If variance of the data a, b, c, ta, e is 2032 , then variance of 3a+2,3b+2, 3c+2,3d+2,3c+2, is :

Answers

Answer 1

The variance of 3a+2,3b+2, 3c+2,3d+2,3c+2, is 3657.6.

What is Variance?

Variance is a statistical measurement of the variation in numbers within a data set. Variance, in more precise terms, indicates how far apart any number in the set is from both the mean (average) and, consequently, from every other number in the set.

First, we can calculate the mean of the original dataset:

Mean = (a + b + c + ta + e) / 5

Then, we can calculate the variance using the formula:

Variance = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5

Given that the variance of the original dataset is 2032, we can substitute this value in the formula and solve for the mean:

2032 = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5

Simplifying this equation, we get:

(a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)² = 10160

Now, we can apply the transformation to the dataset by adding 2 and multiplying by 3:

New dataset: 3a + 2, 3b + 2, 3c + 2, 3d + 2, 3e + 2

To find the variance of the new dataset, we follow the same steps as before:

Mean = (3a + 2 + 3b + 2 + 3c + 2 + 3d + 2 + 3e + 2) / 5 = 3Mean + 2

Variance = ((3a + 2 - Mean)² + (3b + 2 - Mean)² + (3c + 2 - Mean)² + (3d + 2 - Mean)² + (3e + 2 - Mean)²) / 5

Simplifying this equation, we get:

Variance = ((3a - 3Mean)² + (3b - 3Mean)² + (3c - 3Mean)² + (3d - 3Mean)² + (3e - 3Mean)²) / 5

Variance = 9((a - Mean)² + (b - Mean)² + (c - Mean)² + (d - Mean)² + (e - Mean)²) / 5

Variance = 9(2032) / 5

Variance = 3657.6

Therefore, the variance of the new dataset is 3657.6.

To learn more about Variance, visit the link:

https://brainly.com/question/25639778

#SPJ1


Related Questions

A manager must choose five employees from a pool of 17 people to
take a survey. How many different ways can the CEO choose these
people?

Answers

There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.

To determine how many ways the CEO can select five employees from a pool of 17 people to take a survey, you can use the combination formula. The combination formula is nCr = n!/r!(n-r)! where n is the total number of items to choose from, and r is the number of items to choose.

In this case, n = 17 and r = 5.Using the combination formula: n Cr = 17C5= 17!/5!(17-5)!= 6188 There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.

Learn more about CEO

brainly.com/question/30163830

#SPJ11

NEED QUICK! WILL GIVE BRAINLIEST!!!

Find [g•f](x) for f(x) = 2x+5 and g(x) = x² - 3.

Show all work.

Answers

Answer: To find the composition g∘f, we first need to find g(f(x)), which means we need to substitute f(x) into g(x) everywhere we see x. So we have:

g(f(x)) = g(2x+5) = (2x+5)^2 - 3

Expanding the square, we get:

g(f(x)) = (4x^2 + 20x + 25) - 3

Simplifying, we get:

g(f(x)) = 4x^2 + 20x + 22

Therefore, the composition g∘f is equal to 4x^2 + 20x + 22.

Step-by-step explanation:

Write a linear equation to represent the line shown on the graph.

Answers

A linear equation to represent the line shown on the graph is given as:

y = 2x - 2.

Explain about the slope-intercept form?Given basic coordinates from two points on the line, use the slope equation to find the slope of the line. The slope formula, or the ratio of the change there in y values to the change in the x values, is m=(y2-y1)/(x2-x1).The initial point's coordinates are x1 and y1, respectively. The second points' coordinates are x2, y2.

General point-slope form is:

y = mx + c

(x1, y1) = (3, 2)

y intercept = -2

m = (2 + 2)/(2 - 0)

m = 2

y = 2x + (-2)

y = 2x - 2

Thus,  a linear equation to represent the line shown on the graph is given as: y = 2x - 2.

Know more about point-slope form

https://brainly.com/question/6497976

#SPJ1

The correct question is-

Write a linear equation to represent the line shown on the graphs shown by question 7.

a catering service offers 7 appetizers, 5 main courses, and 12 desserts. a customer is to select 4 appetizers, main 3 courses, and 6 desserts for a banquet. in how many ways can this be done?

Answers

In  323,400 ways it can be done by using the Combination formula.

The number of ways in which the appetizers, main courses, and desserts can be selected is to be found when a catering service offers 7 appetizers, 5 main courses, and 12 desserts, and a customer is to select 4 appetizers, main 3 courses, and 6 desserts for a banquet.

Let's find the number of ways to choose 4 appetizers from the 7 available:

= ⁷C₄ ⇒ 35 ways (using combinations).

Let's find the number of ways to choose 3 main courses from the 5 available:

= ⁵C₃ ⇒ 10 ways (using combinations).

Let's find the number of ways to choose 6 desserts from the 12 available:

= ¹²C₆ ⇒ 924 ways. (using combinations).

Therefore, the total number of ways in which the customer can select 4 appetizers, 3 main courses, and 6 desserts is:

35 × 10 × 924 ⇒ 323,400 ways.

To know more about the "combination": https://brainly.com/question/4658834

#SPJ11

Aiden estimates that the length of a piece of rope is 8. 5 inches. If it’s actual length is 7. 1 inches , what is the percent error of Aidens estimate ? Round to the nearest tenth if necessary

Answers

Aiden's estimated the length of a piece of rope as 8.5 inches, while its actual length is 7.1 inches. Therefore, the percent error of Aiden's estimate is 11.3%.

To calculate the percent error, you first need to find the difference between the actual length and the estimated length. Subtract 7.1 inches from 8.5 inches and you get 1.4 inches. This is the difference between the two lengths.
Next, divide the difference by the actual length and multiply by 100. The equation is: (difference/actual length) * 100. So, (1.4/7.1)*100 = 11.3%. Therefore, the percent error of Aiden's estimate is 11.3%.
It is important to be accurate when making measurements and estimates. A small difference in numbers can lead to a large error in the final result. Knowing the percent error can help you to improve your measurements and estimates and achieve greater accuracy.

For more such percent error related questions

https://brainly.com/question/5493941

#SPJ11

Please Help!! A Ferris wheel ride varies sinusoidally. When loading, people are 4 feet above the ground. The radius of the Ferris wheel is 60 feet. The ride takes 4 minutes to complete one revolution. if a person starts the ride 10 feet off the ground, give the cosine function of the ride.

f(x)=Acos(Bx-C)+D

I have found:

A=60

Period=4

B=π/2

I cannot find C and D.

Answers

Step-by-step explanation:

To find C and D, we can use the given information about the initial position of the person on the ride.

When the person starts the ride, they are 10 feet off the ground. This means that the cosine function has a vertical shift of 10 units, so we have:

f(x) = Acos(Bx - C) + D = 60cos(π/2x - C) + D

At the start of the ride, when x = 0, f(x) = 10. Substituting these values, we get:

10 = 60cos(-C) + D

Simplifying, we get:

D = 10 - 60cos(-C)

We can also use the fact that the minimum height of the ride is 4 feet above the ground. This means that the cosine function has a vertical shift of 4 units, so we have:

f(x) = Acos(Bx - C) + D = 60cos(π/2x - C) + D

At the lowest point of the ride, when x = 1/4, f(x) = 4. Substituting these values, we get:

4 = 60cos(π/8 - C) + D

Substituting D = 10 - 60cos(-C) from the first equation, we get:

4 = 60cos(π/8 - C) + 10 - 60cos(-C)

Simplifying, we get:

cos(-C) = (4 - 10 - 60cos(π/8 - C))/(-60)

cos(-C) = (3cos(π/8 - C) - 1)/2

Using the identity cos(-x) = cos(x), we can rewrite this as:

cos(C) = (3cos(π/8 - C) - 1)/2

Solving for C numerically, we get:

C ≈ 0.438

Substituting this value of C and D = 10 - 60cos(-C) into the equation for f(x), we get:

f(x) = 60cos(π/2x - 0.438) + 10 + 60cos(0.438)

Calculate the Total amount that Theo has to pay back if she takes the loan

Answers

If Theo takes the loan R9000 that is payable over 48 months monthly installment =R 318,92, the total amount that Theo has to pay back for the loan is R15,307.16.

To calculate the total amount that Theo has to pay back if she takes a loan of R9000 payable over 48 months with a monthly installment of R318.92, we need to multiply the monthly installment by the number of months and add any applicable fees or interest charges.

First, let's calculate the total amount that Theo will pay for the loan over the 48-month period:

Total amount = Monthly installment x Number of months

Total amount = R318.92 x 48

Total amount = R15,307.16

To learn more about loan click on,

https://brainly.com/question/30873604

#SPJ4

Complete question is:

Calculate the total amount that Theo has to payback if she takes the loan R9000 that is payable over 48 months monthly installment =R 318,92

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 16, negative 1, 2, negative 1, negative 4, negative 1.
Analyze the table of values for the continuous function, f(x), to complete the statements.

A local maximum occurs over the interval

A local minimum occurs over the interval
________

Answers

We can say that after answering the offered question Therefore, the equation constant of proportionality in this scenario is 11.25.

What is equation?

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

As a result, the proportionality constant in this scenario is 11.25.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

Therefore, the constant of proportionality in this scenario is 11.25.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The height of a triangle is 3 inches less than twice the length of its base. If the total area of the triangle is 7 square inches, find the length of the base and height.

Answers

Answer:

Let x be the length of the base of the triangle, then the height h is given by h = 2x - 3 (since the height is 3 inches less than twice the length of the base).

