Seventy-two percent of all observations fall within one standard deviation of the mean if the data is normally distributed. a. True b. False

The number of merchandise return requests for Wyoming is equal to 10.

Let merchandise return requests from Wyoming be W.

Let merchandise return requests from Montana be M.

Given the following data;

Translating the word problem into an algebraic equation, we have;

[tex]W + M = 60[/tex]  .....equation 1

[tex]M = 5W[/tex]        ......equation 2

To find the value of W, we would solve the system of equations by using the substitution method;

Substituting eqn 2 into eqn 1, we have;

[tex]W + 5W = 60\\\\6W = 60\\\\W = \frac{60}{6}[/tex]

Wyoming, W = 10 merchandise return requests.

Therefore, the number of merchandise return requests for Wyoming is equal to 10.

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Step-by-step explanation:

Actually, it tells you exactly what to do.

First, translate, i.e., move over, the coordinates up by 3:

[tex](1, 4)\rightarrow (1+3, 4+3) = (4, 7)[/tex]

Then reflect this point about the x-axis and to do this,

[tex](x, y) \rightarrow (x, -y)[/tex]

[tex](4, 7) \rightarrow (4, -7)[/tex]

Answer:

[tex]0.2564\text{ pounds}[/tex]

Step-by-step explanation:

The 90th percentile of a normally distributed curve occurs at 1.282 standard deviations. Similarly, the 10th percentile of a normally distributed curve occurs at -1.282 standard deviations.

To find the [tex]X[/tex] percentile for the television weights, use the formula:

[tex]X=\mu +k\sigma[/tex], where [tex]\mu[/tex] is the average of the set, [tex]k[/tex] is some constant relevant to the percentile you're finding, and [tex]\sigma[/tex] is one standard deviation.

As I mentioned previously, 90th percentile occurs at 1.282 standard deviations. The average of the set and one standard deviation is already given. Substitute [tex]\mu=5[/tex], [tex]k=1.282[/tex], and [tex]\sigma=0.1[/tex]:

[tex]X=5+(1.282)(0.1)=5.1282[/tex]

Therefore, the 90th percentile weight is 5.1282 pounds.

Repeat the process for calculating the 10th percentile weight:

[tex]X=5+(-1.282)(0.1)=4.8718[/tex]

The difference between these two weights is [tex]5.1282-4.8718=\boxed{0.2564\text{ pounds}}[/tex].

Answer:

0.2564

Step-by-step explanation:

90th percentile, we use the formula X=μ + Zσ,

Where u = mean and  sigma = standard deviation and Z = 1.282

The mean is 5 and sigma = .1

X = 5+1.282(.1)

X = 5.1282

10th percentile, we use the formula X=μ + Zσ,

Where u = mean and  sigma = standard deviation and Z = -1.282

The mean is 5 and sigma = .1

X = 5-1.282(.1)

X = 4.8718

The difference is

5.1282 - 4.8718

0.2564

Answer:

9/10

Step-by-step explanation:

3/8 ÷5/12

Copy dot flip

3/8 * 12/5

Rewriting

3/5 * 12/8

3/5 * 3/2

9/10

Answer:

The correct answer is "[tex]2.633< \sigma < 4.480[/tex]".

Step-by-step explanation:

Given:

n = 21

s = 3.3

c = 0.9

now,

[tex]df = n-1[/tex]

    [tex]=20[/tex]

⇒ [tex]x^2_{\frac{\alpha}{2}, n-1 }[/tex] = [tex]x^2_{\frac{0.9}{2}, 21-1 }[/tex]

                  = [tex]31.410[/tex]

⇒ [tex]x^2_{1-\frac{\alpha}{2}, n-1 }[/tex] = [tex]10.851[/tex]

hence,

The 90% Confidence interval will be:

= [tex]\sqrt{\frac{(n-1)s^2}{x^2_{\frac{\alpha}{2}, n-1 }} } < \sigma < \sqrt{\frac{(n-1)s^2}{x^2_{1-\frac{\alpha}{2}, n-1 }}[/tex]

= [tex]\sqrt{\frac{(21-1)3.3^2}{31.410} } < \sigma < \sqrt{\frac{(21.1)3.3^2}{10.851} }[/tex]

= [tex]\sqrt{\frac{20\times 3.3^2}{31.410} } < \sigma < \sqrt{\frac{20\times 3.3^2}{10.851} }[/tex]

= [tex]2.633< \sigma < 4.480[/tex]

Answer:

This answer is 2487

which will be the third one

Hope this help

9514 1404 393

Answer:

  (−6, −4)

Step-by-step explanation:

Translating a point 12 units left subtracts 12 from its x-coordinate.

  P(6, -4) +(-12, 0) = S(-6, -4)

Answer:

It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.

Answer:

A is the answer I guess so...

The functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.

