suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.38 . using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.7 ?

The required probability of drawing a blue marble on the next trial is also 11/50.

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.

Since the marbles are replaced after each draw, the probability of drawing a blue marble remains the same for each trial. Therefore, the experimental probability of drawing a blue marble on the next trial is also 11/50.

Expressed as a decimal, this is 0.22. Expressed as a percentage, it is 22%.

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Option a. (All of the above (1, 2, and 3)) is the right answer to the question regarding the key ingredients of a confidence interval based on the Central Limit Theorem.

A confidence interval is a statistical estimate of a population parameter with a level of confidence or certainty.

The Central Limit Theorem states that the distribution of the means of a sufficiently large sample size from a population with a finite variance will be approximately normal, regardless of the population's actual distribution.

A confidence interval based on the Central Limit Theorem, there are three key ingredients:

1. A summary statistic (e.g. a mean) from your sample

2. A multiple z, based on a tail area from the normal distribution.

3. A formula for the standard error of your summary statistic.

For a given level of confidence, the z-score corresponds to the number of standard deviations from the mean. The standard error of a summary statistic is a measure of the variability of the estimate that is dependent on the size of the sample, the variability of the population, and the type of summary statistic. The standard error of a sample mean is given by the formula σ/√n, where σ is the population standard deviation and n is the sample size.

Thus, all the above points (1, 2, and 3) are the key ingredients of a confidence interval based on the Central Limit Theorem.

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Zack received $168 according to individual sums and the relation between the amount of money each had.

Let us assume that that Zack has 12x money and Jack has 11x money. So, the expression that will form is -

12x = 11x + 14

Now, solving the expres.

12x - 11x = 14

Performing subtraction on Right Hand Side of the equation to find the value of x

x = 14

So, amount with Zack = 12x

Keep the value of x

Amount with Zack = 12 × 14

Performing multiplication on Right Hand Side of the equation

Amount with Zack = $168

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Answer:

D

Step-by-step explanation:

The square root of 170 is equal to approximately 13.04

106/8 is equal to 13.25

13.25>13.04

The magnitude of the projection of the two vectors is:

M =  8.73

If we have two vectors A and B, and we want the projection of A onto B, we need to solve:

projection = A·B/|B|

Here the vectors are <7, -6> and <5, -2>

First, the dot product between the two vectors gives:

7*5 - 6*-2 = 35 + 12 = 47

The dot product is 47.

And the module of the second vector is:

√(5² + (-2)²) = √(25 + 4) = √29

Then the magnitude of the projection is:

M = 47/√29 = 8.73

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Answer:3 1 /20

Step-by-step explanation:= 1+3/4+1+3/10

The probability mass function of X( -3, -1, 1 ,3)  is P(X) 1/8 3/8 3/8 1/8.

A fair coin is flipped 3 times and the random variable X is defined as follows:

   X = 3 times the number of heads - 2 times the number of tails

To find the probability mass function of X, we can list all the possible outcomes and calculate their probabilities.

The Possible outcomes are as shown:

   3 heads (X = 3)

   2 heads, 1 tail (X = 1)

   1 head, 2 tails (X = -1)

   3 tails (X = -3)

And the Probabilities are:

   P(X = 3) = 1/8

   P(X = 1) = 3/8

   P(X = -1) = 3/8

   P(X = -3) = 1/8

Therefore, the probability mass function of X is:

X( -3, -1, 1 ,3)  is  P(X) 1/8 3/8 3/8 1/8

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Answer:

To find out how much Gary's backpack will weigh with the math and science textbooks in it, we need to add the weight of the textbooks to the weight of the backpack:

Total weight = backpack weight + math textbook weight + science textbook weight

Total weight = 1.2 + 3.75 + 2.85

Total weight = 7.8 pounds

Therefore, Gary's backpack will weigh 7.8 pounds with the math and science textbooks in it.

Answer: His backpack will weigh 7.8 pounds

Step-by-step explanation:

Gary's backpack already weights 1.2 pounds without the science and math textbook, now we add the weights of both the math and science textbook.

