Need with this … substitution method..

Answer:

a) The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

b)

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c) They are respected, as the upper bound of both intervals is below the new FAA recommendations.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve these questions.

Question a:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 100 - 1 = 99

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9842

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.9842\frac{20}{\sqrt{100}} = 4[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 183 - 4 = 179 pounds.

The upper end of the interval is the sample mean added to M. So it is 183 + 4 = 187 pounds.

The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

Question b:

Critical value is the same(same sample size and confidence level).

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.9842\frac{23}{\sqrt{100}} = 4.6[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 190 - 4.6 = 185.4 pounds.

The upper end of the interval is the sample mean added to M. So it is 190 + 4.6 = 194.6 pounds.

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c. The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).

They are respected, as the upper bound of both intervals is below the new FAA recommendations.

Answer:

The probability that X is less than 5 cannot be determined.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

The distribution is right-skewed, which means that the central limit theorem can only be applied for a sample size of at least 30. Since the sample size is 9 < 30, the CLT cannot be applied, and thus the probability that X is less than 5 cannot be determined.

The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

when we have to solve an equation, it does not has an equal sign and inequalities.

When we have to solve an inequality equations usually are exact answers.

The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.

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Answer:

x < [tex]\frac{11}{2}[/tex]

Step-by-step explanation:

=> 10x - 5 < 8x + 6

Subtract 8x from the left and right side of the inequality sign:

=> 2x - 5 < 6

Now, add 5 on both sides of the inequality:

2x < 11

now divide 2 on both sides:

x < [tex]\frac{11}{2}[/tex]

Hope this helps!

Answer:

x = 26

Step-by-step explanation:

m<RTS = 4x - 14 (given)

Based on the inscribed angle theorem, the measure of the inscribed angle in a semicircle = right angle (90°)

Therefore,

4x - 14 = 90

4x - 14 + 14 = 90 + 14 (addition property of equality)

4x = 104

4x/4 = 104/4

x = 26

Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

Given : 9(x - y) = 30,

or (x-y) =30/9

To find :  

a) 18(x - y) = ?

=> 2(9(x - y))

=> 2(30)

=> 60

b)6x - 6y = ?

=> 6(x-y) = 6(30/9)

=> 2*30/3

=> 20

c) 9(x-y)-9

=> 30 -9

=>21

Therefore , the solution of the given problem of  equation comes out to be a.60 , b.20 and c.21.

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'Substitution Property of Equality'  illustrates the statement "If AC = 14, then BD + AC = BD + 14" from the question.

What is property of equality?

The equality characteristics define the relationship between two equal quantities. If a mathematical operation is applied to one side of an equation, it must also be applied to the opposing side to keep the equation balanced.

The Substitution Property of Equality states that if we know that two expressions are equal, we can substitute one of them for the other in any equation.

In this statement, it is stated that "If AC = 14, then BD + AC = BD + 14." Here we substitute 14 for AC in BD + AC = BD + 14. Which means that if we know that AC = 14, we can substitute 14 for AC in any equation, and the equation will still be true.

Therefore, given statement illustrates the Substitution Property of Equality.

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Answer:

Step-by-Step:5 cars and 14 bikes

Answer:

[tex]V = 864cm^3[/tex]

Step-by-step explanation:

Given

[tex]r = 6[/tex]

[tex]\pi = 3[/tex]

Required

The volume of the sphere

This is calculated as:

[tex]V = \frac{4}{3} \pi r^3[/tex]

So, we have:

[tex]V = \frac{4}{3} *3 *6^3[/tex]

[tex]V = \frac{4}{3} *3 *216[/tex]

This gives:

[tex]V = 4 *216[/tex]

[tex]V = 864[/tex]

The value of the quantity after 96 months, to the nearest hundredth is 1146.66

The standard expression for an exponential equation is expressed as:

P(t) = P0e^rt

Given the following parameters

Po = 800

rate r = 4.5% = 0.045

time t = 8 years

Substitute

P(8) = 800e^0.045(8)
P(8) = 1146.66

Hence the value of the quantity after 96 months, to the nearest hundredth is 1146.66

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Answer: A line segment is a part of a line having two endpoints.

Im not sure if you meant to put a picture there. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.

Answer:

B

Step-by-step explanation:

Answer:

3357

Step-by-step explanation:

Answer:

2x^3+5x^2−28x−15

Step-by-step explanation:

Answer:

C. y = 11.76(0.7)×

Step-by-step explanation:

I calculated it logically

The exponential equation that models the data is  y = 16.8×1.7ˣ.

A relation is a function if it has only One y-value for each x-value.

y = a.rˣ is the exponential function.

We can see that the y-values are decreasing, which means that the growth factor must be between 0 and 1.

Additionally, we can divide the y-value for each x by the y-value for the previous x to get an estimate of the growth factor.

Using this method, we find that the growth factor is approximately 0.85, which means that a possible equation is y = a × 0.85ˣ.

To find the value of a, we can substitute one of the data points into the equation.

Lets use the point (-2, 24), we get:

24 = a × 0.85⁻²

a = 24 / 1.551

a = 15.456

Therefore, the exponential equation that models the data is  y = 16.8×1.7ˣ.

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The answer of x is 100 degree.We can find by using percentage formula.

Percentage is a value or ratio that shows a fraction of 100. Percent means per 100. It does not have any units.If we have to calculate percent of a number then we  divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

The formula used to calculate percentage is: (value/total value)×100%.The most basic application of percentages is to compare one quantity against another. When we want to talk about data in this way we use it with the word, "of." To use this data as an example, we would say, for example, "25% of people prefer cake," as in this example.

Now we have

100 = x of 100%

100= x * 100/100

100=  x

Hence we can calculate value of x.

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Answer:332

Step-by-step explanation:

Let x be the number

Using algebra

(x÷4)+75=158

(x÷4)=158-75

(x÷4)=83

x=83×4

x=332

Check

(332÷4)+75=158

Answer:

Acute scalene triangle

9514 1404 393

Answer:

  $6749.29

Step-by-step explanation:

The balance is given by ...

  A = Pe^(rt)

  A = $5000·e^(0.10·3) ≈ $6749.29

Edgar will owe $6749.29.

The coordinates of the vertices of the square with height x is given as follows:

A square is a figure for which all the four side lengths are congruent, that is, they have the same measure.

The side length of the square in this problem is given as follows:

x.

As the height is equals to the base.

The vertex J represents the origin, hence it has coordinates given as follows:

J(0,0).

Then the remaining coordinates of the square are given as follows:

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Answer: obtuse

Step-by-step explanation:

64+47=111

111>39

Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..

A connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation  connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.

Here,

We have the following for the rectangle's perimeter:

2 ( l + w ) = 64

Here,

W = width, and L = length.

We must determine the length and breadth values necessary to make the rectangle's perimeter 64.

Now,

2 ( l + w ) = 64

l + w = 32

Thus, the sum of the length and breadth measurements must equal 32.

The possible widths are 5, 10, 15, 20, and 25.

Now,

l + 5 = 32

l = 27

l + 10 = 32

l = 22

l + 15 = 32

l = 17

l + 20 = 32

l = 12

l + 25 = 32

l = 7

We think about

The domain has widths of 5, 10, 15, 20, and 25.

The range for length is: 27, 22, 17, 12, and 7.

Values for width and length are used as the x- and y-axes, respectively.

Below is a graph of the data.

The following is the reasonable domain for the aforementioned situation:

5, 10, 15, 20, and 25

Below is a graph of the function 2 (l + w) = 64.

Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.

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Answer: #4 x >l 11

Hope this helps

Step-by-step explanation:

Answer:

m=5

c=-7

Step-by-step explanation:

m is slope

c is the intercept on the y axis

Mark me brainliest pls

Hi there!

[tex]\large\boxed{35 \text{ units}^2}[/tex]

Find the area of the parallelogram using the formula:

A = b × h

Thus:

A = 7 × 5 = 35 units²

Answer:

Step-by-step explanation:

I believe that the answer is 85

Answer:

-2[tex]t^{3}[/tex] + 5t - 1

Step-by-step explanation:

(7[tex]t^{3}[/tex] + 3t - 1) + (-9[tex]t^{3}[/tex] + 2t)

7[tex]t^{3}[/tex] - 9[tex]t^{3}[/tex] + 3t + 2t - 1  Combine like terms

-2[tex]t^{3}[/tex] + 5t - 1

Like terms have to have the same variable and the same exponents to be like terms.

Explanation:

The zeros in 0.00798516 are not considered significant because they are not between nonzero values.

If we had something like 1.207, then that zero would be considered significant.

The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.

Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.

Answer: 0.00799

0.00798516 rounded off to three significant figures is 0.00799

hope that helps...