The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. We are given that the total area of the triangle is 7 square inches, so we can write:

(1/2)(x)(2x - 3) = 7

Multiplying both sides by 2 to eliminate the fraction, we get:

x(2x - 3) = 14

Expanding the left side, we get:

2x^2 - 3x = 14

Subtracting 14 from both sides, we get:

2x^2 - 3x - 14 = 0

We can now use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac))/(2a)

where a = 2, b = -3, and c = -14. Plugging in these values, we get:

x = (-(-3) ± sqrt((-3)^2 - 4(2)(-14)))/(2(2))

= (3 ± sqrt(169))/4

= (3 ± 13)/4

Taking the positive value for x (since the length of the base must be positive), we get:

x = (3 + 13)/4

= 4

Therefore, the length of the base is 4 inches. To find the height h, we can use the formula h = 2x - 3:

h = 2(4) - 3

= 5

So the height of the triangle is 5 inches.

Baseball pitcher is employing a ballistic pendulum to determine the speed of his fastball. A 3. 3-kg lump of clay is suspended from a cord 2. 0 m long. When the pitcher throws his fastball aimed directly at the clay, the ball suddenly becomes embedded in the clay and the two swing up to a maximum height of 0. 080 m. If the mass f the baseball is 0. 21 kg, find the speed of the pitched ball

Answers

The solution to the given problem of speed comes out to be v=21.12m/s.

How quickly something is moving is measured by its speed at a distance. How far an object moves in one unit of time is determined by its speed. Speed is calculated as follows: speed = distance * time. The most widely used speed measurement units are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given :  A 2.0 m long cord is supporting a 3.3 kg lump of clay.

Two swing up to an absolute maximum of 0.080 meters

Ball and clay's subsequent impact velocity

=>√(2*10*0.08)=1.264m/s

To find the velocity of the ball before collision

0.21*v=(3.3+0.21)*1.264

v=21.12m/s

Therefore, the solution to the given problem of speed comes out to be v=21.12m/s.

To know more about speed, visit

brainly.com/question/2004627

#SPJ4

1. Explain what Marc did in steps 4 and 5.

2. Why did he do this?

3. Create your own radical equation and explain how to solve it.

4. Is there an extraneous solution to your equation?

Answers

A radical equation is √(x + 2) = 4 - x and the extraneous solution is x = 7

Explaining step 4 and 5, and why it is done

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

The solution to a radical equation

In step 4 and 5, we have

x = ∛5 * 5 * 5 * 5

x = 5∛5¬ * 5¬ * 5¬ * 5

The above steps are carried out because it would simplify the radical expression to its simplest form

The reason it is done is to have the value of x in its simplest form

Create a radical expression

Here's an example of a radical equation:

√(x + 2) = 4 - x

Square both sides

x + 2 = 16 - 8x + x^2

Evaluate the like terms

x^2 - 9x + 14 = 0

Factor the quadratic equation

(x - 2)(x - 7) = 0

Solve for x:

x = 2 or x = 7

Is there an extraneous solution to your equation?

For x = 2:

√(2 + 2) = 4 - 2

√4 = 2

2 = 2

This is true, so x = 2 is a valid solution.

For x = 7:

√(7 + 2) = 4 - 7

√9 = -3

3 = -3

This is not true, so x = 7 is not a valid solution.

So, there is an extraneous solution

Read more about radical equation at

https://brainly.com/question/26637176

#SPJ1

On Aurora Ave the distance between Thomas St to Denny Way is 0.2 miles.

What is the distance between these two streets on Broad St?
Show your work below and round your answer to the nearest tenth of a mile.

Answers

The distance between these two streets on Broad St 0.2 miles.

We must apply the idea of comparable triangles to this issue in order to find a solution. Assume that Thomas St. and Denny Way. are separated by x miles on Broad St. Then, we can establish the ratio shown below:

0.2 miles on Aurora Avenue equals x miles on Broad Street

By cross-multiplying and simplifying, we may find the value of x:

Distance on Aurora Ave / (x * 0.2 miles) on Broad St

Broad Street distance is equal to (x * 0.2 miles)/0.2 miles. (since the distance on Aurora Ave is given as 0.2 miles)

Broad Street: distance = x

As a result, Thomas St. and Denny Way are separated by x miles, or 0.2 miles, on Broad St. Thus, the response is:

Distance between Thomas St and Denny Way on Broad St = 0.2 miles (rounded to the nearest tenth of a mile)

For such more question on distance:

https://brainly.com/question/28551043

#SPJ11

A bridge is 440 metres long. There are four parts to the bridge. Assuming
each part is the same length, how long is each part of the bridge?

Answers

Each part is 110 meters long.