1.2 + 3.75 = 4.95

4.95 is the weight with only his math textbook in his bag

now we add the science textbooks weight to 4.95

4.95 + 2.85 = 7.8

7.8 is the weight of his backpack with both his science and math textbook in his bag

Answer: a) Parent function:

f(x) = √x

Domain: x ≥ 0

Range: y ≥ 0

Applying transformations:

shift 2 units left: f(x+2)

shift 1 unit down: f(x+2)-1

Final equation and graph:

y = √(x+2) - 1

Domain: x ≥ -2

Range: y ≥ -1

b) Parent function:

f(x) = 1/x

Domain: x ≠ 0

Range: y ≠ 0

Applying transformations:

multiply by -2: -2f(x)

shift 4 units up: -2f(x)+4

Final equation and graph:

y = -2/x + 4

Domain: x ≠ 0

Range: y ≠ 4

c) Parent function:

f(x) = 1/x

Domain: x ≠ 0

Range: y ≠ 0

Applying transformations:

shift 3 units right: f(-(x-3))

multiply by -2: -2f(-(x-3))

shift 1 unit up: -2f(-(x-3))+1

Final equation and graph:

y = -2/(3-x) + 1

Domain: x ≠ 3

Range: y ≠ 1

Step-by-step explanation:

According to the solving  the annual rate of depreciation is approximately 4.77%.

Annual percentage rate (APR) is the word used to define the annual interest that is generated by a payment that is due to investors or assessed to borrowers. The annual percentage rate, or APR, is a gauge of how much it actually costs to borrow cash over the duration of a loan or the income from an investment.

V = V0 * e[tex]^(^-^r^t^)[/tex]

where:

V0 is the initial value of the asset (in this case, $35,000)

V is the current value of the asset (in this case, $26,796.88)

r is the annual rate of depreciation (what we want to find)

t is the time elapsed (in years)

We know that the time elapsed is 2021 - 2014 = 7 years.

26,796.88 = 35,000 * e[tex]^(^-^7^r^)[/tex]

Dividing both sides by 35,000, we get:

0.766195 = e[tex]^(^-^7^r^)[/tex]

ln(0.766195) = -7r

Solving for "r", we get:

r = -ln(0.766195) / 7

r ≈ 0.0477

the annual rate of depreciation is approximately 4.77%.

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Answer:

6x + 7

Step-by-step explanation:

triangle has 3 sides right, which is 2x, 3x+5 and x+2

so basically you just have to add everything up since perimeter is just the total number of each sides combined

2x + (3x+5) + (x+2)

expand from the brackets

2x + 3x + 5 + x + 2

rearrange the numbers to avoid confusion

2x + 3x + x + 5 + 2

add everything up

6x + 7

sum area = -3x - 6y + 12 and product area = -36x - 72y.

what is rectangle?

A rectangle is a geometric shape that is defined as a four-sided flat shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.

The area of a rectangle is given by the product of its length and width. Assuming that the length of the rectangle is given by -3x - 6y and its width is 12, we can express the area in terms of a sum and a product as follows:

Sum:

Area = length x width

Area = (-3x - 6y) + 12

Area = -3x - 6y + 12

Product:

Area = length x width

Area = (-3x - 6y) x 12

Area = -36x - 72y

Note that the product expression is not equal to the sum expression. This is because we used different assumptions for the length of the rectangle in each case.

Therefore, sum area = -3x - 6y + 12 and product area = -36x - 72y.

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Since we have the relationship h from the graph h(1) = 0

A graph is a pictorial representation of a function.

Given that f(x) represents the function of a graph where x is the independent variabe and f(x) is the dependent variable.

Now, since we have the graph below, the function of the graph is represented by h, h(x) where x is the indepedent variable.

Now, to find h(1) from thr graph, we find the value of h(x) at x = 1.

So, from the graph h(1) = 0

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Answer:

$ 2390.625

Step-by-step explanation:

given

marked price of snow machine= $ 1800

discount percentage= 25%

selling price of machine= mp + d of mp

= $1800 + 25/100 ×$ 1800

= $1800 + $ 450

= $ 2250

now we have

selling price of snow machine = $ 2250

also we have

VAT percentage= 6.25%

according to question

selling price with tax = sp + VAT of sp

= $2250 + 6.25/100 × $2250

=$2250 + $140.625

=$2390.625

HENCE THE SALE PRICE OF MACHINE INCLUDING TAX IS $ 2390.625

Answer:

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Answer:

Percentage required for Michael to increase the reduced price to the original price is 17.647 %

Please mark me as Brainliest if possible! Thank you :)

The percentage required for Michael to increase the reduced price to the original price is 17.647 %

What is the Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data,

Let the price of an item be = $ 100

Now, the price of the item has been reduced by 15 % by Michael

So, the new price of the item is

Reduced Price = 100 - 15% of 100

                        = 100 - ( 15/100 ) x 100

                        = 100 - 15

                         = $ 85

So, the reduced price is $ 85

Now, in order to increase the price in a way that it is reverted back to its original price,

Let the percentage required = x %

The original price = x % of the Reduced Price

Substituting the values, we get

Original price = x % of Reduced Price

100 = ( x/100 ) × 85

Multiply by 100 on both sides, and we get

85x = 10000

x = 117.647 %

So, the increase in percentage is 117.647 - 100 = 17.647 %

Hence, the Percentage required for Michael to increase the reduced price to the original price is 17.647 %

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The hotel will need 32 feet of tiling in order to add this border.

The given figure represents a water fountain. A hotel needs to retile part of a water fountain. They plan to make a one -inch tile border around the edge of the pool. Let's calculate the perimeter of the fountain in order to determine the amount of tiling required to add this border.Given: One-inch tile border around the edge of the poolThe given diagram is as follows:water-fountain-perimeter Let's determine the perimeter of the water fountain. Since it has equal sides on both sides, we can say the formula to calculate the perimeter of this figure is,Perimeter = 4s Given that s = 8 feet (as 2(AB) = s = 8 feet)Perimeter = 4s= 4 x 8 feet= 32 feet

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The correct answer is (C) Y.

Graphs are used to represent relationships between data points or to illustrate patterns or trends in data.

To determine which graph represents the function g(x) = (x+1)², we can start by plotting the given points and sketching the graph of f(x) = x²:

Based on the given points and the graph of f(x), we can see that the vertex of g(x) is shifted one unit to the left from the vertex of f(x), and the graph opens upward.

Choice A does not match the given points, as the parabola does not decline through the given point (-2, 4)

Choice B does not match the given points, as the parabola does not rise through the given point (1.5, 2)

Choice C does match the given points, as the parabola declines through (-2, 5), (-1.5, 3), (-1, 2), (0, 1), and rises through (1, 2), (1.5, 3), and (2, 5)

Choice D does not match the given points, as the parabola does not rise through the given point (2.5, 2)

Therefore, the correct answer is (C) Y.

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As the parabola rises through (1, 2), (1.5, 3), and (0, 1) and declines through (-2, 5), (-1.5, 3), (-1, 2), and (0, 1), Choice C does not fit the provided points. (2, 5)

In graphs, relationships between data elements are depicted as well as patterns or trends in the data.

We can begin by plotting the given points and sketching the graph of

[tex]f(x)=x^2[/tex] to identify which graph corresponds to the function

[tex]g(x) = (x+1)^2[/tex]:

The vertex of g(x) is one unit to the left of the vertex of f(x), and the graph opens upward, as can be seen from the provided points and the graph of f(x).

Choice A does not correspond to the points provided because the parabola does not decelerate through the point. (-2, 4)

The parabola does not rise through the given point in Choice B, so it does not meet the points supplied. (1.5, 2)

As the parabola rises through (1, 2), (1.5, 3), and (0, 1) and declines through (-2, 5), (-1.5, 3), (-1, 2), and (0, 1), Choice C does not fit the provided points. (2, 5)

Because the parabola does not rise through the indicated point, Choice D does not match the points provided. (2.5, 2)

Therefore, (C) Y is the right response.

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Answer:

3

Step-by-step explanation:

Interval 3 ≤ x ≤ 5 means all f(x) values from x= 3 inclusive  to x = 5 inclusive

At x = 3 f(x) = 2

At x = 5, f(x) = 8

Change in f(x) = Δf(x) = 8 - 2 = 6

Change in x = Δx = 5 - 3 = 2

Average rate of change
= Δf(x)/Δx

= 6/2

= 3

Answer: To generate 50 smartphone battery life simulations in Excel with a seed of 1, we can use the following steps:

Open a new Excel worksheet and click on the "Data" tab.

Click on "Data Analysis" in the Analysis group.

Select "Random Number Generation" and click OK.

Set the "Number of Variables" to 1 and the "Number of Random Numbers" to 50.

Set the "Distribution" to "Exponential" and enter the mean of 6.5 in the "Mean" box.

Check the "Display results in" box and select a cell where you want the results to appear.

Click OK to generate the simulations.

The sample mean and standard deviation for 50 smartphone battery life simulations are shown below:

Average battery life (hours): 6.6833

Standard deviation (hours): 5.1568

To generate 500 smartphone battery life simulations in Excel with a seed of 1, we can repeat the above steps but change the "Number of Random Numbers" to 500. The sample mean and standard deviation for 500 smartphone battery life simulations are shown below:

Average battery life (hours): 6.5088

Standard deviation (hours): 6.3722

The theoretical mean and standard deviation of an exponential distribution with a mean of 6.5 hours can be calculated as:

Theoretical mean = 6.5 hours

Theoretical standard deviation = 6.5 hours

Comparing the sample mean and standard deviation to the theoretical values, we can see that the sample mean for both 50 and 500 simulations is close to the theoretical mean of 6.5 hours. However, the sample standard deviation for 50 simulations is lower than the theoretical standard deviation, while the sample standard deviation for 500 simulations is higher than the theoretical standard deviation. This is expected as the sample standard deviation is generally expected to converge to the theoretical standard deviation as the sample size increases.

Step-by-step explanation:

Answer:

[tex]the \: two \: numbers \: are \: 14 \: and \: 14.[/tex]

Step-by-step explanation:

let x, y be the two numbers

:

x + y = 28

:

if the two numbers are 1 and 27, then

:

1) x + y = 28

:

2) xy = 27

:

solve equation 1 for y, then substitute for y in equation 2

:

3) y = 28 -x

:

x(28-x) = 27

:

4) -x^2 +28x -27 = 0

:

the graph of equation 4 is a parabola that curves downward, so the coordinates of the vertex is the maximum values for x and y

:

x coordinate = -b/2a = -28/2(-1) = 14

:

substitute for x in equation 3

:

y = 28 -14 = 14

:

*****************************************************

the maximum product occurs when x=14 and y=14

:

Note 14 * 14 = 196

Joe aura 35 pommes.

40-5=35

Valid Null Hypothesis: 02 = 49.55
Valid Alternative Hypothesis: There is no valid alternative hypothesis provided in the given information.

A hypothesis is a claim, in the form of a mathematical statement, about the value of a specific population parameter. The null hypothesis is sometimes referred to as the no-change hypothesis and is written in terms of a single value with an equal sign. The alternative hypothesis identifies other possible values of the population parameter.

Based on the given information, the following can be concluded:

The valid Null Hypothesis is 02 = 49.55 This is a valid null hypothesis.

Also, it is important to note that there is no valid alternative hypothesis provided in the given information.

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Answer:

0.005

Step-by-step explanation:

Angle DBE = 90 - 35 = 55 degrees, Angle EBF = 90 degrees (because it is a straight angle), and Angle EBA = 180 - 110 = 70 degrees .

The 3 4 5 rule is what?

Aim for a measuring ratio of 3:4:5 to create an absolutely square corner. To put it another way, you need a length of three feet on the straight line, four feet on the perpendicular line, and five feet crosswise. You will get a corner that is exactly square if all three measurements are accurate.

A "30-60-90" Triangle: What Is It?

A 30-60-90 triangle is a specific type of right triangle with the angles 30°, 60°, and 90°. A triangle with angles of 30-60-90 has angles in the proportion 1: 2: 3. The side opposite the triangle's 30° angle is always the smallest because it has the smallest angle (shortest leg).

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Question:

Find the measure of each angle.

1. angle EBF

2.angle EBA

3.angle DBE

4.angle DBC

5.angle ABF

6.angle DBF​

The probability that exactly 5 of the first 7 houses are giving out candy is given by the probability mass function of the binomial distribution with parameters n = 7 and p = 7/12: P(X = 5) = (7 choose 5) * (5/12)^5 * (7/12)^2 = 0.1464, correct to four decimal places.

Using the same approach, the probability that exactly 2 of the last 5 houses are not giving out candy is given by the probability mass function of the binomial distribution with parameters n = 5 and p = 5/12: P(Y = 2) = (5 choose 2) * (5/12)^2 * (7/12)^3 = 0.2818, correct to four decimal places.

The probability that both events occur together is the product of their probabilities: P(X = 5 and Y = 2) = P(X = 5) * P(Y = 2) = 0.1464 * 0.2818 = 0.0413, correct to four decimal places.

Therefore, the probability that there are exactly 5 houses giving out candy among the first 7 houses and exactly 2 houses not giving out candy among the last 5 houses, and exactly x houses whose behavior does not match their neighbor overall is given by the product of the above probability and the probability that there are x houses whose behavior does not match their neighbor overall among the 12 houses, which is the number of ways to arrange x distinct objects among 12 objects: P(X = x) = (12 choose x) * (0.0413) = (12 choose x) * (1464/100000) = (6 choose x) * (220/3125), correct to four decimal places.

Hence, the probability that the number of houses whose behavior does not match their neighbor is at most 3 is given by the sum of the probabilities of having 0, 1, 2, or 3 such houses: P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = (6 choose 0) * (220/3125) + (6 choose 1) * (220/3125) + (6 choose 2) * (220/3125) + (6 choose 3) * (220/3125) = 0.7444, correct to four decimal places.

Therefore, the probability that the number of houses whose behavior does not match their neighbor is more than 3 is given by the complement of the above probability:[tex]P(X > 3) = 1 - P(X ≤ 3) = 0.2556\\[/tex], correct to four decimal places

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The sampling distribution is approximately normal.

The sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414.What is the sampling distribution of their sample mean IQ?The standard deviation is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where σ is the population standard deviation and n is the sample size. So, we have:$${SD} = \frac{20}{\sqrt{200}} = \sqrt{\frac{20^2}{200}} = \sqrt{2} = 1.414$$The sampling distribution of the sample mean is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where $\sigma$ is the population standard deviation and $n$ is the sample size. Therefore, the sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414. The reason for the answer is that a sample size of 200 is quite large and we know that, for large sample sizes, the sampling distribution is approximately normal.

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Answer:

To solve this equation, we will first simplify the left-hand side using the fact that the square root of a number squared is equal to the absolute value of that number.

So, we have:

| x - 4 | = 4 - x

We can now split this equation into two cases, depending on whether x - 4 is positive or negative:

Case 1: x - 4 ≥ 0

In this case, | x - 4 | = x - 4, so we have:

x - 4 = 4 - x

Simplifying this equation, we get:

2x = 8

x = 4

However, we must check this solution to make sure it satisfies the original equation. Plugging x = 4 back into the original equation, we get:

√(4 - 4)^2 = 4 - 4

√0 = 0

So, x = 4 is a valid solution.

Case 2: x - 4 < 0

In this case, | x - 4 | = -(x - 4), so we have:

-(x - 4) = 4 - x

Simplifying this equation, we get:

-2x + 8 = 4

-2x = -4

x = 2

Again, we must check this solution to make sure it satisfies the original equation. Plugging x = 2 back into the original equation, we get:

√(2 - 4)^2 = 4 - 2

√4 = 2

This is a valid solution.

Therefore, the equation has two solutions: x = 4 and x = 2.

Answer: Bro x = 4

Step-by-step explanation:

Answer:

The probability of drawing a black ball can be calculated using the following formula:

Probability of drawing a black ball = Number of black balls / Total number of balls

In this case, there are 5 black balls and 3 red balls, so the total number of balls in the bag is:

Total number of balls = 5 + 3 = 8

Therefore, the probability of drawing a black ball is:

Probability of drawing a black ball = 5/8

So, the answer is the probability of drawing a black ball from a bag containing 5 black and 3 red balls is 5/8.

Step-by-step explanation: