Question 1 3 pts F = (AB)'(A+B+C)' is equivalent to:
O C
O A'+B'
O A'B'C'
O A'+B'+C'
O None of the above

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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Answer:

A (-2,1) B(3,3)

C(1,-1) D(4,1)

For

A&B: m=2/5

C&D: m=2/3

Answer:

I can't see the images so if you can attach a link i will do it

Step-by-step explanation:

Let b be the price of the bath towels and h be price of the hand towels. For Helen, we can write the following equation

And for Althea, we have

Then, we have 2 equations in 2 unknowns. By multipliying the first equation by -2, we have the following equivalent system of equation

By adding both equations, we have

Then, b is given by

Therefore, 1 bath towel cost $12, which corresponds to option 3

Answer:16X + 24 D

Step-by-step explanation:

Length of rectangle = 3(2X + 3) = 6X +9

Width = 2X + 3

Perimeter = 2(Lengtb + Breadth)

= 2(6X +9) + 2(2X +3)

(a) Coefficient of determination, R² = 0.911.R² = 0.911 tells us that 91.1% of the variation in sales is explained by the variation in total square footage. The remaining 8.9% of the variation is unexplained and is due to other factors or to sampling error. Thus, option A is correct.

(b) We have to find the standard error of estimate, se.s = sqrt[ Σ(y - ŷ)² / (n - 2) ]s = sqrt[ Σ(y - mx - b)² / (n - 2) ]Substitute the values in the above formula,s =

sqrt[ Σ(y - mx - b)² / (n - 2) ]s = sqrt[ Σ(y² - 2xyŷ + ŷ²) / (n - 2) ]s = sqrt[ Σy² - 2ŷΣy + Σŷ² / (n - 2) ]s = sqrt[ Σy² - 2(mΣx + bΣx)Σy + (m²Σx² + 2mbΣx + nb²) / (n - 2) ]s =

sqrt[ Σy² - 2(mΣx + bΣx)Σy + m²Σx² + 2mbΣx + b² / (n - 2) ]

On substituting the values, we get,s = 83.290Therefore, the standard error of estimate is 83.290 billion dollars. Hence, option B is correct.How can the standard error of estimate be interpreted?B. The standard error of estimate of the sales for a specific total square footage is about se billion dollars.

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Answer:

40.5

Step-by-step explanation:

i would recommend changing the 90% into a decimal

90% ⇒  .90

then now you can just multiply .90x45

.90x45=40.5

Answer:

40.5

Step-by-step explanation:

The answer is 40.5!

Hope this helps!

Answer:

x=1

Step-by-step explanation:

it is

Answer: 2 5/6 I think.

Wait no. I just did the math and it would be 2 1/2

Answer:

Its 12.5 squares eric deleted my answer!

Step-by-step explanation:

Answer: B. 13

Step-by-step explanation: On Edge!!!!

The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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Answer:

\(a = b\sqrt{5} - 8\sqrt{5}\\b = -8 - \frac{a\sqrt{5}}{5}\)

Step-by-step explanation:

working attached

Answer:

\(\frac{21}{2}\)

Step-by-step explanation:

Given

a₁ = 6

a₂ = 12 , then

a₃ = \(\frac{6+12}{2}\) = \(\frac{18}{2}\) = 9 ← an integer

a₄ = \(\frac{12+9}{2}\) = \(\frac{21}{2}\) ← not an integer

Thus the fourth term is not an integer

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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First lets define what is the equation of a line:

equation of a line is

y=mx +b

So, equation in slope intercept form would be y=mx +b

To calculate the slope m we would have to use the points (2, -1) and (-3,-1)​ and calculate the following formula:

slope= y2-y1/x2-x1

slope=-1+1/-3-2

slope=0

Therefore, equation in slope intercept form would be for points x -1 and y -1 would be:

-1=0*-1 + b

-1=b

Hence, y= -1

A sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion.

To calculate the required sample size, we can use the formula:

n = (\(z^2\) * p * q) /\(e^2\)

where n is the sample size, z is the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence), p is the estimated population proportion (0.165, based on the NWBC's finding), q is 1-p, and e is the maximum error we want to tolerate (in this case, 0.06 or 6 percentage points).

Substituting the values, we get:

n = (2.576^2 * 0.165 * 0.835) / \(0.06^2\)

Solving for n, we get:

n ≈ 329

Therefore, a sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion. Note that this assumes a simple random sample and that the population size is much larger than the sample size, so the finite population correction is not needed.

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Answer:

A (7,2)

Solution is in the photo :)

Answer:

18.

Step-by-step explanation:

3 x 6 = 18. He eats 3 slices every 5 minutes so 5 minutes x 6 is half an hour. so 18 is your answer.

If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

The Linear equation in one variable is an algebraic equation of degree one.

it can be expressed in the form of Ax +B = 0 where x is a variable, and A and B are two integers.

Takaya can eat three slices of pizza in five minutes.

for half an hour it would be 6 times five minutes.

So, in half an hour Takaya can eat 3 × 6 = 18

Therefore, If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

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Answer:

The first one is 6√10

The second one is −48√3

The last one is 28√2

Step-by-step explanation:

The actual distance between the two cities is 288 miles.

A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio.  This means that the scale drawing of the two cities would be smaller than the actual cities.

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.

The actual distance between the two cities = (3 x 24) ÷ 1/4

= 3 x 24 x 4 = 288 miles

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Answer:

The average GPA would be 1.8

Step-by-step explanation:

Hope this is helpful. I did a test like this exact question and I got it right.

Using correlation coefficients, it is found that the value of r is greater than 0 and close to 1, as the scatter-plot is increasing linearly.

Researching the problem on the internet, it is found that the relation is modeled by an increasing scatter-plot, hence r > 0. There are very few points in which there are oscillations, which indicate a strong relationship, hence r is closer to 1.

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You get D(7, -3) and D'(2, 5).

So apply the transformation rule

D'(x,y) → D(x-5, y+8) .

Then

x=7 → x=7-5 = 2

y=-3 → y=-3+8 = 5

Answer:

D (x-5, y+8) → D'

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The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.

Two important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.

The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.

Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.

Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}

On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.

Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.

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The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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The value of n that makes the sixth term in the expansion contains x²⁵ is n = 5.

What is binomial expansion?

The binomial theorem (or binomial expansion) is a result of expanding the powers of binomials or sums of two terms. The coefficients of the terms in the expansion are the binomial coefficients (kn).

The general term in the binomial expansion of (a + b)ⁿ is given by:

\(T(r+1) = (n \, choose \, r) * a^{(n-r)} * b^r\)

where "n choose r" represents the binomial coefficient, which is given by:

(n choose r) = n! / (r! * (n-r)!)

In this case, a = 2/x² and b = -5x⁵. We want to find the value of n such that the sixth term in the expansion contains x²⁵.

To find the term that contains x²⁵, we need to set the exponent of x in the general term equal to 25 and solve for r:

(n-r) = 25

n = r + 25

The exponent of x in the general term is given by:

\((2/x^2)^{(n-r)} * (-5x^5)^r = 2^{(n-r)} * (-5)^r * x^{(5r - 2(n-r))}\)

Setting 5r - 2(n-r) = 25, we get:

7r - 2n = 25

We know that the sixth term has r = 5, so we can substitute this into the equation:

7(5) - 2n = 25

35 - 2n = 25

2n = 10

n = 5

Therefore, the value of n that makes the sixth term in the expansion contains x²⁵ is n = 5.

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Answer:

ax^2 + bx + c = 0

Step-by-step explanation:

The approximate value of the probability of three or more errors in 106 digits by using the Poisson distribution approximation is 0.393.

Given data; Error probability, p = 10^(-6) Probability of no error in 10^6 digits, P(no error) = 1 - p = 1 - 10^(-6) = 0.999999

The exact value of the probability of three or more errors in 10^6 digits;

Using binomial distribution; Total number of trials, n = 10^6Probability of success, p = 10^(-6)

Probability of failure, q = 1 - p = 1 - 10^(-6) = 0.999999

The random variable x = number of errors in n trials = 0, 1, 2, 3, .... , n

The probability mass function of the binomial distribution is;

P(x) = ( nCx ) * (p^x) * (q^(n-x))

Where, nCx = n! / x! (n-x)!

P(3 or more errors) = P(x ≥ 3) = P(x = 3) + P(x = 4) + P(x = 5) + ..... + P(x = n)P(x = 3) = ( 10^6 C 3 ) * (10^(-6))^3 * (0.999999)^10^6-3P(x = 4) = ( 10^6 C 4 ) * (10^(-6))^4 * (0.999999)^10^6-4P(x = 5) = ( 10^6 C 5 ) * (10^(-6))^5 * (0.999999)^10^6-5......P(x = n) = ( 10^6 C n ) * (10^(-6))^n * (0.999999)^10^6-n

To find this probability, we need to evaluate these probabilities. But evaluating such a large number of probabilities is a very difficult task. So, we use Poisson distribution to approximate this binomial distribution. Approximate value of the probability of three or more errors in 10^6 digits by using the Poisson distribution approximation;

In Poisson distribution, λ = np

The random variable x = number of errors in n trials = 0, 1, 2, 3, ....

The probability mass function of Poisson distribution is;

P(x) = ( e^(-λ) ) * (λ^x) / x!

Here,

λ = np = 10^6 * 10^(-6) = 1P(x ≥ 3) = P(x = 3) + P(x = 4) + P(x = 5) + .....P(x) = ( e^(-1) ) * (1^x) / x!P(x = 3) = ( e^(-1) ) * (1^3) / 3! = 0.0613201P(x = 4)

= ( e^(-1) ) * (1^4) / 4! = 0.0153300P(x = 5) = ( e^(-1) ) * (1^5) / 5! = 0.003065662......P(x ≥ 3) = 0.0613201 + 0.0153300 + 0.003065662 + .....

= 1 - {P(x = 0) + P(x = 1) + P(x = 2)}

= 1 - [ ( e^(-1) ) * (1^0) / 0! + ( e^(-1) ) * (1^1) / 1! + ( e^(-1) ) * (1^2) / 2! ]

= 1 - [ ( 1 / e^1 ) + ( 1 / e^1 ) + ( 1 / 2e^1 ) ]

= 1 - [ ( 2 + 1 ) / 2.7183 ]

= 1 - 0.607

= 0.393 (approx.)

Therefore, the approximate value of the probability of three or more errors in 106 digits by using the Poisson distribution approximation is 0.393.

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