A particle moves on a circle of radius 9 cm, centered at the origin, in the xy-plane (x and y measured in centimeters). It starts at the point (0, 9) and moves counterclockwise, going once around the circle in 6 seconds. Write a parameterization for the particle's motion. x (t) = What is the particle's speed? Speed =

Answer: 35/10

Step-by-step explanation:

if you have 7/2 and need a denominator of 10 all you need to do is multiply 7/2 by 5/5.

7  by  5     35

2  by  5     10

The value of 7/2 with a denominator of 10 is 35/10

Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]

Then the conjugate of the denominator is given by b - c

Thus, rationalizing the fraction will give us

[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]

(we used the identity [tex](b-c)(b+c) = b^2 - c^2 )[/tex]

We actually rationalize just for the use of that later denominator or numerator

We have 7/2 and need a denominator of 10 all you need to do is multiply 7/2 by 5/5.

7 × 5 = 35

2 × 5 = 10

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Answer: 226.19

Step-by-step explanation:

Using the formula for a cyclinder{ V=πr2h} and inputing the values given in the diagram, (the radius and height given) you get 28.27.

Then adding the cone's volume (V=πr2h/3) and inputing that values in the diagram (the radius and height) you get 197.92.

Adding those values you got from the cyclinder and cone together, you get the volume of the composite solid.

When t = 3869, the rate of change of p is proportional to p.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three. Due to the prevalence of these relationships, differential equations are widely used in many fields, including engineering, physics, economics, and biology.

The primary focus of studying differential equations is on the solutions—the collection of functions that satisfy each equation—as well as the characteristics of those solutions.

Only the most basic differential equations can be solved using explicit formulas, but many features of a particular differential equation's solutions can be deduced without doing an exact calculation.

When a closed-form expression is used, it is common for.

According to our question-

The revised equation is then

P=5000exp(-0.0513t)

Find P at t=5 now.

P=5000 exp(-0.0513×5)

P=5000 ×exp(-0.25647) (-0.25647)

P=5000 × 0.77378

P=3868.89.

P = 3869. Roughly

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The weighted average of the average weights of each individual subgroup, where the weights represent the population proportions in each subgroup, provides the average weight of the population's constituents.

This can be mathematically represented as: average population weight = _(i=1) r P i * w i, where P i is the population's share of subgroup I and w i is the weight of the subgroup's average members.

For instance, if the population is divided into three subgroups with proportions of P1 = 0.2, P2 = 0.5, and P3 = 0.3, and the subgroups' average weights are P1 = 150 lbs, P2 = 200 lbs, and P3 = 175 lbs, respectively, then the population's average weight is P1 * 150 lbs 180 lbs is equal to +0.5 * 200 lbs + 0.3 * 175 lbs.

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The maximum area of rectangle is 24, that can be calculated using the derivatives.

The area of rectangle = length * breadth,

The length of the rectangle is 2x units and the breadth is 3x+12 units,

So, A(x)=2x*(-3x+12)

=2x(-3x+12)

=-6x^2+24x

The derivative A'(x)=0

-12x+24=0

x=+2

Therefore, x=+2 is the critical point.

The second derivative.

The 2d derivative measures the immediately rate of alternate of the 1st derivative. The signal of the second derivative tells us whether or not the slope of the tangent line to is growing or decreasing.

A"(x)=-12<0

By the second derivative test, A(x) has maximum value at x=+2

Thus, the maximum are is

A(x)=2x(-3x+12)

A(2)=2(2)(-3(2)+12)

=4(6)

=2

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There are 1307674368000 possible methods to remove each ball from the box one at a time.

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.  examination of events subject to probability.

given,

the quantity of balls inside a box ,

four red balls

6 balls in blue

four green balls

The variety of ways the balls can be taken out of the box one at a time must be determined.

Here,

Combination is possible because order is imperceptible;

mixture formula; nCr is equal to n!/r1(n-r)!

Here, There are 15 balls in the box overall (5 + 4 + 6 balls).

Then.

¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000

that is

There are 1307674368000 ways in which we can take the balls out of the box one at a time.

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Answer:

2

Step-by-step explanation:

First, we must add 14 to both sides to put the variable and coefficient alone.

4s - 14 = -6

   +14     +14

4s = 8

s = 2

(a) There are 10 units must be sold to maximize profit.

(b) The maximum profit is 480.

what is profit?

A profit is an income that is given to the owner in an efficient market production process in accounting. The owner's primary interest in the income-formation process of market production is profit, which is a measure of profitability. Different profit metrics are frequently employed.