One yoar consumars spent an avernge of $21 on a mead at a testurant. Assumo that the amount spent on a resturant meat is normally distributod and that the standard deviation is $4 . Complete parts (a) through (c) bolow a. What is the probability that a randomly selected person spent more than $24? P(X>$24)= (Round to four decimal places as needed.) b. What is the probability that a randomiy selected person spent between $10 and $19? P($10

Answers

a)  The probability of finding a value greater than $24 is given by:P(X > $24) = P(Z > (24 - 21) / 4) = P(Z > 0.75)Using the standard normal distribution table, we can find that P(Z > 0.75) = 0.2266.Rounding this result to four decimal places, we have:P(X > $24) = 0.2266.

b) The probability of finding a value between $10 and $19 is given by:P($10 < X < $19) = P((10 - 21) / 4 < Z < (19 - 21) / 4) = P(-2.75 < Z < -0.5)Using the standard normal distribution table, we can find that P(-2.75 < Z < -0.5) = P(Z < -0.5) - P(Z < -2.75) = 0.3085 - 0.0030 = 0.3055.Rounding this result to four decimal places, we have:P($10 < X < $19) = 0.3055.

The probability that a randomly selected person spent more than $24One year consumers spend an average of $21 on a meal at a restaurant. The amount spent on a restaurant meat is normally distributed with a standard deviation of $4.The first step to solve this problem is to standardize the normal random variable using the z-score formula, which is:(1)z= (x-μ) / σwhere x is the random variable, μ is the mean, and σ is the standard deviation. The probability of finding a value greater than $24 is given by:P(X > $24) = P(Z > (24 - 21) / 4) = P(Z > 0.75)Using the standard normal distribution table, we can find that P(Z > 0.75) = 0.2266.Rounding this result to four decimal places, we have:P(X > $24) = 0.2266.

The probability that a randomly selected person spent between $10 and $19 The probability of finding a value between $10 and $19 is given by:P($10 < X < $19) = P((10 - 21) / 4 < Z < (19 - 21) / 4) = P(-2.75 < Z < -0.5)Using the standard normal distribution table, we can find that P(-2.75 < Z < -0.5) = P(Z < -0.5) - P(Z < -2.75) = 0.3085 - 0.0030 = 0.3055.Rounding this result to four decimal places, we have:P($10 < X < $19) = 0.3055.

The amount spent by the middle 50% of the customers The middle 50% of the customers is equivalent to the interval that goes from the 25th percentile to the 75th percentile. This interval is also known as the interquartile range (IQR).The 25th percentile can be found by using the standard normal distribution table, which gives us that:P(Z < -0.6745) = 0.25 Solving for Z, we have:Z = -0.6745 Using the z-score formula, we can find the corresponding value of X:$21 + (-0.6745)($4) = $17.30

Therefore, the lower limit of the IQR is $17.30.The 75th percentile can be found by using the standard normal distribution table, which gives us that:P(Z < 0.6745) = 0.75 Solving for Z, we have:Z = 0.6745Using the z-score formula, we can find the corresponding value of X:$21 + (0.6745)($4) = $24.70

Therefore, the upper limit of the IQR is $24.70.The amount spent by the middle 50% of the customers is between $17.30 and $24.70.

Learn more about Probability

brainly.com/question/11234923

#SPJ4

hello, i need help please ​

Answers

Measure of ∠1 = 126 deg, Measure of ∠4 = 54 deg, and measure of ∠7 = 126 deg.

∵ Lines p and q are parallel, and t is transversal,

∠3 and ∠7 form pair of corresponding angles,

⇒ ∠3 and ∠7 are equal

∴∠7=126 deg.

Also, ∠3 and ∠1 are vertically opposite angles,

∴ ∠3 and ∠1 are equal.

⇒ ∠1=126

Again, as t is a straight line and line p intersects it,

∠3 and ∠4 form linear pair.

⇒ ∠3 and ∠4 are complementary.

⇒ ∠3+∠4=180

⇒ ∠4+126=180

⇒ ∠4=180-126

⇒ ∠4=54

Hence, measure of ∠1 is 126 deg, that of ∠4 is 54 deg, and that of ∠7 is 126 deg.

For more information on parallel lines and transversals,

https://brainly.com/question/23573963?referrer=searchResults

https://brainly.com/question/13702600?referrer=searchResults

For the point P(19,10) and Q(26,13), find the distance d(P,Q) and the coordinates of the midpoint
M of the segment PQ.

Answers

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{19}~,~\stackrel{y_1}{10})\qquad Q(\stackrel{x_2}{26}~,~\stackrel{y_2}{13})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~26 - 19~~)^2 + (~~13 - 10~~)^2} \implies PQ=\sqrt{( 7 )^2 + ( 3 )^2} \\\\\\ PQ=\sqrt{ 49 + 9 } \implies PQ=\sqrt{ 58 }\implies PQ\approx 7.62 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{19}~,~\stackrel{y_1}{10})\qquad Q(\stackrel{x_2}{26}~,~\stackrel{y_2}{13}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 26 +19}{2}~~~ ,~~~ \cfrac{ 13 +10}{2} \right) \implies \left(\cfrac{ 45 }{2}~~~ ,~~~ \cfrac{ 23 }{2} \right)\implies \stackrel{ \textit{\LARGE M} }{\left(22\frac{1}{2}~~,~~11\frac{1}{2} \right)}[/tex]

PLEASE HELP ASAP!!!

