ANSWER ASAP !! NEED HELP ASAP

Observe the pattern below. (The alternate numbers form a pattern)2, 3, 4, 6, 6, 9, 8, 12, 10, 15, 12, ….The next two numbers in the series:

18 , 14 ...

The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.

It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.

It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.

Therefore the arrival rate per hour is given by the following relation:

Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes

Given here,

No. of minutes in an hour = 60 minutes

Inter arrival time of the email taken in minutes = 2 minutes

∴ Arrival rate in 1 hr = 60 / 2

                                = 30 emails / hr

Hence the arrival rate is 30 emails per hour.

Now for finding out the service rate we have the following formula:

Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email

Given here,

No. of minutes in an hr = 60 minutes

No. of employes answering = 3

Average time that for writing response email = 2 minutes

∴ Service rate = 60 * 3 / 4

                       = 45 emails / hr

Hence the service rate is 45 emails per hour.

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The value of X is 1.318116071 radians

Given equation is 100 cos²X - 25 = 0.

We need to solve for X.

Step 1: Simplifying the equation100 cos²X - 25 = 0100 cos²X = 25cos²X = 25/100cos²X = 1/4

Step 2: Finding the angleTo find the angle we use the inverse cosine function.

It is given by;cos⁻¹(1/4) = 1.318116071 radians

Step 3: SolutionThus the value of X is 1.318116071 radians. Answer: X = 1.318116071

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The equation :

x = π/3 + 2πn, 2π/3 + 2πn, 4π/3 + 2πn, 5π/3 + 2πn

where n is an arbitrary integer.

To solve the equation 100cos²(x) - 25 = 0, we can start by isolating the cosine term:

100cos²(x) = 25

Divide both sides by 100:

cos²(x) = 25/100

Simplify the right side:

cos²(x) = 1/4

Taking the square root of both sides:

cos(x) = ±√(1/4)

cos(x) = ±1/2

Now, we need to find the values of x that satisfy this equation. Using the unit circle or reference angles, we can determine the solutions.

For cos(x) = 1/2, the solutions are x = π/3 + 2πn and x = 5π/3 + 2πn, where n is an arbitrary integer.

For cos(x) = -1/2, the solutions are x = 2π/3 + 2πn and x = 4π/3 + 2πn, where n is an arbitrary integer.

Combining all the solutions, we have:

x = π/3 + 2πn, 2π/3 + 2πn, 4π/3 + 2πn, 5π/3 + 2πn

where n is an arbitrary integer.

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The slope of a plot of ln k versus 1/t equal to: −E_a/R

The Arrhenius equation is one that describes the relation between the rate of reaction and temperature for many physical and chemical reactions.

Arrhenius equation is expressed as:

k = \(Ae^{-E_{a}/RT }\)

Taking natural log on both sides,

ln k = ln \(Ae^{-E_{a}/RT }\)

In k = In A - E_a/RT

In k = In A - (E_a/R * (1/T))

This equation is in the form of y = mx + c

The plot of ln k vs 1/T gives a straight line with negative slope.

Slope = −E_a/R

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Answer:

3

Step-by-step explanation:

First right out all the data in numerical order from left to right.

2, 2, 2, 3, 4, 5, 7

The median is the middle number in the set.  If there is an even amount of data points, find the average of the two middle numbers.  If there is an odd number of data points, like in this data set, just take the middle number as you median.

There are 7 data points in this set so the fourth number in the set written in numerical order would be your median.

When writing this set out in numerical order, repeated numbers must be repeated, we find that the fourth, or middle, number is 3.  Therefore, 3 is the median of this data set.

Answer:

\(\frac{8}{21}\)

Step-by-step explanation:

\(\frac{2}{7}\) ÷ \(\frac{3}{4}\)

to divide fraction, take the reciprocal of the second fraction and multiply it by the first fraction:

\(\frac{3}{4} = \frac{4}{3}\)

\(\frac{2}{7}\) × \(\frac{4}{3}\)

multiply like normal:

\(\frac{2}{7}\) × \(\frac{4}{3}\) = \(\frac{8}{21}\)

Answer:

8/21

Step-by-step explanation:

2/7 * 4/3 = 8/21

Answer:

3^2+4^2=5^2

Step-by-step explanation:

shown in the answer

Answer:

7.1

Step-by-step explanation:

area of a circle is pi times the radius squared

so divide the diameter by 2 to get the radius

then thats 1.5 so square that then multiply by pi

Answer:

ur answer is 7.1

Step-by-step explanation:

Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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Answer:

x=36.1

supplementary angle = 143.9 degrees

Step-by-step explanation:

angle: x

supplementary angle: 180-x

x = (180-x)-107.8

2x = 72.2

x = 36.1 degrees

180-x =  143.9 degrees

supplementary angle = 143.9 degrees

x measures 107.8 less than 180-x

x=180-x-107.8

x=72.2-x

Add x to both sides

2x=72.2

Divide both sides by 2

x=36.1

_________________________________

hope this helps, I just solved this so probably should get it fact checked.

