 110! ÷ (110 - 3)! 3!

110C3 = 110! ÷ 107! 3!

110C3 = (110 * 109 * 108) / (3 * 2 * 1)

110C3 = 1294920 / 6

= 215820 ways

Answer:

Step-by-step explanation:

Given that:

Tip left = $1.30

Tax = 7%

Tip = 10% of after tax cost

The tax percentage is not needed in calculating the bill after tax and tip

Hence,

Let after tax cost = x

10% of x = 1.30

0.1x = 1.30

x = $13

After tax cost = $13

Hence, the Total bill after tax = $13

The probability that a model will be defective is 0.0975 (rounded to 3 decimal places). The given information is shown below: Model I - accounts for 75% of unit sales and has 7% defects. Model II - accounts for 25% of unit sales and has 18% defects. We need to find the probability that a model will be defective.

For that, we will use the formula:

Probability of Defects (D) = P(Model I) x P(D|Model I) + P(Model II) x P(D|Model II)Here,P(Model I)

= 75/100

= 0.75P(D|Model I)

= 7/100

= 0.07P(Model II)

= 25/100

= 0.25P(D|Model II)

= 18/100 = 0.18

Putting the given values in the above formula, we get:

Probability of Defects (D) = 0.75 x 0.07 + 0.25 x 0.18

= 0.0525 + 0.045

= 0.0975

Therefore, the probability that a model will be defective is 0.0975 (rounded to 3 decimal places).

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Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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If Johnny has g gumballs, then Tucker has 32 fewer gumballs than Johnny.

To represent the number of gumballs Tucker has, we can subtract 32 from the number of gumballs Johnny has (g):

Tucker's gumballs = g - 32

Therefore, the expression that shows how many gumballs Tucker has is g - 32.

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Answer:

D

Step-by-step explanation:

edge 2021

Answer:

46 + W = 231

Step-by-step explanation:

Answer:

My guess: 231 = 46 + b

Step-by-step explanation: Because they didn't mention how many were colored brown, we would use a variable to represent them, in this case I use b. But we do know 46 of them were white. so the equation would simply be 231 = 46 + b. After you add 46 and b you will get the total to 231. You can find b from subtracting 231 to 46. Then add b to 46 and get the total of 231

Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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The probability that a randomly selected board cut by the machine has a length greater than 89.09 inches is approximately 0.3821. the probability that the mean length of a sample of 38 boards is greater than 8909 inches is approximately 0.

To find the probability that a randomly selected board cut by the machine has a length greater than 89.09 inches, we can use the Z-score formula and the standard normal distribution.

(a) Calculate the Z-score:

Z = (X - μ) / σ

where X is the given length, μ is the mean, and σ is the standard deviation.

Z = (89.09 - 89) / 0.3

Z = 0.09 / 0.3

Z = 0.3

Now, we need to find the probability corresponding to this Z-score. Using a standard normal distribution table or a calculator, we can find the probability.

P(Z > 0.3) ≈ 0.3821

Therefore, the probability that a randomly selected board cut by the machine has a length greater than 89.09 inches is approximately 0.3821.

Please note that the result is rounded to four decimal places as requested.

(b) To calculate the probability that the mean length of a sample of 38 boards is greater than 89.09 inches, we need to use the Central Limit Theorem. Since the sample size is large (n > 30), the distribution of sample means will be approximately normal.

The mean of the sample mean (μX) will be equal to the population mean (μ), which is 89 inches.

The standard deviation of the sample mean (σX) can be calculated using the formula:

σX = σ / √n

where σ is the population standard deviation and n is the sample size.

σX = 0.3 / √38 ≈ 0.0488 (rounded to four decimal places)

Now, we calculate the Z-score for the sample mean:

Z = (X - μX / σX

where X is the given sample mean.

Z = (8909 - 89) / 0.0488 ≈ 180998.36 (rounded to two decimal places)

Again, using a standard normal distribution table or a calculator, we find the probability:

P(Z > 180998.36) ≈ 0

Therefore, the probability that the mean length of a sample of 38 boards is greater than 8909 inches is approximately 0.

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Answer:

D. 3.57

Step-by-step explanation: Edmentum

Answer:

(a) hundreds = 817

(b) hundredths = 817.09

(c) 3 d.p = 817.086

(d) 4 s.f. = 817.1

(e) whole number = 817

Answer:

i can teach you how to solve it on calculator if u want

The Celsius temperature that has the same value as when converted to a Fahrenheit temperature is -40

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

F = 9/5C + 32

The Celsius temperature that has the same value as F implies that

C = F

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

C = 9/5C + 32

So, we have

C - 9/5C = 32

Evaluate the like terms

-4/5C = 32

So, we have

C = -32 * 5/4

Evaluate

C = -40

Hence, the value of C is -40

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