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

The  given function f(x)= 18/x - 9

Let us replace f(x) by y

y=18/x - 9

Now  x=18/y-9

Add 9 on both sides

x+9=18/y

Apply cross multiplication

y(x+9)=18

Divide both sides by x+9

y=18/(x+9)

f⁻¹(x)=18/(x+9)

Hence, the functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.

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Answer:

3y-a

3.3-7

9-7

2

Step-by-step explanation:

first we have to do multiply by replacing the value of y and the subtract by using the value of a.

Hope this will be helpful for you

Answer: 51 liters of fuel are required

Step by step: start by seeing how many times 476 can go into 1428

(1428/476=3)

Then take your sum of that and multiply it by 17 since that’s the number that correlates with 476

(17x3=51) therefore your answer is 51 liters

Answer:

0.26684

Step-by-step explanation:

Given that :

Mean, μ = 62.5

Standard deviation, σ = 1.96

P(Z ≥ 63.72)

The Zscore = (x - μ) / σ

P(Z ≥ (x - μ) / σ)

P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)

P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)

1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684

Answer:

The answer is 1/9 and 1/2

Answer:

x = 11 * sqrt(2)

y = 11

Step-by-step explanation:

Use the ratios of the lengths of the sides of a 45-45-90 triangle.

y = 11

x = 11 * sqrt(2)

Answer:

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

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.

Mean 5,500 and standard deviation 1,000.

This means that [tex]\mu = 5500, \sigma = 1000[/tex]

What is the probability that the call center will get between 4,800 and 5,000 calls in a day?

This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So

X = 5000

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

[tex]Z = \frac{5000 - 5500}{1000}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.3085.

X = 4800

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

[tex]Z = \frac{4800 - 5500}{1000}[/tex]

[tex]Z = -0.7[/tex]

[tex]Z = -0.7[/tex] has a p-value of 0.2420.

0.3085 - 0.2420 = 0.0665

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

Answer:

B

Step-by-step explanation:

Given

[tex]\sqrt{ab}[/tex] = [tex]\sqrt{bc}[/tex] ( square both sides )

ab = bc ( divide both sides by b ) , then

a = c

Given

[tex]\sqrt{ac}[/tex] = [tex]\sqrt{4c^4}[/tex] ( square both sides )

ac = 4[tex]c^{4}[/tex] ( but a = c) , so

4[tex]c^{4}[/tex] = c² ( subtract c² from both sides )

4[tex]c^{4}[/tex] - c² = 0 ← factor out c² from each term on the left side

c²(4c² - 1) = 0 ← 4c² - 1 is a difference of squares

c²(2c - 1)(2c + 1) = 0

Equate each factor to zero and solve for x

c² = 0 ⇒ c = 0

2c - 1 = 0 ⇒ 2c = 1 ⇒ c = [tex]\frac{1}{2}[/tex]

2c + 1 = 0 ⇒ 2c = - 1 ⇒ c = - [tex]\frac{1}{2}[/tex]

But c > 0 , then c = [tex]\frac{1}{2}[/tex] → B

Answer:

Step-by-step explanation:

The order matters

stuwxyz is different than zyxwuts

You have 7 letters

The number of permutations is 7! which is 7*6*5*4*3*2*1 = 5040

Answer:

its 6.78 i believe

Step-by-step explanation:

Answer:

This question is formatted incorrectly

Step-by-step explanation:

Answer:

5 bags of cement are required.

Step-by-step explanation:

Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:

Cement = 1

Sand = 3

3 = 15

1 = X

15/3 = X

5 = X

Therefore, 5 bags of cement are required.

Answer:

B

Step-by-step explanation:

B is the correct answer

Answer:

(r/s)(6) = r(6)/s(6) = 3(6)-1 / 2(6)+1 = 18-1 / 12+1 = 17/3

So basically the first one is the correct answer.

Step-by-step explanation:

I hope this helped and please kindly mark Brainliest. Thank You <3

Answer:

it's true

Step-by-step explanation:

To factorise you need to work out a number that add up to the number with a letter and multiply to the last number

I assume the up arrows are supposed to indicate exponents, so that the equation is

sin²(θ) = 2 sin²(θ/2)

Recall the half-angle identity for sine,

sin²(θ/2) = (1 - cos(θ))/2,

as well as the Pythagorean identity,

sin²(θ) + cos²(θ) = 1

Rewrite the equation in terms of cosine and solve:

1 - cos²(θ) = 1 - cos(θ)

cos²(θ) - cos(θ) = 0

cos(θ) (cos(θ) - 1) = 0

cos(θ) = 0   or   cos(θ) - 1 = 0

cos(θ) = 0   or   cos(θ) = 1

[θ = arccos(0) + 2nπ   or   θ = arccos(0) - π + 2nπ]   or

… … … [θ = arccos(1) + 2nπ]

(where n is any integer)

[θ = π/2 + 2nπ   or   θ = -π/2 + 2nπ]   or   [θ = 2nπ]

In the interval 0 ≤ θ < 2π, we get the solutions θ = 0, π/2, and 3π/2.