To perform a statistically valid comparison of the two loader options, we can use simulation and common random numbers. We simulate the process over a 40-hour time horizon and compare the mean system response times for each loader option.

For the two slower loaders, we generate random numbers uniformly distributed between 1 and 27 minutes to represent the time taken to fill a truck. For the fast loader, we generate random numbers uniformly distributed between 1 and 19 minutes.

By simulating the process multiple times using the same set of random numbers (common random numbers), we can compare the mean system response times between the two loader options.

After running the simulation, we calculate the mean system response time for each loader option by averaging the response times of all trucks. We repeat the simulation multiple times (e.g., 100 or more) to obtain reliable estimates of the mean system response times.

Once we have the mean system response times for each loader option from multiple simulation runs, we can perform a statistical analysis to determine if there is a significant difference between the two options.

This analysis can be done using a suitable statistical test, such as a t-test or confidence interval analysis, depending on the distribution of the response time data and the assumptions made.

The statistical analysis will provide insights into whether the fast loader option significantly reduces the mean system response time compared to the slower loader options. A lower mean system response time would indicate better performance in terms of faster truck processing.

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The gradient of the curve at the point (3,9) is 21.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

To find the gradient of the curve at the point (3,9)

we need to differentiate the equation of the curve with respect to x, and then substitute x=3 to obtain the slope at that point.

y = x²(x - 2)

Differentiating both sides with respect to x, we get:

dy/dx = 3x² - 4x

Substituting x=3, we get:

dy/dx = 3(3)² - 4(3) = 9(3) - 4(3) = 21

Therefore, the gradient of the curve at the point (3,9) is 21.

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Work Shown:

\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-5\pm\sqrt{(5)^2-4(3)(-1)}}{2(3)}\\\\x = \frac{-5\pm\sqrt{37}}{6}\\\\x \approx \frac{-5\pm6.08276253}{6}\\\\x \approx \frac{-5+6.08276253}{6} \ \text{ or } \ x \approx \frac{-5-6.08276253}{6}\\\\x \approx \frac{1.08276253}{6} \ \text{ or } \ x \approx \frac{-11.08276253}{6}\\\\x \approx 0.18046042 \ \text{ or } \ x \approx -1.84712707\\\\x \approx 0.18 \ \text{ or } \ x \approx -1.85\\\\\)

I used the quadratic formula.

Visual confirmation is shown below. The solutions are the x coordinates of the x intercepts, aka roots. GeoGebra is another tool you can use if you prefer that over Desmos. Both are free apps.

Answer: 45

Step-by-step explanation:

2x² + (2-7)x - 12 = 0

2x² - 5x - 12 = 0

x = 5 ± √(5² - 4 × 2 × (-12) ) /(2×2) = (5 ± √121)/4

x = (5+11)/4 = 4 and x = (5-11)/4 = - 3/2

Answer:

\(\frac{4}{3} *\pi * r^{3}\)

r is radius of the sphere

Answer:

52

you take 5 ÷ it by 7 the ×it by 595

A ratio is an ordered pair of numbers a and b written as a/b where b is not equal to zero.

if the number of women in the social club is 595 then the number of men in the social club is 425.

A ratio is an ordered pair of numbers a and b written  as:

a / b where b does not equal 0.

A proportion is an equation in which two ratios are equal to each other.

We have,

The ratio of men to women:

= 5:7

= 5/7

Let,

The number of men = 5x

The number of women = 7x

Now,

If the number of women = 595

We have,

7x = 595

Multiplying both sides by 5/7 we get,

5/7 x (7x) = 5/7 x 595

5x = 5/7 x 595

5x = 5 x 85

5x = 425

This means if there are 435 men in the social club if the number of women is 595.

Thus if the number of women in the social club is 595 then the number of men in the social club is 425.

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The fraction of infants that are expected to have birth weights between 3210 g and 4480 g is 0.893.

The fraction of infants that are expected to have birth weights below 3210 g is 0.011.

The weight below which an infant will be included in the study is approximately 3151 g.

A standard normal distribution, also known as the Gaussian distribution or the z-distribution, is a specific type of probability distribution. It is a continuous probability distribution that is symmetric, bell-shaped, and defined by its mean and standard deviation.

