is the following sentence a statement? why or why not? the sentence in this box is a lie. statement. the sentence is neither true nor false, and so it is a statement. statement. the sentence is true. therefore, it is a statement. statement. the sentence is false. therefore, it is a statement. not a statement. the sentence is false, and so it is not a statement. not a statement. the sentence is neither true nor false, and so it is not a statement.

The appropriate hypotheses using a significance level of 0.05 reject H0.

The hypothesis :

H0 : μL - μP ≥ 25

H0 : μL - μP < 25

The sample mean difference; Xd

d = L - P

Xd = Σd/n

d = -198,-336,-70,-18,-122,-9,-50,-5,-163,-86

Xd = - 1057 / 10

Xd = - 105.7

Using calculator ;

Standard deviation of difference, Sd = 103.845

The test statistic :

T = Xd ÷ (Sd/√n)

T = -105.7 ÷ (103.845/√10)

T = - 3.219

Decision region :

Reject H0 ; If P-value < α

The P-value : df = n - 1 ; 10 - 1 = 9

P-value(-3.219, 9) ; two-tailed = 0.00525

Hence the answer is, the appropriate hypotheses using a significance level of 0.05 reject H0.

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Answer:

x = [tex]\frac{-5 + \sqrt{17} }{2}[/tex]

Step-by-step explanation:

HOW TO SOLVE YOUR PROBLEM

1. Move terms to the left side

x² + 5x = -2

x² + 5x - (-2) = 0

2. Use the quadratic formula

x = [tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x² + 5x + 2 = 0

a = 1

b = 5

c = 2

x = [tex]\frac{-5 + \sqrt{5^2 - 4 * 1 * 2} }{2 * 1}[/tex]

3. Simplify

Evaluate the exponent

Multiply the numbers

Subtract the numbers

Multiply the numbers

Solution:

x = [tex]\frac{-5 + \sqrt{17} }{2}[/tex]

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 12 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The correct option is B ,  the sum of all allele frequencies is 1.

What is allele frequencies?

Allele frequency, or gene frequency, is that the frequency of allele cistron at a selected locus in a very population, expressed as a fraction or proportion. Specifically, it's the fraction of all chromosomes within the population that carry that allele over the full population or sample size.

Main body:

Allele frequency is totally different from genotype frequency or makeup frequency. Genotype and makeup frequencies may also be calculated and square measure vital for understanding however populations evolve, however they're not identical issue as allele frequency.

Hence the correct option is B.

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The mean square error (MSE) for that multiple regression model is 0.604

How to calculate MSE?

MSE = mean square error

n = total data

[tex]x^*[/tex] = predictor

[tex]\bar x[/tex] = mean

df = degree of freedom

α = significance level = 1 - 95% = 0.05

x, y = variable

assumed,

[tex]\hat y[/tex] = predicted value = 0

Formula for confidence interval (CI) for mean response is

CI = [tex]\hat y\pm t_{\alpha/2,df}\times \sqrt{MSE(\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]

Formula for confidence interval (CI) for prediction response is

CI = [tex]\hat y\pm t_{\alpha/2,df}\times \sqrt{MSE(1+\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]

Since, given confidence interval for mean response is (-1,1) and confidence interval for prediction response is (-2,2) at 95% confidence.

CI for mean response,

For CI = 1 = [tex]0+ t_{\alpha/2,df}\times \sqrt{MSE(\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]

For CI = -1 = [tex]0- t_{\alpha/2,df}\times \sqrt{MSE(\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]

simplified to

[tex]2\times t_{\alpha/2,df}\times \sqrt{MSE(\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 2

[tex]t^2_{\alpha/2,df}\times MSE\times (\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 1

CI for predicted response,

For CI = 2 = [tex]0+ t_{\alpha/2,df}\times \sqrt{MSE(1+\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]