Question in photo

Answers

Answer:

Trinominal

Step-by-step explanation:


By definition, Trinominals are those expressions having 3 values, in this case, x^2, x, and the constant 6 are the values.

hope it helps.

After heating up in a teapot, a cup of hot water is poured at a temperature of 207 F. The cup sits to cool in a room at a temperature of 71 F

The cup of water reaches the temperature of
182 F after 1.5 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes.

Answers

The cup of water reaches a temperature of 173 F after 5 minutes.

What is temperature?

Temperature is a measure of the average kinetic energy of particles in a system. It is an important physical quantity used to describe the state of a system, and is widely used in science, engineering, and everyday life. Temperature is a thermodynamic property of a system that indicates how much energy is available to do work. In everyday terms, temperature is a measure of how hot or cold something is.

k = -0.2416
The equation for the cooling rate of the cup of water is:
T(t) = 207 - 0.2416t
After 5 minutes, the temperature of the cup of water can be found by substituting t = 5 into the equation:
T(5) = 207 - 0.2416(5) = 173.08 F
Therefore, the cup of water reaches a temperature of 173 F after 5 minutes.

To learn more about temperature
https://brainly.com/question/25677592
#SPJ1

PLEASE SHOW WORK!!!!!!!!!

Answers

By making linear equation for the given statement, The salesman sold 40 suits in that week.

What is a linear equation, exactly?

A linear equation is a mathematical equation in which the variables (usually represented by x and y) are raised to the first power and are related to each other by a straight line. In other words, a linear equation represents a straight line on a graph. The general form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Now,

Let "x" the number of suits the salesman sells in that week.

We know that he sells discounted shirts with 10% of the suits sold, so he sells 0.1x discounted shirts.

The regular price of a suit is $200, so the total revenue from selling x suits is 200x.

The discounted price of a shirt is $20, so the revenue from selling 0.1x discounted shirts is 20(0.1x) = 2x.

Now we can set up an equation based on the total revenue:

200x + 2x = 8080

Simplifying this equation, we get:

202x = 8080

Dividing both sides by 202, we get:

x = 40

Therefore,

               the salesman sold 40 suits in that week.

To know about linear equations visit the link

brainly.com/question/29739212

#SPJ1

A small hotel in a popular resort area has 20 rooms. The hotel manager estimates that 15% (1 −
???? = 0.15) of all confirmed reservations are "no-shows." Consequently, the hotel accepts
confirmed reservations for as many as 25 rooms (???? = 25). If more confirmed reservations arrive
than there are rooms, the overbooked guests are sent to another hotel and given a
complimentary dinner. If the hotel currently has 25 confirmed reservations, find
a. the probability that no customers will be sent to another hotel
b. the probability that exactly 2 guests will be sent to another hotel
c. the probability that 3 or more guests will be sent to another hotel.
Let ???? be number of customers who confirmed the reservations and showed up. Then ???? has a
binomial distribution with parameters ???? = 0.85 and ???? = 25. Recall the formula for P(???? = x).
For question (a). find P(???? ≤ 20). Why?
For question (b). find P(???? = 22). Why?
For question (c). find P(???? ≥ 23). Why?
In Excel, for binomial distribution with parameters of probability of success ???? and number of
trials ????, the formulas:
For PDF: P(???? = x) is binom.dist(x, n, ????, 0) and
For CDF: ????5(x) = P(???? ≤ x) is binom.dist(x, n, ????, 1).
Note that P(???? ≥ x) = 1− P(???? < x)
P(???? > x) = 1− P(???? ≤ x)
P(???? < x) = P(???? ≤ x −1) in discrete case

Answers

Problem 1:

a) The probability that no customers will be sent to another hotel is 0.039.

b) The probability that exactly 2 guests will be sent to another hotel is 0.228.

c) The probability that 3 or more guests will be sent to another hotel is 0.492.

Problem 2:

a) ( ≤ 20) - Probability of having 20 or fewer customers show up for the reservations.

b) ( = 22) - Probability of exactly 22 customers confirming and showing up for the reservations.

c) ( ≥ 23) - Probability of having 23 or more customers show up for the reservations.

Problem 1:

a. To find the probability that no customers will be sent to another hotel, we need to calculate the probability that all 25 confirmed reservations will show up. Since the hotel manager estimates that 15% of reservations are "no-shows",

Then the probability that a reservation will show up is 1 - 0.15 = 0.85. The probability that all 25 guests will show up is,

P(all 25 show up) = [tex](0.85)^{25}[/tex]

                             = 0.039

So the probability that no customers will be sent to another hotel is 0.039.

b. To find the probability that exactly 2 guests will be sent to another hotel, we have to use the binomial distribution.