(That is, for n = 0 in the first and third solution families, and n = 1 in the second family.)

Answer:

The slope is 3 and equation of the line is y=3x. I think the answer is the 1st option

Step-by-step explanation:

Given:

y=3x

Direct variation equations have the form:

y=kx,

where

k is the constant of proportionality

so k=3

Answer:

0.65 is the correct answer

Step-by-step explanation:

hopes it helps

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\boxed{\frac{13}{20}}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\\frac{1}{4} +\frac{4}{10}\\------------\\LCM(4,10) = 20\\\\\rightarrow \frac{1}{4}=\frac{1*5}{4*5} = \frac{5}{20}\\\\\rightarrow \frac{4}{10}=\frac{4*2}{10*2}=\frac{8}{20}\\\\\\\rightarrow\frac{5}{20}+ \frac{8}{20} = \boxed{\frac{13}{20}}\\\\\\\text{The answer is in it's simplest form.}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.    

Answer:

[tex] x = 8.57[/tex]

Step-by-step explanation:

Here two triangles are given to us , which are attached to each other . Here we can use the concept of Trigonometry to find out the value of x. The angles of the triangle are 60° and 45° . Let the common side be p .

Step 1: Use the ratio of tan in upper triangle

[tex]\rm\implies tan60^o = \dfrac{perpendicular}{base} [/tex]

Substitute the respective values ,

[tex]\rm\implies \sqrt3=\dfrac{p}{7} [/tex]

Cross multiply ,

[tex]\rm\implies p = 7\sqrt3 [/tex]

Step 2: Use the ratio of cos in lower triangle

[tex]\rm\implies cos45^o = \dfrac{base}{hypontenuse} [/tex]

Substitute the respective values ,

[tex]\rm\implies \dfrac{1}{\sqrt2}=\dfrac{x}{7\sqrt3} [/tex]

Cross multiply ,

[tex]\rm\implies x= \dfrac{7\sqrt3}{\sqrt2} [/tex]

Put the approximate values of √2 and √3

[tex]\rm\implies x= \dfrac{7\times 1.732}{1.414} [/tex]

This equals to ,

[tex]\rm\implies \boxed{\blue{\rm \quad x = 8.57\quad}} [/tex]

Hence the value of x is 8.57 .

Answer:

The value of x is [tex]\frac{7\sqrt{6}}{2}[/tex]

Solution given:

AB=7

BD=x

<BAC=60°

<DBC=45°

In right angled triangle ABC

Tan 60°=opposite/adjacent

Tan 60°=BC/AB

Substitute value

[tex]\sqrt{3}[/tex]=[tex]\frac{BC}{7}[/tex]

BC=[tex]7\sqrt{3}[/tex]

again

againIn right angled triangle BCD

againIn right angled triangle BCDUsing Cos angle

Cos 45=adjacent/hypotenuse

Cos45°=BD/BC

Substituting value

[tex]\frac{\sqrt{2}}{2}=\frac{x}{7\sqrt{3}}[/tex]

Doing criss cross multiplication

[tex]\frac{\sqrt{2}}{2}*7\sqrt{3}=x[/tex]

x=[tex]\frac{7\sqrt{6}}{2}[/tex]

=============================================================

Explanation:

We'll use these two properties of integrals [tex]\displaystyle \text{If f(x) is an even function, then } \int_{-a}^{a}f(x)dx = 2\int_{0}^{a}f(x)dx[/tex]

[tex]\displaystyle \text{If f(x) is an odd function, then } \int_{-a}^{a}f(x)dx = 0[/tex]

These properties are valid simply because of the function's symmetry. For even functions, we have vertical axis symmetry about x = 0; while odd functions have symmetry about the origin.

------------------------

Here's how the steps could look

[tex]\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}((ax^8+c)+bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}(ax^8+c)dx+\int_{-7}^{7}(bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\left(2\int_{0}^{7}(ax^8+c)dx\right)+(0)\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=2\int_{0}^{7}(ax^8+c)dx\\\\\\[/tex]

Therefore, the given statement is true. The values of a,b,c don't matter. You could replace those '7's with any real number you want and still end up with a true statement.

We can see that ax^8+c is always even, while bx is always odd.

------------------------

Side note:

For the second step, I used the idea that [tex]\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx\\\\[/tex]

which allows us to break up a sum into smaller integrals.

Answer:

A one solution

Step-by-step explanation:

4(x - 5) = 3x + 7

Distribute

4x - 20 = 3x+7

Subtract 3x from each side

4x-3x-20 = 3x+7-3x

x -20 = 7

Add 20 to each side

x -20+20 = 7+20

x = 27

There is one solution

Answer:

Step-by-step explanation:

Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.

4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:

1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.