For CI = -2 = [tex]0- t_{\alpha/2,df}\times \sqrt{MSE(1+\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]

simplified to

[tex]2\times t_{\alpha/2,df}\times \sqrt{MSE(1+\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 4

[tex]t^2_{\alpha/2,df}\times MSE\times (1+ \frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 4

[tex]t^2_{\alpha/2,df}\times MSE+ t^2_{\alpha/2,df}\times MSE \times (\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 4

substitute CI for mean response to CI for predicted response

[tex]t^2_{\alpha/2,df}[/tex] x MSE + 1 = 4

[tex]t^2_{\alpha/2,df}[/tex] x MSE = 3

Now, for [tex]t^2_{\alpha/2,df}[/tex], we first find degree of freedom

df = n - 4

= 14 - 4

= 10

Look on t table for [tex]t_{0.05/2,10}[/tex], and we get 2.228. So,

MSE = [tex]\frac{3}{2.228^2}[/tex]

MSE = 0.604

Thus, the MSE is 0.604 for that multiple regression model.

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If the scale factor is greater than 1, the image is larger than the preimage

A transformation called dilatation alters a figure's size without altering its shape. A figure might become bigger or smaller due to dilation. The initial figure in dilatation is referred to as the preimage. The image is an enlarged figure. The center of dilatation is a fixed location from which figures are distorted.

The scale factor specifies how much smaller or larger the picture will be when you dilate a figure.

• The picture is smaller than the preimage when the scaling factor is between 0 and 1. Reductions are referred to as dilations with scale factors between 0 and 1.

• The picture is larger than the preimage if the scale factor is greater than 1. Enlargements are defined as a dilation with a scale factor greater than 1. The prime sign, ', can be used to identify each new point in a dilated figure. For instance, point ', which stands for "prime," would be the dilated image of point.

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If a between-subjects experiment produces 50 scores in treatment 1 and 50 scores in treatment 2, then the experiment must have employed 100 participants.

Why do between-subjects experimental designs employ random assignment?

Because it ensures that there are no systematic differences between the participants in each group, random assignment improves the study's internal validity. You can draw the conclusion from this that the independent variable is to blame for the results.

What is the metric that denotes the degree to which all scores typically differ from the mean?

Because it is reported in the original units of measurement and takes into account all of the scores in the data set, the standard deviation is the most widely used measure of variability. It reveals the average (or standard) distance that separates each score from the distribution's mean.

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Full Question = If a between-subjects experiment produces 50 scores in treatment 1 and 50 scores in treatment 2, then the experiment must have employed ____.​

a. 100 participants

b. 25 participants

c. 50 participants

d. 200 participants​

The velocity v=15 m/s that is equal to the speed of a car on a local street. So the option 2 is correct.

In the given question we have to find the velocity of light in this gas is closest to which of these.

A researcher has created a Bose-Einstein condensate in which the index of refraction is 20,000,000.

The given options are;

Refractive index of B-E condensate(n) = 20,000,000 = 2×10^7

n = c/v

v=c/n

where v = speed of light in B-E condensate

As we know that c=3×10^8 m/s

So v=3×10^8/2×10^7

v=30×10^7/2×10^7

v=15 m/s

This is the velocity equal to the speed of a car on a local street.

So the option 2 is correct.

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The equation for the given phrase is 1/2(x)+2y=14.

Given that, Diego then says if we take half of the first number and double the second the sum is 14.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the first number be x and the second number be y.

Now, half of the first number and double the second the sum is 14

So, 1/2(x)+2y=14

Hence, the equation for the given phrase is 1/2(x)+2y=14.

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Concept and uses of image translation are explain below.

In math, a change is an activity that moves, flips, or changes a shape (called the preimage) to make another shape (called the picture). An interpretation is a sort of change that moves each point in a figure a similar distance in a similar course.

