Extended Response
1. (6) The weights of grapefruits, G, of a certain variety are approximately Normally
distributed with a mean of 1 pound and a standard deviation of 0.12 pounds.
a. Let T = 3G. Find the mean and standard deviation of T.
b. Let R = G+ G + G. Find the mean and standard deviation of R.
c. Let Q=T-R. Find the mean and standard deviation of Q.

Answer:

C

Step-by-step explanation:

hope this helps with the work don't know how I keep finding your questions

The inverse function as g⁻¹ (h)  = [(h+6)/10]² which is the correct answer would be an option (E).

The inverse function is defined as a function obtained by reversing the given function.

To determine the inverse of a function, all you have to do is switch where h and g are and resolve for g.

So after switching h and g,

g = g(h) = 10√h - 6

becomes

h = 10√g - 6

Now, we solve for h regularly.

h + 6 = 10√g

(h + 6)/10 = √g

[(h+6)/10]² ⇒ g = [(h+6)/10]² = g(x)

Therefore the inverse of g(x) is g⁻¹ (h)  = [(h+6)/10]²

Hence, the inverse function as g⁻¹ (h)  = [(h+6)/10]²

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Answer:£61.6 in 7 hours

Step-by-step explanation:

£8.80*7=£61.6

The total marks scored by Noor are 80 marks.

The total marks scored by Noor will be calculated through substitution. As Noor did not answer any short items correctly, we will keep 0 as the value of s. Also, Noor scored 16 multiple - choice items correctly, so the value of m will be 16.

Keeping the values in formula to find the score of Noor.

Total marks of Noor = 10×0 + 5×16

The first part of equation will be 0, as multiplication of any number with 0 will give result as 0. The second part will give the multiple result.

Total marks of Noor = 80

Therefore, Noor scored 80 marks.

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Answer:

12 adults

Step-by-step explanation:

Given that :

Let :

Number of children = x

Number of adult = y

x = 32 + y - - - - - (1)

Ratio of adult to children

3 : 11

x = (11/3)y - - - (2)

Put x = 11/3y in (1)

(11/3)y = 32 + y

11y/3 - y = 32

(11y - 3y) / 3 = 32

11y - 3y = 32 * 3

8y = 96

y = 96/8

y = 12

Hence, number of adults = 12

Answer:

what equation.?

Step-by-step explanation:

You would need to walk approximately 11 miles to burn off all the calories from the "Big Breakfast with Hotcakes

To calculate the number of miles you need to walk to burn off all the calories from breakfast, we can use the following steps:

1. Convert the provided calorie value to kilojoules:

  Calories = 1090

  1 Calorie = 4.184 kJ

  Energy in kilojoules = Calories * 4.184 kJ/Calorie

  Energy in kilojoules = 1090 * 4.184 kJ/Calorie

2. Determine the amount of energy burned per mile:

  Energy burned per mile = 418 kJ/mile

3. Divide the total energy from breakfast by the energy burned per mile to obtain the number of miles needed to be walked:

  Miles = Energy in kilojoules / Energy burned per mile

  Miles = (1090 * 4.184 kJ/Calorie) / 418 kJ/mile

Simplifying the expression:

  Miles = (1090 * 4.184 kJ/Calorie) / 418 kJ/mile

  Miles = 11

Hence, in order to eliminate the calories consumed from the "Big Breakfast with Hotcakes," you would have to walk for about 11 miles.

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Answer:

-5.09

Step-by-step explanation:

Convert 5 1/11 to an improper fraction.

Exact Form:

-56/11

Decimal Form:

-5.09

Mixed Number Form:

-5 1/11

The initial amount that was deposited by Clare is $725.

The equation for the amount of money in Clare's bank account after x months will be 725 + 175x

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let the amount deposited initially be x.

Based on the information, this will be illustrated as:

x + 175(10) = 2475

x + 1750 = 2475

Collect like terms

x = 2475 - 1750

x = 725

The initial amount is $725.

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To the nearest whole number, the probability of rolling a 2 and a 4 is 2.8%.

A 2 rolling up on the first throw has a 1/6 chance of happening. Given that a 2 was rolled on the first throw, the likelihood of rolling a 4 on the second throw is equally 1/6. We will have to multiply the probabilities to get the probability of both the events happening,

= (1/6)x(1/6)

= 1/36.

We get 2.8% after converting to a percentage and rounding to the next full amount. So, the chance of rolling a 2 and then a 4 is found to be 2.8% chance.

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Answer:

\(\displaystyle y = -\frac{x}{5} - 2\frac{1}{5}\)

Step-by-step explanation:

\(\displaystyle x + 5y = -11 → 5y = -x - 11 → \frac{5y}{5} = \frac{-x - 11}{5} \\ \\ y = -\frac{1}{5}x - 2\frac{1}{5}\)

I am joyous to assist you at any time.

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

Answer:

Hello the required image is missing attached below is the missing box

answer : FHGE

Step-by-step explanation:

The plane representing the top surface of the box is FHGE. there are still other planes there but do not represent the entire top surface of the Box and they are : FGE, HGE, FHG and FHE. This is because a plane can be represented by three to four Noncollinear points on a solid like a box.

For linear trigonometric equations involving only sine or cosine, there will be solutions if the constant term on the other side of the equation falls within the range of -1 to 1.

When solving linear trigonometric equations in terms of only sine or cosine, we can determine whether there will be solutions by considering the range of values that sine and cosine can take.

For sine (sin) and cosine (cos), their values range from -1 to 1. If the equation involves only sine or cosine and is linear, it means the variable is not squared or involved in any higher powers. In such cases, the equation will have solutions if the constant term on the other side of the equation is within the range of -1 to 1.

For example, if we have the equation sin(x) = 0.5, it will have solutions because 0.5 is within the range of -1 to 1. However, if we have the equation sin(x) = 2, it will not have any solutions because 2 is outside the range of -1 to 1.

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The area of the trapezium shown is 284.31 in²

An equation is an expression that shows the relationship between variables and numbers.

The area is calculated for a two dimensional shape. It shows the amount of space occupied for that shape.

The area of a trapezium is given by:

Area = (1/2)(sum of parallel sides) * height

For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches, hence:

Area = (1/2)(17 + 31.6)(11.7) = 284.31 in²

The area is 284.31 in²

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Answer:

Step-by-step explanation:

It's 10 since it's a whole number.

The keyspace for an affine cipher with a 40-letter alphabet would have size c. 640. Therefore, the answer is c. 640.

To understand why, let's first review what an affine cipher is. An affine cipher is a type of substitution cipher where each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. This fixed number is called the "shift" or "key" value. In an affine cipher, the shift value is multiplied by the plaintext letter's position in the alphabet, and then a second value (the "additive constant") is added to the result.

In an affine cipher with a 40-letter alphabet, there are 40 possible values for the shift and 40 possible values for the additive constant. Therefore, the total number of possible keys is the product of these two values: 40 x 40 = 1600.

However, not all of these 1600 keys will be valid. In particular, we need to ensure that the shift value is coprime with the size of the alphabet (i.e., there is no common factor between them other than 1). If the shift value is not coprime with the size of the alphabet, then some letters in the plaintext will map to the same letter in the ciphertext, which would weaken the security of the cipher.

In this case, the size of the alphabet is 40, and there are 16 numbers less than 40 that are coprime with 40: 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, and 39. For each of these 16 shift values, there are still 40 possible values for the additive constant, so the total number of valid keys is 16 x 40 = 640.

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The admission fee for the zoo and for the state park is given as follows:

For the zoo, the costs are divided as follows:

20 students are going to the zoo, hence the total cost spent at the zoo is given as follows:

20(2x + 3.25) = 40x + 65.

For the state park, the costs are divided as follows:

25 students are going to the state park, hence the total cost spent at the state park is given as follows:

25(x + 6.50) = 25x + 162.50.

The costs spent at both parks are the same, hence the value of x can be obtained as follows:

40x + 65 = 25x + 162.5

15x = 97.5

x = 97.5/15

x = 6.5.

Hence the admission fees are given as follows:

The table is given by the image presented at the end of the answer.

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Answer:

d + (4)

Step-by-step explanation:

y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D

Answer:

30

Step-by-step explanation: First take the fastest speed of the squirrel, and then you multiply it by the percentage (250%). You can this by moving on decimal point to the left from the zero (250% = 2.50). Then multply the speed of the squirrel by said percentage of the girrafe,

12 x 2.5 = 30

The statement is false. A process chart is a graphical tool used to monitor processes in production and service industries. The average process performance and the upper and lower limits are calculated and displayed on an X-bar chart, which is a common process chart.

An \( \bar{X} \) chart is NOT used to track a process with binary outcome variables. The statement is false.

Explanation: A process chart is a graphical tool used to monitor processes in production and service industries. The average process performance and the upper and lower limits are calculated and displayed on an X-bar chart, which is a common process chart. The values for a variable can be collected and analyzed using process charts. An \( \bar{X} \) chart, commonly known as an x-bar chart, is used to monitor a process with continuous numerical data. A binary outcome variable, on the other hand, has only two possible outcomes (e.g., yes/no, pass/fail, etc.). As a result, binary data is unsuitable for an \( \bar{X} \) chart, which is only used to monitor continuous numerical data.

Variables are values that may be altered in a process, which can affect its results. Variables may be categorized as continuous or discrete, depending on whether they can be measured or counted. Discrete variables, such as the number of employees working on a task or the number of items produced in a process, are quantifiable and can be measured precisely. Continuous variables, such as the temperature, length, or weight, can take on any value over a range and are therefore less specific. The reasons for holding inventory include serving as a buffer against uncertainties, ensuring product availability and preventing stockouts, reducing lead times and transportation costs, taking advantage of discounts and bulk purchasing opportunities, and providing a hedge against inflation and price fluctuations.

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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Answer

QR= PQ= PR

18x+1= 24x-17

18x-24x= -17-1

-6x= -18

x= 3

QR= 24(3)-17= 55

PQ= 18(3)+1= 55

PR= 15(3)+10=55

Answer:

The value of x is 3. The length of PQ, QR and PR are 55.

Step-by-step explanation:

Given that the lengths in an equilateral triangle are all the same. We can assume that PQ = QR = PR. So we can choose any 2 lengths and compare it :

\(PQ = QR\)

\(18x + 1 = 24x - 17\)

\(1 + 17 = 24x - 18x\)

\(6x = 18\)

\(x = 18 \div 6\)

\(x = 3\)

Next, we have to substitute x = 3 into the expressions :

\(PQ = 18(3) + 1 = 55\)

\(QR = 24(3) - 17 = 55\)

\(PR = 15(3) + 10 = 55\)

Answer:

yes

Step-by-step explanation:

Answer:

Yup it’s rational

Step-by-step explanation:

Have a great night!!

~ jassy ❤️

We shall proceed in hit and trial method

Find some nearest multiples of 252

Yes last one is square of 42

So smallest no is 7

Answer:

The answer is 44

Step-by-step explanation:

How you find your answer is you add up all of the numbers IN ORDER( you get 352) then you divide by how many numbers are it the parentheses and you get 44 as your answer.

Answer:

Hey there!

p(x)=x+30

p(13)=13+30

p(13)=43

5(43)=215

Let me know if this helps :)