Given:

A company sales x units of a product, its profits P can be determined

using the profit function P(x) = -2x² + 40x + 280       ..(1)

We have to find the maximum profit.

Differentiate equation (1) w.r.t x

     P'(x) = -4x +40            ..(2)

-4x + 40 = 0

        4x = 40

          x = 10

Again differentiate equation (2) w.r.t x

P''(x) = -4 which is negative.

Hence, there are 10 units must be sold to maximize profit.

Now, to find the maximum profit.

Plug x = 10 in equation (1)

P(10) = -2(10)^2 + 40(10) + 280

        = -200 + 400 + 280

P(10) = 480

Hence, the maximum profit is 480.

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Answer:it isA

Step-by-step explanation:

Answer:

8x^6

Step-by-step explanation:

Add the exponents and multiply the numbers

(a) The standard deviation of the large wild cats is 25.5 (b)  The standard deviation of the birds in flight is 33 (c) The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate  more from the mean than the fastest recorded speeds of birds in flight . Option A

We should understand that standard deviation looks at the amount of deviation from the means of the set of data.

(a) (70+45+25+45+35+35+40+40+25)÷9 = 40

mean is = 40

(x-m) =30+5+-15+5+-5+-5+0+0+-15)

(x-m)²=(900+25+225+25+25+25+0+0+225)=1450/9

Standard deviation = √650

Standard deviation = 25.5

(b) x= (216+103+96+56+63+35+50+32+55+25+25+20)=776

Mean(m)=776/12=65

(x-m)=151+38+31+-9+-2+-30+-15+-33+-10+-40+-40+-45

Now the square of the deviations from the mean is

(x-m)²=(7396+1444+961+81+4+900+225+1089+100+1600+1600+2025)÷12

=1452

Standard deviation = √1452=33

(c) Therefore, from the calculations, the standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight

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Answer:  15,507.44.

Step-by-step explanation: To find the original price of the home before the down payment was made, you need to use the following formula:

Original price = Mortgage amount / (1 - Down payment percentage)

Plugging in the values given in the question, you get:

Original price = $170,000 / (1 - 8.6%)

The original price of the home before the down payment was made is $<<170000/(1-.086)=185507.44>>185,507.44.

This means that the down payment amount was $185,507.44 - $170,000 = 185507.44-170000=15,507.44.

a) X1+X2 have distribution Bi(n1+n2, p)

b) P(X1 + X2 = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹

Since both variables are independent but they have the same probability parameter, you can interpret that like if the experiment that models each try in both variables is the same. When you sum both random variables toguether, what you obtain as a result is the total amount of success in n1+n2 tries of the same experiment, thus X1+X2 have distribution Bi(n1+n2, p).

b)

Note that, if X2 = k, then X1+X2 = 1 is equivalent to X1 = 1-k. Since X1 and X2 are independent, then P(X1+X2 = 1| X2 = K) = P(X1=1-k|X2=k) = P(X1 = 1-k).

If k = 0, then this probability is equal to P(X1 = 1) = np(1-p)ⁿ¹⁻¹

If k = 1, then it is equal to P(X1 = 0) = (1-p)ⁿ¹

Thus,

P(X1+X2 = 1) = P(X1+X2 = 1| X2 = 1) * P(X2=1) + P(X1+X2 = 1| X2 = 0) * P(X2 = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹

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The unit rates for each animal in mass per heart rate (beats/minute) are as follows:

Cat               13.33g/1 beat per min

Cow           12,307.69g/1 beat per min

Hamster       1.36g/1 beat per min

Horse          2,666.67g/1 beat per min

The unit rate is the ratio of two different variables expressed in a common denominator.

The unit rate is the quotient of the division operation between, for instance, the mass of an animal and its heart rate.

In this instance, the mass of the animal is the numerator with the heart rate used as the denominator.

Animal      Heart Rate     Mass (g)        Unit Rate

                (beats/min)                      (mass per heart rate)

Cat                150            2,000             13.33g/1 beat per min (2,000/150)

Cow               65         800,000    12,307.69g/1 beat per min (800,000/65)

Hamster        44                60                 1.36g/1 beat per min (60/44)

Horse          450      1,200,000   2,666.67g/1 beat per min (1,200,000/450)

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First possibility:  2 positive roots  0 negative roots  4 imaginary roots

Second possibility:  0 positive   0 negative   6 imaginary

Let f(x) = 4x6-4x3+8

f(x) has 2 sign changes.  So, by Descartes's Rule of Signs, f(x) has either                                                    2 positive roots or none.

f(-x) = 4(-x)6-4(-x)3+8 = 4x6+4x3+8

f(-x) has no significant changes.  So, by Descartes's Rule of Signs, f(x) has no negative roots.

f(x) has degree 6.  So, by counting multiplicities, there are a total of 6                                                                                               roots.

First possibility:  2 positive roots   0 negative roots  4 imaginary roots

Second possibility:  0 positive   0 negative   6 imaginary

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Answer:

[tex]\pi[/tex]

Step-by-step explanation:

Area = [tex]\pi x^{2}[/tex]  For a full circle.  This is 1/4 of a circle

A= [tex]\frac{\pi 2^{2} }{4}[/tex] = [tex]\frac{\pi 4}{4}[/tex] = [tex]\pi[/tex]

Answer : The area of the shape is, 111.02 units 2

Answer:

The division algorithm is an algorithm that specifies how to perform the division of one number (called the dividend) by another number (called the divisor) to obtain the quotient and the remainder.

For example, if we want to divide 15 by 4, we can use the division algorithm to find the quotient and remainder. In this case, we have:

15 = 4 * 3 + 3

So, the quotient is 3 and the remainder is 3.

If it's not clear for you yet, you can wait for another answer, maybe better explained.

Easier example (the classic one with apples):

Imagine you have a bunch of apples, and you want to divide them equally among a group of friends. The division algorithm can help you figure out how many apples each friend gets, and how many apples are left over.

Here's an example, let's say you have 15 apples, and you want to divide them among 4 friends. Using the division algorithm, we can figure out that each friend gets 3 apples, and there will be 3 apples left over.

To use the division algorithm, you start by dividing the number of apples (15) by the number of friends (4). This gives us the number of apples each friend gets, which is called the "quotient." In this case, the quotient is 3.

Then, we take the remainder, which is the number of apples that are left over after we divide them evenly among the friends. In this case, the remainder is 3.

So, each friend gets 3 apples, and there are 3 apples left over.

For two events M and N, P(M)=0.6, P(N|M)=0.9, and P(N|M′)=0.2. Then P(M′|N.) is 0.7

This can be easily solved if we know the formula:

P(A or B) = P(A) + P(B) - P(A and B)

So, for this problem, we can modify the formula to be:

P(M or N) = P(M) + P(N) - P(M and N)

Using given information, we can solve:

P(M or N) = P(M) + P(N) - P(M and N)

P(M or N) = 0.6 + 0.2 - 0.1

P(M or N) = 0.7

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After solving the equation by Completing the square , the answer is x = 0.4 , x = -8.4  .

In the question ,

it is given that ,

the equation is x² + 10x + 2 = 2x + 5,

rewriting the equation ,

we get ,

x² + 8x - 3 = 0

adding 3 to both sides ,

we get ,

x² + 8x = 3 ,

For the method of completing the square ,

we take half of the second term's coefficient, and square it, then add it to both sides.

that is 8/2 = 4 .

the equation becomes ;

x² + 2*x*4 + 4² = 3 + 4²

(x + 4)² = 3 + 16

(x + 4)² = 19

taking root on both the sides ,

we get ,

x + 4 = ±√19

So , x = -4 + √19    or   x = -4 - √19

Simplifying further ,

we get ,

x = 0.35889   or x = -8.35889

rounding to the nearest tenth we get

x = 0.4   or x = -8.4  .

Therefore , the solution of the given equation is x = 0.4 , x = -8.4  .

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Answer:

7 13/21 months

Step-by-step explanation:

10 2/3 ÷ 1 2/5 =

= 32/3 ÷ 7/5

= 32/3 × 5/7

= 160/21

= 7 13/21

Answer: 7 13/21 months

The distance between Little Gold town and Old Gold town is 805km-107km.

What is distance?

The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common usage can refer to a physical length or an estimation based on other factors.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending point.

Given: 107 km Big Gold town. 805km Little Gold town. 107km Old Gold town.

We have to find the distance between little gold town and old gold town.

Here, 805km Little Gold town. 107km Old Gold.

Hence, the distance between Little Gold town and Old Gold town is 805km-107km.

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If the nail is measured with a ruler and its length is 5.46 cm , then the correct statements are :

(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ;

(b) The uncertainty is in the final digit of the measurement .

The Uncertainty of a number helps to estimates in comparison of experimental numbers .

it is given that , the reported length of the ruler is = 5.46 cm ;

we know that ,

the uncertainty In any number , is present in last digit only ,

the place value of the last digit in 5.46 is 0.01 .

So , uncertainty can be expressed by reporting measurement as 5.46 ± 0.1 cm

Therefore , the correct statements about the certainty and uncertainty are (a) and (b) .

The given question is incomplete , the complete question is

A nail is measured with a ruler and its length is reports as 5.46 cm.

Select ALL the statements that are correct about the certainty and uncertainty represented in this recorded measurement.

(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ,

(b) The uncertainty is in the final digit of the measurement ,

(c) All three digits shown in the measurement are known with certainty ,

(d) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.01 cm  .

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Answer:

25456

Step-by-step explanation:

592 over 43

592

x 43

multiply 3 by 2, 9 and 5. 3 by 2 is 6. 3 by 9 is 27. 3 by 5 is 15.

add a zero at the second row then,

multiply 4 by 2, 9, 5. 4 by 2 is 8. 4 by 9 is 36. 4 by 5 is 20.

if you aligned them properly, when you add them you should get 25456

I'll try to include a picture of my work, hopefully you can see it**

The number of solution to the equation is 210 when consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃.

Given that,

Consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃ . acting as the three categories into which these items are sorted. Since each x is a true affirmative, your response is accurate. Put one item in each category to begin with, then divide the remaining items across the categories. The number of classification schemes for all the objects is the number of solutions to the equation satisfying the given criteria. In light of this, your response of 20 is erroneous.

We know that,

Number 22 is divided into 22 individual items ,

The three categories in which these items are placed are x₁, x₂ and x₃ .

x₁+x₂+x₃=22----->equation(1)

(x₁-1)+(x₂-1)+(x₃-1)=22-3=19

Let

a=x₁-1,

b=x₂-1 and

c=x₃-1.

So,

a+b+c= 19 ----->equation(2)

So , the number of ways of arranging 21 characters in which 19 are same(A) and 2 are same (J)

= 21!/(2! × 19!)

= 21×10 = 210

Therefore, the number of solution to the equation is 210 when consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃.

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Answer:

(7, 8)

Step-by-step explanation:

equation 1:  [tex]6x+6y=90[/tex]

equation 2: [tex]9x+2y=79[/tex]

This system of equations can be solved for using the elimination method.

First, multiply both sides of the first equation by 3/2 to match the number of x's in both equations so that when we subtract the first equation from the second, the x's cancel and we can solve for y.

[tex]\left(\dfrac{3}{2}\right)\left(6x+6y\right)=(90)\left(\dfrac{3}{2}\right)[/tex]

[tex]9x + 9y = 135[/tex]

Next, subtract this from the second equation.

    [tex]9x+2y=79[/tex]       ← eq. 2

[tex]\underline{- (9x+9y=135)}[/tex]    ← modified eq. 1

     [tex]0 - \, 7y \, = -56[/tex]

Then, solve for y by dividing by 7.

[tex]7y = 56\\\overline{\, 7 \ } \ \ \ \ \overline{\ 7 \: }[/tex]

[tex]y=8[/tex]

So, the y-coordinate of the solution pair is 8.

Now that we've solved for the y, all we have to do to get x is plug the solved y-value back into one of the equations. I'll use the first equation.

[tex]6x+6y=90[/tex]

[tex]6x + 6(8) = 90[/tex]

↓ multiplying out 6 and 8

[tex]6x + 48 = 90[/tex]

↓ subtracting 48 from both sides

[tex]6x = 90 - 48[/tex]

[tex]6x = 42\\\overline{\: 6 \: } \ \ \ \ \, \overline{\: 6 \: }[/tex]

[tex]x = 7[/tex]

So, the x-coordinate of the solution pair is 7.

Finally, put the x- and y-coordinates together into an ordered pair in the form [tex](x, y)[/tex].

(7, 8)

Answer:

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

First, simplify the first equation by dividing all terms by 6:

Then solve it for y:

Now, substitute this into the second equation:

Finally, find the value of y:

The pair of numbers is (7, 8).

The interval for horizontal distance is

(59.9 ,74.2)  ( ranging from 59.9 feet to 74.2 feet)

As per given in the question,

The length of the ladder (l) is 40feet

The angle of elevation in the triangle is [tex]60^0[/tex]

a) In a Δ ABC

One angle is given as 60 and the one side length (length of ladder) is given as 40 feet

The height of the slide is

[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]

[tex]sin60^0[/tex] = [tex]\frac{h}{40}[/tex]                                 where the value of   ( [tex]sin60^0={\frac{\sqrt{3} }{2} }[/tex])

=> [tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{h}{40}[/tex]

=> h = 20[tex]\sqrt{3}[/tex]

Approximately the height of the slide is 34.64 feet

b)    In Δ DEF,

        [tex]\theta = tan^{-1} \frac{h}{d}[/tex]                                                           ----( 1)

=>  [tex]Tan^{-1} (\frac{34.6}{d} )[/tex]

c)  the angle of depression is [tex]\theta=25^0[/tex] and [tex]\theta=30^0[/tex]

first for the value [tex]\theta=30^0[/tex]

substitute the value of [tex]\theta[/tex] in equation (1)

[tex]tan30^0=(\frac{34.63)}{d})[/tex]            where the value of ( [tex]Tan 30^0=\frac{1}{\sqrt{3} }[/tex])

=> [tex]\frac{1}{\sqrt{3} } =\frac{34.63}{d}[/tex]

=> d = 59.99

now

substitute the value [tex]\theta=25^0[/tex] in equation (1)

[tex]tan25^0=(\frac{34.6}{d} )[/tex]

=> d = 74.28

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The equivalent expression for the given expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression ∛x⁵y.

expression is equivalent to ∛x⁵y is

[tex](x^5y)^{\frac{1}{3} }[/tex]

= [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]

The equivalent expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.

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63 mg of anesthetic is present in the patient’s circulatory system.

The operation can last for 20 minutes.

During surgery, a patient’s circulatory system requires at least 50 mg of an anesthetic. The amount of anesthetic present t hours after 70 mg of anesthetic is administered is given by the following,

T(t) = 70 × (0.727) ^t

Time = 1/3 hours

T (1/3) = 70 × (0.727) ^1/3

            = 70 × ∛ 0.727

             = 70 × 0.899176

            = 62.94232

To the nearest mg: 63mg

Now,

63 = 70 × (0.727) ^t

63/70 = (0.727) ^t

0.9 = (0.727) ^t

Log0.9 = log (0.727) ^t

Log0.9 = t × log (0.727)  

T = log0.9 / log0.727

T = 0.330461

T = 0.330461 hours

  = 20 minutes

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The equation in x and y for the line tangent to the curve is x - √3y - √3 = 0

A given curve can be defined by both its cartesian coordinates that is in x-y  form or in polar coordinates that is in terms of r and θ there exists a relationship between two sets of coordinates

x = r cosθ

y = r sinθ

The tangent to any curve f(x) is defined by f'(x) . In order to find tangent to a given terms of r and θ , we can calculate from the above to expressions f'(x)

f'(x) = dy/dx = dx/dθ ÷ dy/dθ

It is given in the question that

r = 2 sinθ

Replacing the value of r to the standard equation,

x = (2 sinθ )cosθ = sin2θ

At θ = π/3 , x = √3 / 2

y = (2 sinθ)sinθ = 2sin²θ

At θ = π/3 , y = 3/2

Differentiating both w.r.t θ

=> dx / dθ = 2cosθ

=> dy/dθ = 4sinθcosθ

So, dy/dx = 2cosθ / 4sinθcosθ

=> 1 / 2sinθ

Therefore , slope of tangent : m = 1/2sinθ ( θ = π/3)

=> m = 1 / 2sin(π/3)

=> m = 2 / 2√3

=> m = 1 /√3

Hence , the equation of line is

( y - 3/2 ) = 1 /√3 (x -  √3 / 2)

=> √3y - 3√3/2 = x - √3/2

=> x - √3y - √3 = 0

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The volume of the gas becomes 4L. Option B is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,

From the ideal gas equation, we know that,

Volume is directly proportional to the temperature,

So,

V₁ / V₂ = T₁ / T₂

Where,

V₁ and T₁ are the initial pressure and temperature,

V₂ and T₂ are the final pressure and temperature.

Substitute the values,

8 / V₂ = 400 / 200

V₂  = 4

Thus, the volume of the gas becomes 4L. Option B is correct.

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449.86

To compute the moment of the second sample, we need to compute the sum of the squares of the sample values.

This formula is:

Sum = ∑(x_i^2)

After inserting the example values:

Sum = 6.2^2 + 7.4^2 + 9.6^2 + 11.5^2 + 13.5^2

Simplifying this formula to:

Total = 38.44 + 54.76 + 92.16 + 132.25 + 181.25

Adding these terms gives us the following final result:

Total = 449.86

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