Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis.
y = x4, y = x7

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:

1 - 4

2 - 2

3 - 5

4 - 3

5 - 1

Step-by-step explanation:

Hope this helps

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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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 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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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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Answer:

Step-by-step explanation:

so we are told that he deposited 7/9 of  his money.  that mean the remaining is  2/9.   because 9/9 - 7/9 = 2/9   get it?

we are also told that 2.50 = 2/9 of his pay

so use that info to find the total pay

also using my calculator tells me that 2/9 = 0.22222222222222222222

knowing that,  we can divide 2.50 by 0.222222222222

2.50 / 0.2222222222  = 11.25

we now know that  2.50 is 0.222 of  11.25

if you want to check your answer just multiply 11.25 x .222222222  to see if you get 2.50

Do you understand?

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 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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The equation of Straight line, perpendicular to line [k]would be y = - x + 5

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of straight line also represents the directly proportional relation as -

y = mx + c

y = mx         {c = 0}

m = y/x    

or

m = Δy/Δx  

where [m] is constant of proportionality.

We have a line [k] that has an equation of y = x - 7

We have the given equation of line -

y = x - 7

Slope of line will be 1.

Slope of the line perpendicular to line [k] will be -

m[p] = -1

Then, the general equation would become -

y = - x + c

For point (7, - 2), we can write -

- 2 = - 7 + c

c = - 2 + 7

c = 5

Therefore, the equation of Straight line, perpendicular to line [k]would be y = - x + 5

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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​

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

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.

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 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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Three cards are drawn from a standard deck. Thus, the probability to get an ace, followed by a king, and then a queen, is  16/34,425

The formula for conditional probability is:

P(A∩B) = P(B|A) . P(A)

In the given problem:

P(ace) = 4 / 54

After an ace was drawn, the number of cards now is 51.

Hence,

P(king | ace) = 4/51

After the second drawn, the remaining cards is 50. Hence,

P(queen | (king | ace)) = 4/50

Therefore,

P(ace,king,queen) = 4/54 x 4/51 x 4/50 = 64 / 137,700 = 16/34,425

Thus, the probability to get an ace, followed by a king, and then a queen, is  16/34,425

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Three years ago , mine age was 6 years

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Let my present age be x

Age of mine , 20 years ago = x - 20

Age of mine , 10 years ago = x - 10

According to question,

(x - 20) = 13(x - 10)

⇒ x - 20 = 13x - 130

⇒ 13x - x = 130 - 20

⇒ 12x = 110

⇒ x = 110/12

⇒ x = 9.17

Age of mine , theree years ago = x - 3

= 9.17 - 3

= 6.17

≈ 6

Therefore, three years ago , mine age was 6 years

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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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Answer: (x-8)(x-8) = 4 (yes)

Step-by-step explanation:

x²-16x+64 = 4

(x-8) (x-8) =4

(x+8)(x+8)=4 NO

(x-8)2 =4 NO

(x-8)(x+8)=4 NO

(x+8)2 = 4 NO

(x-8)(x-8) = 4 YES

The required P-values for the result is 0.05.

The p-value is determined utilizing the inspecting conveyance of the test measurement under the invalid speculation, the example information, and the kind of test being finished (lower-followed test, upper-followed test, or two-sided test).

The hypothesis test was done to claim that the weight of participants has changed.

The null and alternative hypothesis could be written as:

H₀ : a =0

Hᵃ : a [tex]\neq[/tex] 0

being μ the population mean change in weight.

With that data, we can perceive that is a two followed test. Test implies that fall in any of the tails, with a z-measurement over 1.96 or under - 1.96 (at an importance level of 0.05), will be proof to dismiss the invalid speculation.

The data we have about the example is the 95% certainty stretch determined from the example data.

This certainty stretch does exclude the worth μ=0.

Then, there is 2.5% of probability that the populace mean is under 2.177, the lower bound of the stretch, which incorporates the worth μ=0.

Thus, we can reason that the P-esteem must be under 0.05.

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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!

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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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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The probability that she will have no spelling mistakes on at least one of them = 0.9919.

Let, X be the random variable denoting the no. of pages among those 444 pages which Julia writes where she makes no spelling mistake.

clearly we know that,

X Binomial (444, 0.7)

So,      P(X = x) = [tex]4c_{x} * (0.7)^{x} * (0.3)^{(4-x)}[/tex]

                           [when  x = 0, 1, 2, 3, 4 ..... so on until 444]

                        = 0 otherwise

According to the question, we have to find out  P(X ≥ 1) .

Now, P(X ≥ 1)

    = 1 - P(X = 0)

    = [tex]1 - (444c_{x} * (0.7)^{0} * (0.3)^{(4)})[/tex]

    = 1 - 0.0081

    = 0.9919

So, the required probability is  given by, 0.9919

Hence the answer is the probability that she will have no spelling mistakes on at least one of them = 0.9919.

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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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x = I9I

or:

x = I-9I

so:

x = 9 or -9

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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The transformations that could be used is option D) ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.

A geometric transformation known as a stiff transformation of a Euclidean space maintains the Euclidean distance between each pair of points. Stiff transformations include rotations, translations, reflections, or any combination of these. A rotation is known as a rigid transformation or isometry when the image and the pre-image are of the same size and shape. Despite the fact that the figures may be in different positions, an object's size, form, and rotation are all the same. These are the two different categories of transformations: The rigid transition does not change the size or shape of the preimage. The preimage's size but not its shape will change as a result of the non-rigid transformation.

Note that the full question is:

Is there a series of rigid transformations that could map ΔQRS to ΔABC? If so, which transformations could be used?

A No, ΔQRS and ΔABC are congruent but ΔQRS cannot be mapped to ΔABC using a series rigid transformations.

B No, ΔQRS and ΔABC are not congruent.  

C Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.

D Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.

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The first molecule will have a ZERO dipole moment since all the F atoms are at 120 degree making the net dipole zero.

A molecule is a group of two or more atoms held together by chemical bonds; depending on the context, the term may or may not include ions that meet this criterion.

A molecule is a particle composed of two or more atoms that are chemically bonded together; the number of atomic nuclei constituting a molecule is fixed. HCl(g), for example, is a molecule composed of one hydrogen atom bonded to one chlorine atom. It is a diatomic molecule because it is composed of two atoms.

The second molecule will have a NON ZERO dipole moment. The net dipole moment will be downwards. The third molecule will have a NON ZERO dipole moment.

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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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