An interpretation is a kind of change that takes each point in a figure and slides it a similar distance in a similar course. This interpretation maps △ X Y Z \triangle{XYZ} △XYZtriangle, X, Y, Z onto the blue triangle. The outcome is another figure, called the picture. The picture is consistent to the first figure.

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The parent of a function is the simplest form of a group of functions.

Parent functions are the simplest form of a given family of functions. A family of functions is a group of functions that share the same highest degree and the same shape for their graphs.

The graph shows four graphs that exhibit the parabola. Since they all share the same highest degree of two and the same shape, we can group them as one family of function.

These four are all quadratic functions, and their simplest form would be[tex]y = x^2[/tex].

Hence, the parent function for this family is [tex]y = x^2[/tex]

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Answer:

Step-by-step explanation:

y = (2x^2-2x+3x-3)(x-4)

y = (2x^2+x-3)(x-4)

y = 2x^3+x^2-3x-8x^2-4x+12

y = 2x^3-7x^2-7x+ 12

a : 2x^3

b : 2

c : 3

d

lim x-> +oo x^3(2-7/x-7/x^2 + 12/x^3)

lim x-> +oo  +oo(2-7/oo - 7/oo + 12/oo)

lim x->+oo   +oo(2-0-0+0)

lim x->+oo    +oo

lim x-> -oo x^3(2-7/x-7/x^2 + 12/x^3)

lim x-> -oo  -oo(2-7/-oo - 7/-oo + 12/-oo)

lim x-> -oo   -oo(2-0-0+0)

lim x-> -oo    -oo

e

y = 2x^3-7x^2-7x+ 12

y’ = [2(x+h)^3 - 7(x+h)^2 - 7(x+h) + 12 - 2x^3 +7x^2 + 7x - 12]/h

y’ = [2(x^3+h^3+3x^2h+3h^2x) -7(x^2+h^2+2xh)-7x-7h-2x^3+7x^2+7x]/h

y’ = [2x^3+2h^3+6x^2h+6h^2x-7x^2-7h^2-14xh-7h-2x^3+7x^2]/h

y’ = [2h^3+6x^2h+6h^2x-7h^2-14xh-7h]/h

y’ = h (2h^2 + 6x^2 + 6hx - 7h - 14x - 7)/h

y’ = 2h^2 + 6x^2 + 6hx - 7h - 14x - 7

lim h->0  (6x^2 - 14x - 7)

y’ = 6x^2 - 14x - 7

y’’ = [6(x+h)^2 - 14(x+h) - 7 - 6x^2 + 14x + 7]/h

y’’ = [6(x^2+h^2+2xh) -14x-14h -6x^2+14x]/h

y’’ = [6x^2+6h^2+12xh-14h-6x^2]/h

y” = h(6h+12x-14)/h

y” = 6h + 12x - 14

lim h->0 (12x-14)

y” = 12x -14

12x - 14 = 0

6x - 7 = 0

x = 7/6

(2 *7/6+3)(7/6-1)(7/6-4)

(7/3 + 3) ( 1/6) (-17/6)

(16/3)(-17/36)

4/3 * -17/9

-68/27

turning point (7/6 ; -68/27)

f

(2x + 3)(x - 1)(x - 4) = 0

x = -3/2

x = 1

x = 4

A( -3/2,0)

B (1,0)

C (4,0)

g

y= 12

D (0, 12)

Answer:

a.  2x³

b.  2

c.  3

d.  As x → -∞, f(x) → -∞.   As x → ∞, f(x) → ∞.

e.  (-0.4, 13.6) and (2.8, -18.6).

f.  (-1.5, 0),  (1, 0),  (4, 0)

g.  (0, 12)

h.  See attachment.

Step-by-step explanation:

Given polynomial:

[tex]y=(2x+3)(x-1)(x-4)[/tex]

Leading term and Leading coefficient

The given polynomial is in factored form.

To find the leading term and the leading coefficient, simply multiply the variable terms of the factors:

[tex]\implies 2x \cdot x \cdot x = 2x^3[/tex]

Therefore:

Degree of the polynomial

The degree of the polynomial is the exponent of the leading term.

Therefore, the degree of the given polynomial is 3.

End behaviour

As the degree of the polynomial is odd and the leading coefficient is positive, the end behaviour of the function is:

Turning points

The x-values of the turning points are when the derivative of the function equals zero.

Expand the polynomial:

[tex]\implies y=(2x+3)(x-1)(x-4)[/tex]

[tex]\implies y=(2x+3)(x^2-5x+4)[/tex]

[tex]\implies y=2x^3-10x^2+8x+3x^2-15x+12[/tex]

[tex]\implies y=2x^3-7x^2-7x+12[/tex]

Differentiate:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=6x^2-14x-7[/tex]

Set it to zero and solve for x:

[tex]\implies 6x^2-14x-7=0[/tex]

Solve using the quadratic formula:

[tex]\implies x=\dfrac{-(-14) \pm \sqrt{(-14)^2-4(6)(-7)}}{2(6)}[/tex]

[tex]\implies x=\dfrac{14 \pm \sqrt{364}}{12}[/tex]

[tex]\implies x=\dfrac{14 \pm 2\sqrt{91}}{12}[/tex]

[tex]\implies x=\dfrac{7\pm \sqrt{91}}{6}[/tex]

[tex]\implies x \approx-0.4, \;2.8\; \; \sf (1\;d.p.)[/tex]

Substitute the found values of x into the original polynomial to find the y-values of the turning points:

[tex]x=\dfrac{7- \sqrt{91}}{6}\implies y=13.6\; \; \sf (1\;d.p.)[/tex]

[tex]x=\dfrac{7+ \sqrt{91}}{6}\implies y=-18.6\; \; \sf (1\;d.p.)[/tex]

Therefore, the turning points of the polynomial (to the nearest tenth) are:

x-intercepts

The x-intercepts are when the function equals zero.

As the function is already in factored form, simply equal each of the factors to zero and solve for x:

[tex]\implies (2x+3)=0 \implies x=-1.5[/tex]

[tex]\implies (x-1)=0 \implies x=1[/tex]

[tex]\implies (x-4)=0 \implies x=4[/tex]

Therefore, the x-intercepts are:

y-intercept

The y-intercept when x = 0:

[tex]\implies y=(2(0)+3)(0-1)(0-4)[/tex]

[tex]\implies y=3 \cdot -1 \cdot -4[/tex]

[tex]\implies y=12[/tex]

Therefore, the y-intercept is:

Sketch the graph

To sketch the graph:

By using Unitary method, it can be calculated that

[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]2.53 \times 10^{-17}[/tex] g of camphor

What is Unitary Method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here, Unitary method will be used

Formula for Camphor = [tex]C_{10}H_{16}O[/tex]

Gram Molecular mass = [tex]12 \times 10 + 16 \times 1 + 16[/tex] = 152g

[tex]10 \times 6 \times 10^{23}[/tex] atoms of carbon is contained in 152 g of camphor

1 atoms of carbon is contained in [tex]\frac{152}{6 .023 \times 10^{24}}[/tex] g of camphor

[tex]1 \times 10^{7}[/tex] atoms of carbon is contained in [tex]\frac{152 \times 1 \times 10^7}{6 .023 \times 10^{24}}[/tex] g of camphor

[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]\frac{152 \times 1 \times 10^7}{6 .023 \times 10^{24}}[/tex] g of camphor

[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]2.53 \times 10^{-17}[/tex] g of camphor

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The 10 yearly payments worth is $ 7299806.

The current value of a future sum of money or stream of cash flows at a certain rate of return is known as present value (PV). A discount rate or the interest rate that could be earned if invested is added to the future value for present value.

it is given that

PMT =$ 900000

Rate = 4%

years = 10

using the formula

PV = [tex]A * \frac{1 - \frac{1}{(1+R)^{N} } }{R}[/tex]

PV = (900000/0.04) × (1 - (1/ (1+0.04)^10))

PV = $ 7299806

the payment you receive today is $7299806

so, it is better to accept 10 annual payments as it has a higher value.

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The confidence interval methods for the mean are robust against departures from​ normality, meaning they work well with distributions that​ aren't normal, provided that departures from normality are not too extreme.

A confidence interval for a mean is a range of values that is likely to contain a population mean with a certain level of confidence.

We use the following formula to calculate a confidence interval for a mean:

Confidence Interval = x  +/-  z*(s/√n)

where:

x: sample mean

z: the chosen z-value

s: sample standard deviation

n: sample size

They work well with distributions that​ aren't normal, provided that departures from normality are not too extreme.

This means that the methods of this section are not robust against poor sampling method.

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The value of 18.92/11 is 1.72.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given term is 18.92 divided by 11,

The mathematical expression for 18.92 divided by 11,

= 18.92/11

= 1.72

The value of 18.92 divided by 11 is 1.72.

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There is sufficient evidence to conclude that the average number of hours women work each week is more than 80 hours

The hypothesIs are

Ha : μ>80

Given the sample size n=68 and sample mean X 83 , sample standard deviation s=10

The test statistic is

t = x~ - 80/s/√n

t= 83-80/10/√68

t- 2.4738634

The P-value of the test is

P-value P(T> 2.4738634)

P-value 0.0080

When  α=0.05,

Reject the null hypothesis since P-value 0.0080 a 0.05

i) The -a) 10090 two-sided confidence interval for mean based on the sample data is

{x}\pm t_{1-\α /2,n-1}\frac{s}/{√n}

Here the 95% confidence interval is

= 83 ± t1-0.05/2,67 10/V68

= (80.58,85.42)

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According to the 2010 u. S. Census, there are approximately 8 million people living in Virginia.  Hence ,the population of Nevada is 2.7 million.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

For example, we might have an equation like 4 + 1 = 2 + 3. This is an addition equation that has already been solved because both sides equal the same thing. 4 + 1 is equal to 5, and so is 2 + 3. This is called a balanced addition equation.

The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.

According to the question ,the first step is to add 2.8 on both sides , then second step is to divide by 4 on both sides. And thus The population of Nevada is 2.7 million.

Given:

The population of Virginia is 8 million.

Let x be the population of Nevada

It is also given that the population of Virginia is 2.8 million less than 4 times the population of Nevada.

So,

4x - 2.8 = 8

Add 2.8 on both sides ,

4x - 2.8 +2.8 = 8 + 2.8

⇒ 4x = 10.8

Divide both sides by 2.8

⇒ x = 10.8/4

⇒ x = 2.7

Hence ,the streps involved are :

Hence, The first step is to add 2.8 on both sides add 2.8The second step is to divide by 4 on both sides.

The population of Nevada is 2.7 million.

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Answer: A, D, B

Step-by-step explanation:

The first step is to

✔ add 2.8

on both sides.

The second step is to

✔ divide by 4

on both sides.

The population of Nevada is

✔ 2.7

million.

Have a nice day

A Treaty is important because it settled downs the global issues with diplomatic approach.

A treaty is an agreement between two countries with the set of rules defining the responsibilities and obligations for the countries.

Some issues which are not only important for the country but also for the issues which need attention globally.  

A Treaty can be made for any purpose. It is stabilizes the relationship between two countries in a diplomatic manner without the unnecessary loss of resources and valuable human life.

A Treaty is a long term solution for the problems.

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The time Fireman Fred spends running in 4 weeks, found from the average time it takes him to run 1 kilometer is 6.6 hours.

An average is the ratio of the sum of a set of values to the number of values in the set.