In a standard normal distribution, the mean (μ) is 0, and the standard deviation (σ) is 1. The distribution is often represented by the letter Z, and random variables that follow this distribution are referred to as standard normal random variables.

The probability density function (PDF) of the standard normal distribution is given by the formula:

f(z) = (1 / √(2π)) * e^(-z^2/2)

where e represents the base of the natural logarithm (2.71828) and π is a mathematical constant (3.14159).

The z-score of an infant who weighs 4584 g can be calculated as follows: Since the mean is 3432 g and the standard deviation is 482 g, the z-score is given by;(4584 - 3432) / 482 = 2.39

Therefore, the z-score of an infant who weighs 4584 g is 2.39.

Approximate fraction of infants with birth weights between 3210 g and 4480 g can be calculated as follows: The standard normal distribution will be used to find this fraction. The z-scores for 3210 g and 4480 g can be computed by;(3210 - 3432) / 482 = -2.3 and (4480 - 3432) / 482 = 2.18

The fraction can be found by subtracting the areas below the curve corresponding to the z-score 2.18 from the area corresponding to the z-score -2.3. That is; Approximately 0.893 is the fraction of infants that are expected to have birth weights between 3210 g and 4480 g.

Approximately what fraction of infants would you expect to have birth weights below 3210 g? Since the mean is 3432 g and the standard deviation is 482 g, the z-score is given by;(3210 - 3432) / 482 = -2.3

The area to the left of this z-score can be obtained from a standard normal distribution table or by using technology. This is approximately 0.0107. Therefore, approximately 0.011 is the fraction of infants that are expected to have birth weights below 3210 g.

Below what weight must an infant's birth weight be in order for the infant to be included in the study ?The lowest 17% of birth weights will be included in the study, so the birth weight must be less than or equal to the 17th percentile. The z-score corresponding to the 17th percentile can be found from the standard normal distribution table or by using technology.

It is approximately -0.17. The weight corresponding to this z-score can be calculated as follows;

(-0.17 x 482) + 3432 = 3151 g

Therefore, the weight below which an infant will be included in the study is approximately 3151 g.

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Answer: A. 0.25

Step-by-step explanation:

You need to divide 40 by 160 to calculate the percentage.

The probability of X being between 6 and 8 is 0.1747. The probability of X being greater than 4 is 0.5987. The probability of X being less than 2 is 0.2266.

These probabilities provide insights into the likelihood of X falling within specific ranges or exceeding certain values based on its distribution characteristics.

a. To find P(6≤X≤8), we need to calculate the cumulative probability between the values 6 and 8 using the given mean and standard deviation.

Using the standard normal distribution, we can standardize the values by subtracting the mean from each value and dividing by the standard deviation.

Z1 = (6 - 5) / 4 = 0.25

Z2 = (8 - 5) / 4 = 0.75

Then, we can use a standard normal distribution table or a calculator to find the probabilities associated with these standardized values.

P(6≤X≤8) = P(0.25 ≤ Z ≤ 0.75)

From the standard normal distribution table, we can find the corresponding probabilities:

P(Z ≤ 0.75) = 0.7734

P(Z ≤ 0.25) = 0.5987

Therefore, P(6≤X≤8) = P(0.25 ≤ Z ≤ 0.75) = P(Z ≤ 0.75) - P(Z ≤ 0.25) = 0.7734 - 0.5987 = 0.1747.

b. To find P(X > 4), we again standardize the value of 4 and calculate the probability associated with it.

Z = (4 - 5) / 4 = -0.25

Using the standard normal distribution table or a calculator, we can find P(Z > -0.25) = 1 - P(Z ≤ -0.25).

From the standard normal distribution table, P(Z ≤ -0.25) = 0.4013.

Therefore, P(X > 4) = 1 - P(Z ≤ -0.25) = 1 - 0.4013 = 0.5987.

c. P(X < 2) can be calculated by standardizing the value of 2 and finding the probability associated with it.

Z = (2 - 5) / 4 = -0.75

Using the standard normal distribution table or a calculator, we can find P(Z < -0.75).

From the standard normal distribution table, P(Z < -0.75) = 0.2266.

Therefore, P(X < 2) = P(Z < -0.75) = 0.2266.

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Answer:

Please check the explanation.

Step-by-step explanation:

Given

C=24x+80

R=44x

To determine

What is the break-even point?

Given that

C represents the cost in dollars

R represents the revenue in dollars.