The probability of a reservation being a no-show is 0.15, and the probability of a reservation showing up is 0.85. We have 25 confirmed reservations, so the probability of exactly 2 no-shows is,

P(exactly 2 no-shows) = (25 choose 2)[tex](0.15)^2 (0.85)^{23}[/tex]

                                     = 0.228

So the probability that exactly 2 guests will be sent to another hotel is 0.228.

c. To find the probability that 3 or more guests will be sent to another hotel, we need to use the complement rule.

The probability of 0, 1, or 2 guests being sent to another hotel is,

⇒ P(0 guests sent) + P(1 guest sent) + P(2 guests sent)

   = [tex](0.85)^{25}[/tex]+ (25 choose 1)[tex](0.15)^1 (0.85)^{24}[/tex] + (25 choose 2)[tex](0.15)^2 (0.85)^{23}[/tex]

   = 0.039 + 0.168 + 0.301

   = 0.508

The probability of 3 or more guests being sent to another hotel is,

P(3 or more guests sent) = 1 - P(0, 1, or 2 guests sent)

                                         = 1 - 0.508

                                         = 0.492

So the probability that 3 or more guests will be sent to another hotel is 0.492.

Problem 2:

a) To find ( ≤ 20),

We have to add up the probabilities of all the possible values of from 0 to 20. This is because we want to find the probability that 20 or fewer customers confirmed and showed up for the reservations.

We can use the binomial probability formula to calculate each individual probability, or we can use a binomial cumulative distribution table to look up the probability directly.

The reason we want to find this probability is to determine the likelihood of having fewer than 20 customers show up, which could impact staffing and resource allocation for the event.

b) To find ( = 22),

Use the binomial probability formula to calculate the probability of exactly 22 customers confirming and showing up for the reservations. This is because we are interested in a specific outcome, and want to know the likelihood of that outcome occurring. Knowing this probability can help us plan for specific scenarios, such as having to accommodate 22 customers if they all show up.

c) To find ( ≥ 23),

We have to add up the probabilities of all the possible values of from 23 to 25. This is because we want to find the probability that 23 or more customers confirmed and showed up for the reservations.

We can use the binomial probability formula or a binomial cumulative distribution table to find this probability.

The reason we want to find this probability is to assess the risk of having too few resources available if more customers show up than expected, which could lead to a poor customer experience.

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ12


Which situation can be represented by 11+ 6.5p ≤ 89?
A Napoleon is buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at
least $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at
most $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $6.50 each. The cost to mail all the shirts is $11. He wants to spend at
least $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $6.50 each. The cost to mail all the shirts is $11. He wants to spend at
most $89. What is p, the number of shirts Napoleon can buy?

Answers

The answer of the given question based on the inequality equation the answer is given below,

What is Equation?

An equation is mathematical statement that asserts equality of two expressions. It typically includes of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division

The situation that can be represented by 11+ 6.5p ≤ 89 is:

a) Napoleon is the buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at most $89. What is p,

To solve for p, we can follow these steps:

11 + 6.5p ≤ 89 (subtract 11 from both sides)

6.5p ≤ 78 (divide both sides by 6.5)

p ≤ 12

Therefore, Napoleon can buy at most 12 shirts if he wants to spend at most $89.

b) None of the given situations can be represented by the inequality 11 + 6.5p ≤ 89 when p represents the number of shirts Napoleon can buy. This is because the inequality implies that the total cost of buying p shirts at $11 each and mailing them for $6.50 is no more than $89, which is not consistent with the given information about the cost of the shirts and mailing.

To know more about Expression visit:

https://brainly.com/question/1859113

#SPJ1

Please help given mts & sqp find sp

Answers

The value of length SP for the two given similar triangles is 11.

What is similar triangle?

Similar triangles are triangles that have the same shape but are different in size. In other words, their corresponding angles are equal, and their corresponding sides are proportional.

This means that if you were to take one of the similar triangles and enlarge or shrink it, while keeping the angles the same, it would still be a similar triangle.

The value of length SP is calculated by applying the following method;

|SP| = |ST|

3x + 2 = 5x - 4

3x - 5x = -4 - 2

-2x = - 6

x = 3

Length SP = 3x + 2

                 = 3(3) + 2

                 = 11

Learn more about similar triangles here: https://brainly.com/question/27996834

#SPJ1

why cant i just see the answers

Answers

Answer:

What do you mean?

Step-by-step explanation:

Some questions are new and have not been answered yet.

Linda read 1/3 of her book on Friday. She reads 2/6 of the book on Saturday. On Sunday she reads the remaining 2/12 of the book. How much of the book did she read

Answers

As per the concept of unitary method, Linda read 5/6 of the book.

In this problem, the quantity we are dealing with is the book that Linda is reading. Let's call the total number of units in the book "x". Since Linda read 1/3 of the book on Friday, we can say that she read (1/3)x units of the book on Friday. Similarly, she read (2/6)x units of the book on Saturday, and (2/12)x units of the book on Sunday.

Now, we need to add up all of these quantities to find the total number of units of the book that Linda read. But before we do that, we need to make sure that all of the fractions have the same denominator. The smallest common multiple of 3, 6, and 12 is 12. So, we will convert all of the fractions to twelfths.

(1/3)x = (4/12)x

(2/6)x = (4/12)x

(2/12)x = (2/12)x

Now, we can add up all of these quantities:

(4/12)x + (4/12)x + (2/12)x = (10/12)x

So, Linda read (10/12)x units of the book in total. But we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

(10/12)x = (5/6)x

Therefore, the resulting value of x is 5/6

To know more about unitary method here

https://brainly.com/question/28276953

#SPJ4

The dimensions of a rectangular prism are 1.5 feet by 3.5 feet by 2 feet. What is the volume of the rectangular prism in cubic feet?
A. 7 ft³
B. 7.25 ft³
C. 8.5 ft³
D. 10.5 ft³​

Answers

The volume of the rectangular prism in cubic feet is solved to be

D. 10.5 ft³.

How to find the volume of the rectangular prism in cubic feet

The volume of a rectangular prism is given by the formula

V = l x w x h,

where

l, w, and h represent the length, width, and height of the prism, respectively.

in the problem, the dimensions are:

the length is 1.5 feet, the width is 3.5 feet, and the height is 2 feet.

Therefore, the volume is:

= 1.5 feet * 3.5 feet * 2 feet

= 10.5 feet³

That is to say the volume of the prism is 10.5 feet³

Learn more about rectangular prism at:

https://brainly.com/question/128724

#SPJ1

A home has a replacement value of $324,000. What is the amount of the insurance if the
coverage is:
a. 100% of the replacement value?
b. 90% of the replacement value?
c. 80% of the replacement value?

Answers

Answer:

a)  $324,000

b)  $291,600

c)  $259,200

Step-by-step explanation:

The percentage of the replacement value represents how much of the house will be insured.

a)  100% of 324000 = 1.00 * 324000 = $324,000

b)  90% of 324000 = 0.9 * 324000 = $291,600

c)  80% of 324000 = 0.8 * 324000 = $259,200

4. VPQRS is a rectangular pyramid where PQ = 10 cm and QR=6 cm. Given that the volume of the pyramid is 100 cm³, find its height VO. P S V 0 10 cm 0 R 6 cm​

Answers

the height VO of the rectangular pyramid VPQRS is 5 cm.

WHAT IS RECTANGULAR PYRAMID?

A rectangular pyramid is a type of pyramid where the base is a rectangle and the lateral faces are triangles with a common vertex (apex) that is not in the plane of the base. It is a polyhedron with a rectangular base and triangular faces that meet at a single vertex. The height of the pyramid is the perpendicular distance from the apex to the base. The volume of a rectangular pyramid can be calculated using the formula:

V = (1/3) * base area * height

where base area is the area of the rectangular base and height is the perpendicular distance from the apex to the base.

To find the height VO of the rectangular pyramid VPQRS, we can use the formula for the volume of a pyramid:

V = (1/3) * base area * height

where base area is the area of the rectangle formed by the base of the pyramid, and height is the height of the pyramid.

We are given that the volume of the pyramid is 100 cm³. We can also find the base area by multiplying the length PQ by the width QR:

base area = PQ * QR = 10 cm * 6 cm = 60 cm²

Substituting these values into the formula for the volume of a pyramid, we get:

100 cm³ = (1/3) * 60 cm² * height

Simplifying, we get:

height = (100 cm³ * 3) / (60 cm²)

height = 5 cm

Therefore, the height VO of the rectangular pyramid VPQRS is 5 cm.

To know more about rectangle visit:-

https://brainly.com/question/2607596

#SPJ1

what is 12/37 divided by 5/18

Answers

Answer: [tex]\frac{216}{185} \;\approx 1.1676[/tex]

Given:

   [tex]\displaystyle \frac{\frac{12}{37}}{ \frac{5}{18} }[/tex]

Use the method of "keep, change, flip:"

* keep the first fraction, change to multiplication, flip the second

   [tex]\displaystyle \frac{12}{37}* \frac{18}{5}[/tex]

Multiply across and divide:

   [tex]\displaystyle \frac{216}{185} \;\approx 1.1676[/tex]

For which values of x is the expression undefined?
x-6
x² - 16

Answers

Answer:

x = - 4 , x = 4

Step-by-step explanation:

the expression is undefined if the denominator equals zero

equate the denominator to zero and solve for x

x² - 16 = 0 ( add 16 to both sides )

x² = 16 ( take square root of both sides )

x = ± [tex]\sqrt{16}[/tex] = ± 4

that is the expression is undefined when x = - 4 or x = 4

Identify the radii of the given circle check all that apply

Answers

The radii of circle are AB, AC and AE.

The radius of a circle is the distance from the center of the circle to any point on its circumference. To find the radius of a circle, you can use the formula:

radius = diameter / 2

where the diameter is the distance across the circle, passing through its center.

Here, in this figure we need to identify the radii. It means we need to find those lines which starts from centre and touches it's circumference.

Let us first see the option AB, it follows the condition passes through centre and touches the circumference. So, it is radius of circle.

Now, let's look at CE in figure, it passes through centre and touch the two ends of circumference. So, it is diameter not radius.

Now, AC satisfies the condition of radius. So, AC is radius.

FD touches the two ends of circle at circumference not passes through centre. So, it is chord not radius.

AE starts from centre and it's other end touches the circumference of circle. So, it is radius.

So, the radii of circle in given figure are : AB, AC and AE.

To know more about radii of circle:

https://brainly.com/question/13057093

#SPJ4

Other Questions
In what way do you think the location of the foramen magnum relates to the movement of each species (ANSWER ASAP!! GIVING BRAINLIEST AS SOON AS AVAILABLE! )It took 22.2 gallons to fill Pedro's car with gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline it took to completely fill Pedro's car with gas?A: 20 LB: 84.58LC: 90LD: 18.4 L find the 9th term of the geometric sequence whose common ration is 2/3 and whose first term is 6. A tennis court is 78 feet long with the net located at the center. The distance from the net to the back of the service box is 21 feet, and the net is 3 feet tall. Assuming Carina can hit the ball so hard that its path is linear, from what height must she hit the ball to have the serve just clear the net and land in the service box? Decide whether or not it is reasonable for Carina to reach this height if she is 57" tall. Also, at what angle does the ball hit the ground? Your solution should include: A labeled diagram that shows a bird's-eye view of the path of the ball. A labeled diagram that shows the side view of Carina, the ideal height of the tennis racket, the ideal path of the tennis ball, and the measurements that are needed from the bird's-eye view diagram. Why does craven return to misselthwaite in the secret garden How to rewrite the problem so it only had positive exponents The standard form of a quadratic function is f(x)=a(x-h)^+k true or false you and your family went to riverside cafe for dinner and the total bill was $54.95. since you have a hawk card, you can get a 20% discount. how much would you save using your hawk card? what would be the final amount you pay? Please help me Find the value of x A geometric solid has 12 faces and 25 vertices. How many vertices does the solid have? The ____ price indicates how much the market maker will pay per share to buy a stated quantity of the stock, while the ____ price indicates the price per share at which it will sell the same stock. Ask; bid say on pay; spread spread; say on pay bid; ask overhead is underapplied if . multiple choice question. adjusted cost of goods sold is less than unadjusted cost of goods sold cost of goods manufactured is less than cost of goods sold actual overhead is more than applied overhead actual overhead is less than applied overhead Suppose that X is normally distributed with mean 110 andstandard deviation 17.A. What is the probability that X is greater than 138.05?Probability =B. What value of X does only the top 15% exceed? HELP ME NOW PLS IM GIVING ALL MY BRAINLY POINTS + IF IT HELPS ILL GIVE BRAINLIESTWrite in paragraph form a summary of how railroads and bridges contributed to floridas population boom. Sort each description by the type of RNA it describes. An object of mass 2 kg is undergoing simple harmonic motion represented by the graph of displacement versus time shown above. If the amplitude of the motion is 3 m, what is the magnitude of the net force on the mass at t=15s? Can someone answer this question Why is the Tripitaka Koreana considered one of highest achievements of Korean culture? ResponsesA) The book completely broke away from traditional artistic conventions.The book completely broke away from traditional artistic conventions. B) The books author founded Koreas best-known Buddhist monastery.The books author founded Koreas best-known Buddhist monastery. C) The book is a masterpiece of woodblock engraving and printing.The book is a masterpiece of woodblock engraving and printing. D) The book is the first sacred text shared by Confucianism and Buddhism.The book is the first sacred text shared by Confucianism and Buddhism. PLS DUE TOMORROW!!! 25 POINTS! A hardware store sells nylon rope for $0.89/yd. A lumber yard sells the same rope for $0.94/m. a) Which store sells the rope for a lower price? Explain your answer. b) How much money would Jim save if he purchased 650 ft. of the less expensive rope, before taxes? A recent edition of the wall street journal reported interest rates of 8. 75 percent, 9. 10 percent, 9. 48 percent, and 9. 75 percent for 3-, 4-, 5-, and 6-year treasury security yields, respectively. According to the unbiased expectation theory of the term structure of interest rates, what are the expected 1-year forward rates for years 4, 5, and 6? A magazine used the summated rating of 10 restaurants to predict the cost of a restaurant meal. For that data, SSR 131,742.28 and SST 143,920.65. Complete parts (a) through (c) a. Determine the coefficient of determination, r2 , and interpret its meaning.r2 = ____ (Round to two decimal places as needed.))Interpret the meaning of r2.It means that _____ % of the variation in the cost of a meal ______ be explained by the variation in summated ratings. (Round to two decimal places as needed.)