The distance Fireman Fred runs 4 morning in a week = 3 kilometers

The time it takes to run a kilometer = 8 minutes and 15 seconds

15 seconds = 0.25 minutes, therefore;

The time it takes to run a kilometer = 8.25 minutes

The time Fireman Fred spends running in 4 weeks is found as follows;

The distance Fireman Fred runs in a week = 3 × 4 kilometers = 12 kilometers per week

The total distance he runs in 4 weeks, D, is obtained using the equation;

D = 4 weeks × 12 kilometers per week = 48 kilometers

The total time = Time per kilometer × Number of Kilometers

The total time = 8.25 minutes/kilometer × 48 kilometers = 396 minutes

There are 60 minutes in one hour, therefore;

396 minutes = 396 minutes × (1/60) hour/minutes = 6.6 hours

The time Fireman Fred spends running over 4 weeks is 6.6 hours

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Answer:

Slope of line e is 2/3

Step-by-step explanation:

you know that equation for line d is y= 2/3x+3. because that line e is parallel to line d, it means that line e and d will never intersect which can only happen if both lines have the same slope. so that means line e's slope is 2/3

Answer:

2/3

Step-by-step explanation:

when a line is parallel to another line we say that the slopes are equal hence the slope of line e is 2/3.

NOTE: if a line is perpendicular to another the slope of line B the line is the negative reciprocal of the slope of Line A

for instance: if the slope was 2/3 the slope of the perpendicular line is -3/2

hope this helps.

Annual percentage rate is 14.925% of credit card rate 0.04089.

The phrase annual percentage rate of charge (APR), which can also be referred to as a nominal APR or an effective APR (EAPR), refers to the interest rate for the entire year (annualized), as opposed to only a monthly fee or rate, as applied on a loan, home loan, credit card, etc. An annual percentage rate, or APR, is a figure that expresses the entire cost of borrowing money as a proportion of the loan's principle. An accurate picture of how much it costs to borrow money is intended to be provided by the APR on a loan or credit card.

Given,

Daily rate = 0.04089

Rate = 365

Annual percentage rate = Daily Rate% ×Rate

Annual percentage rate = 0.04089 × 365

Annual percentage rate = 14.925%

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Answer:

sqrt9 and sqrt16

Step-by-step explanation:

Since you're trying to find the sqrt10, find a perfect square less than 10 and another perfect square greater than 10.

sqrt9 is 3. And sqrt16 is 4. So the estimate of sqrt10 is much closer to sqrt9.

sqrt10 ~= 3.2

The number of many managers were in the meeting is

information from the problem

At a company meeting, there were 30 people in attendance.

60% of them were managers

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

60%

= 60 percent

= 60 / 100

= 0.6

The factor 0.6 of the total number of people in attendance are managers

0.6 * 30 = 18

The number of managers  is 18

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Answer:

x = 10

Step-by-step explanation:

[tex]\frac{x-4}{4}[/tex] = [tex]\frac{15}{x}[/tex]  ( x > 0 )

x(x - 4) = 15(4)

x² - 4x - 60 = 0

( x + 6 )( x - 10 ) = 0

x = 10

The correct value of the moment of inertia is 128.

Let us consider the shaded area as rectangle 1 of 16 x 16 in minus the rectangle 2 of 12 x 4

Area of rectangle 1 = A₁ = 16 x 16

                                  A₁ = 96

Area of rectangle 2 = A₂ = 12 x 4

                                   A₂ = 48

y- coordinate of the centroid

y = [A₁*(6/2) - A₂*(2+2)] / (A₁-A₂)

y = [(96*3)-(48*4)] / 48

y = 2 in

Moment of inertia of 1 about x-axis

Iₓ = [{16*(6)²} / 12] + [A₁(3-2)²]

Iₓ = 384

Moment of inertia of 2 about x-axis

Iₓ' = [12(4)²/12] + A₂[2+(4/2)-2]²

Iₓ' = 256

Moment of inertia of the entire shaded area

Iₐ = Iₓ - Iₓ'

Iₐ = 384 - 256

Iₐ = 128

Therefore the moment of inertia of the cross sectional area with respect to x-axis is 128.

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The correct answers listed below :

A)The percentage of fencers that don't utilize the foil as their primary weapon in A.

B.) X : 0, 1, 2, 3,..., 21

C.) X ~ p(X) ; 10.4

D.) 21 ~ 0.4

E.) 0.0895

F.) Yes. There is a low (less than 1%) chance that all 21 fencers will not use the foil as their primary weapon.

A.) Considering that 60% of fencers reportedly utilize the foil as their primary weapon;

Number of fencers who do not utilize foil as their primary weapon is the random variable (x);

( 100% - 60%) = (1 - 0.6) = 0.4

B.) Possible values for X include:

The sample size is 26;

X : 0, 1, 2,..., 26

The breakdown of X

X ~ B ; X ~ p(X) ; 26 *0.4

=10.4

How many fencers are anticipated to not utilize the foil as their primary weapon in Part (d)?

X * p(x) (x)

=26 * 0.4

= 8.4

= 8 (nearest whole number) (nearest whole number)

Determine the likelihood that eleven will not utilize the foil as their primary weapon in part (e).

P(x = 11)

Using the link between binomial probabilities:

P(x =x) is equal to nCx * px * (1 - p) (n - x)

P(x = 11) = 26C11 * 0.4^11 * 0.6^10

P(x = 11) = 0.0895

Would you be shocked if none of the 21 used foil as their primary weapon based on the numbers?

P(x = 26) = 26C21 * 0.4^26 * 0.6^0

P(x = 26) = < 0.00001 ( about 0) ( approximately 0)

It will therefore be surprising if all 26 do not employ foil as their primary weapon given this extremely low value, which is virtually equal to 0.

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The sample mean is 16 times used to compute the confidence interval.

What is the z test?

If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.

The given sample value 100 observation,

Sample mean = (Lower limit + Upper limit) / 2 = (14.355 + 17.645) / 2 = 16

Hence, the sample mean is 16 time used to compute the confidence interval.

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In 2018 there are 1079 restaurants using the equation y=980+16.5x .

What is equation?

In algebra, in its simplest form, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x 5 = 14 is an equation where 3x 5 and 14 are two terms separated by an equal sign. There are two types of equations: identities and conditionals. Equality applies to all values ​​of the variable. A conditional expression applies only to specific values ​​of a variable. Equations are written as two expressions joined by an equal sign ("=").

Here  restaurants in the United States is ,

=> 2012 = 980

=> 2016 = 1,046

Here in 4 years difference  (2016 - 2012),

=> 1046-980 = 66 more restaurants .

Then in 4 years = 66 restaurants, Then

In 1 year = 66/4 = 16.5 .

Now slope m = 16.5

The order pair of the relationship between years and restaurants ,

(0, 980) and (4, 1,046)

Now the equation ,

=> y = 980+16.5 x

where Y = number of restaurants in one year

x = number of years in the past.

Number of restaurants in 2018,

=> Y = 980 + 16.5x

Years 2018-2012 = 6 years

Forecast number of restaurants,

=> Y = 980 + 16.5(6)

=> 1,079

Therefore the equation is y=980+16.5x and In 2018 there are 1079 restaurants.

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The relationship between SST, SSB and SSW is SST = SSB + SSW

The SSW is stands for sum of squares within and the SSW is defined as the sum of squared differences between a number and its sample mean for all numbers

The SSB stands for sum of squares between and the SSB is defined as the  the sum of squared differences between a value and the grand mean.

The SST stands for the the total sum of squares and SST is defined as the the squared differences between the observed dependent value and the mean

The total sum of squares is the sum of the sum of squares between and the sum of square within

Therefore

SST = SSB + SSW

Hence, the relationship between SST, SSB and SSW is SST = SSB + SSW

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