At the break-even point Cost (C) equals Revenue (R), so

R = C

44x = 24x+80

44x-24x = 80

20x = 80

divide both sides by 20

20x/20 = 80/20

x = 4

Thus, at x = 4 the value of Cost (C) equals Revenue (R).

i.e.

C = 24x+80 = 24(4)+80 = $176

R = 44x = 44(4) = $176

Answer:

(4, 176)

Step-by-step explanation:

Cause im smart and its right :3

To guarantee having at least 3 animals of the same type, you would need to adopt a total of 5 animals.

In the worst-case scenario, you would first adopt 2 cats and 2 dogs. By adopting a 5th animal, you would then have at least 3 animals of the same type, either 3 cats and 2 dogs, or 3 dogs and 2 cats. This is due to the Pigeonhole Principle, which states that if you have n categories and n+1 items, at least one category will contain more than one item.

In order to guarantee having at least 3 cats, you would need to adopt a total of 13 animals. This is because, in the worst-case scenario, you could first adopt all 10 dogs, followed by 3 cats. After adopting 13 animals, you would be certain to have at least 3 cats, as you would have exhausted the entire population of dogs in the shelter.

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Answer:

Step-by-step explanation:

Law of Sines  recall   Sin(A) /a  = Sin(B) /b  

does the above make sense?

Next we need to find  the angle of A

notice that 16+75=91  :o

so angle A is only 89° ..(b/c all the way around then inside of a triangle is 180)  so this is NOT a right triangle but that's okay, b/c law of sines still works fine.

then we want to find length of line AB

and if 89 = A  then a = BC

and if  75 = B the  b = AB (note that in the given triangle this is angle C, i'm using B , b/c you can see the difference between capital B and  lower case b much easier than you can with C, & c  :/   )

capitals are the angles while lower case are the length of the sides

then

Sin(89) / 29 = Sin(75) / b

solve the parts that can be put into numbers or solve for 'b' first, that means isolate 'b' all by itself on one side of the equal sign .

0.034477 = 0.965925/ b

b = 0.965925 / 0.034477

b = 28.0165

b = 28.0 ( to the nearest 10th)

we have the parts to plug in now

Sin(75) /

Answer:

top right one

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

The derivative of the function y = x(6x + 1)⁵ is: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴

To find the derivative of the given function, we can apply the rules of differentiation. Using the product rule, we differentiate each term separately and then add them together.

For the first term x, the derivative is simply 1.

For the second term (6x + 1)⁵, we apply the chain rule. The derivative of (6x + 1)⁵ with respect to x is 5(6x + 1)⁴ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get (6x + 1)⁵ * 6 = 6(6x + 1)⁵.

For the third term x(6x + 1)⁴, we again apply the product rule. The derivative of x is 1, and the derivative of (6x + 1)⁴ is 4(6x + 1)³ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get x * 4(6x + 1)³ * 6 = 24x(6x + 1)³.

Finally, we add the derivatives of each term to get the derivative of the entire function: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴.

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Complete question:

Use the rules of differentiation to find the derivative of the function y= x(6x + 1)⁵

(6x + 1)⁵ + 30x(6x + 1)⁴

(6x + 1)⁴ (36x + 1)

x-1/6

No correct answer provided.

The study found that preschoolers in the grasp and baseline conditions recognized the actor who hid the ball as the one with knowledge of its location, suggesting that pointing gestures influenced their judgments.

In this study, 48 preschoolers participated, ranging in age from 3 years 6 months to 4 years 5 months, with an equal distribution of 24 boys and 24 girls. The children watched a video featuring two female actors seated side by side.

The actors engaged in a task where they hid a ball under one of four cups, while the other actor covered her eyes and turned around. A small barrier was placed in front of the cups, preventing the children from seeing the specific cup where the ball was hidden.

In the grasp condition, the actors simultaneously grasped the tops of different cups.

The baseline condition served as a comparison, where the actors simply sat with their hands in their laps. After the actors performed the gestures or remained in the baseline condition, the video was paused, and the children were asked, "Who knows where the ball is?"

The results showed that children in the grasp and baseline conditions selected the actor who hid the ball as the one who knew its location more frequently than would be expected by chance.

In contrast, children in the point condition performed at chance level, indicating the hider on just 2.13 out of 4 trials

An analysis of variance revealed a significant effect of condition, suggesting that the pointing gesture influenced the children's judgments.

The possibility that children in the point condition ignored the test question and instead reflexively indicated where they would search for the ball was considered.

The results showed that children correctly indicated the hider more often than expected by chance, indicating that they were not simply responding to the pointing gesture.

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Answer:

w=4

Step-by-step explanation: