Find the volume of the solid obtained by rotating the region enclosed by the curves y = 4x and y = x3 about the y-axis, where

Hi! ❄

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There are really two ways to solve this problem. One of them is the slope formula. You can familiarise yourself with this formula

[tex]\sf{\dfrac{y2-y1}{x2-x1}}[/tex]

SUBSTITUTE the values

[tex]\sf{\dfrac{-13-8}{17-17}}[/tex]

[tex]\sf{\dfrac{-21}{\bf{0}}[/tex] (notice the zero was in bold-face)

Dividing by zero is an operation we cannot do.

So the slope of this particular line is not defined.

The other way is looking at the first co-ordinates of the points given

Notice that they are exactly the same. Whenever that happens, the slope of that line is not defined.

Hope that made sense !!

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[tex]\star\tiny\pmb{\tt{calligraphy}}\star[/tex]

Using sampling concepts, the correct option regarding the validity of the inference is given as follows:

B) Yes, this is a valid inference because she took a random sample of the neighborhood.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. If I had taken 1000 residents just from Buffalo, it would not be a representative sample.

In this problem, all addresses in the neighborhood are considered, hence a random sample was taken and the correct option is given as follows:

B) Yes, this is a valid inference because she took a random sample of the neighborhood.

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Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment: FALSE

As it is given in the description, centipedes have only one pair of legs on each body segment. So, the whole statement becomes False.

Therefore, the statement "centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment" is FALSE.

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Complete question:

Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment. TRUE or FALSE

so here you the answer is 9

1. The number of gallons of water produced is 460 gallons

2. The amount in cm the sea would increase after 6 years is 392 cm

We'll begin by by converting 1.9 m³ to cm³. This is illustrated below:

1 m³ = 1×10⁶ cm³

Therefore,

1.9 m³ = 1.9×10⁶ cm³

Next, we shall determine the volume of water produced from 1.9 m³ (i.e 1.9×10⁶ cm³) of ice. This is illustrated below:

From the question given,

1 cm³ of ice = 0.92 cm³ of water

Therefore,

1.9×10⁶ cm³ of ice = 1.9×10⁶ × 0.92

1.9×10⁶ cm³ of ice = 1.748×10⁶ cm³ of water

Finally, we shall determine the number of gallons produced. This is illustrated below:

From the question given,

3800 cm³ of water = 1 gallon

Therefore,

1.748×10⁶ cm³ of water = 1.748×10⁶ / 3800

1.748×10⁶ cm³ of water = 460 gallon

Thus, 460 gallons were produced

From the question given above,

1000 Km³ = 364 cm

Therefore,

179.4 Km³ = (179.4 × 364) / 1000

179.4 Km³ = 65.3016 cm per year

To obtain the increase after 6 years, multiply 65.3016 by 6 as shown below:

65.3016 × 6 = 392 cm

Thus, the sea will increase 392 cm after 6 years

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Answer:

[tex]\frac{\sqrt{731}}{30}[/tex]

Step-by-step explanation:

We first observe that the angle is located in quadrant III

This allows us to draw a triangle as attached in the attachments.

Using this triangle, we can find sin([tex]\theta_1[/tex]).

Remembering that sin(theta) = [tex]\frac{opp}{hypo}[/tex], we can see from the attached image that it is [tex]\frac{\sqrt{30^2 - 13^2}}{30}[/tex], then simplifying [tex]\sqrt{30^2 - 13^2}[/tex] using a calculator, we get [tex]\sqrt{731}[/tex].

So our final answer is the answer shown above.

You may be wondering how did the side lengths appear on the triangle.

From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.

The expression which represents the given conditional statement in shorthand is: S → W.

A conditional statement can be defined as a statement that can be written to contain both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."

Where:

P and Q represent sentences.

If Megan is swimming = S

It is warm outside = W

Therefore, if Megan is swimming, then it is warm outside is represented by S → W.

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Answer: 102 degrees

Step-by-step explanation:

The remote angle theorem is that two remote angles are equivalent to the exterior angle. Both 51 degrees are remote angles, and angle 4 is the exterior.

51 + 51 = Angle 4

Angle 4 = 102 degrees

Answer:

972π  or 3052.08 if π=3.14(remember to label the answer with your units)

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}\\[/tex]π[tex]r^{3}[/tex]. So, just plug the radius into the formula. [tex]r^{3}[/tex] in this case is [tex]9^{3}[/tex] which is 729. For, [tex]\frac{4}{3}[/tex]×729, the 3 and 729 cancel out to create 4×243 which is 972. Just add π to this and you get 972π. If π is 3.14 just multiple 972 and 3.14 to get 3052.08.

Answer:

12, 14, 16, 18

Step-by-step explanation:

(x + (x+2) + (x+4) + (x+6))/4 = 15

^ solve algebraically

you'll get (4x+12)/4 = 15

then: 4x + 12 = 60

then 4x = 60-12

then 4x = 48

then x = 12

x is 12 so then do substitution

so you get

12 + (12+2) + (12+4) + (12+6)

12, 14, 16, 18

The process is Capable.

According to statement

When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits

and when these conditions are fulfilled then the process is to be called CAPABLE.

So, The process is Capable.

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Answer:48

Step-by-step explanation:

Answer:

  P = 160/A

Step-by-step explanation:

For P to vary inversely with A, we must have P be proportional to the reciprocal of A. The constant of proportionality is given.

Two quantities are directly proportional if there is a constant of proportionality (k) that multiplies one of them to give the value of the other:

  y = kx

They are inversely proportional if the inverse of one of them can be multiplied by a constant of proportionality to give the value of the other:

  y = k(1/x) = k/x

In this problem, the variables P and A are said to be inversely proportional. That means the equation that relates them will be of the form ...

  P = k/A

You are given such a form with k=160, which is an appropriate value for the relation given by the problem. All you need to do is fill in the variable:

  P = 160/A

Answer:

7 - 10

Step-by-step explanation:

Because it is -3 and 7 - 10 = -3

Answer:

just divide 3125 by 5 and your answer is 625

Step-by-step explanation:

Using division, 3125 by 5 and get answer 625.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

If 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus,  a / b = a divided in b equal parts.

We have been given 5x = 3125

Divide by 5 each sides;

x = 3125/5

x = 645

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Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2the number represented by point B is 1⁴/₅

The question has to deal with proportion

Proportion is the measure of a variable or quantity relative to another.

Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2, the measure of a sub-unit between 1 and 2 is

= 1/5

So, each sub-unit measure 1/5

Since point B is one mark to the left of 2, we have that point B is y = 2 - 1/5 = (10 - 1)/5

= 9/5

= 1⁴/₅

So, the number represented by point B is 1⁴/₅

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The maximum value of the product of two number whose difference is 14 is 49.

The maximum or minimum value of a function is the highest or lowest value of that function.

Let the numbers be x and y

Their product f(x,y) = xy

Since their difference is 14, x - y = 14

So, x = 14 - y

Substituting x into f(x,y), we have

f(x,y) = xy

= (14 - y)y

= 14y - y²

To find the maximum or minimum value of f(x,y) we differentiate it with respect to y and equate to zero.

So, f(x,y) = f(y) = 14y - y²

df(y)/dy = d(14y - y²)/dy

df(y)/dy = d(14y)/dy - dy²/dy

df(y)/dy = 14 - 2y

Equating to zero, we have

df(y)/dy = 0

14 - 2y = 0

14 = 2y

y = 14/2

y = 7

To determine if this gives a maximum or minimum for f(y) = f(x,y), we differentiate f'(y) again

So, df'(y)/dy = d(14 - 2y)/dy

= d14/dy + d(-2y)/dy

= 0 - 2

= -2 < 0.

Since f"(y) = -2 < 0, then y = 7 gives a maximum for f(x,y)

So, since y = 7,

x = 14 - y = 14 - 7 = 7

So, f(x,y) is maximum at x = 7 and y = 7

So, f(7,7) = 7 × 7

= 49

So, the maximum value of the product of two number whose difference is 14 is 49.

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After enlargement, the new photo would be 16 times larger. The answer is C: 16.

An enlargement can be described as a type of dilation in transformation which involves increasing the dimensions of an original image by a given scale factor, so that the new image is similar to the original image. Their sizes would be different while their shapes remain the same. Also, the ratio of their corresponding dimensions would be the same.

Given the following:

Dimension of original photo = 6 inches by 8 inches

Scale factor = 4

To find the new dimensions of the new photo, multiply the corresponding dimensions of the original photo by 4, thus:

6 × 4 = 24 inches

8 × 4 = 32 inches

New dimensions = 24 by 32

Area of original photo = 6 × 8 = 48 in.²

Area of new photo = 24 × 32 = 768 in.²

768/48 = 16

This means that the new photo is 16 times larger than the original photo.

The answer is: C. 16.

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Answer:

The expression for area is (x)(x+10).

Step-by-step explanation:

Area=(w)(l)

Area=(x)(x+10)

(Note: This expression can be expanded, but then it wouldn't be fully simplified)

Hope this helps!

Answer:

false

Step-by-step explanation:

X is equal to Y

therefore,

X = Y

X= false

Y = false

so,

false = false

The theorems that prove that lines are parallel includes:

Parallel lines are the lines that do not intersect or meet each other at any point in a plane.

Theorems that prove that lines are parallel includes:

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Answer: 60 degrees

Step-by-step explanation:

An interior angle of a polygon and its corresponding exterior angle are supplementary (add to 180 degrees).

The measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). This can be obtained by plotting the quadrilaterals on a graph paper and comparing the figures.

Given that,

vertices of quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)

vertices of quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4)

(x,y) ; (x, y-8)

ABCD is reflected across the line y=4 to get the quadrilateral EFCD.

Reflection means the size and shape of the quadrilaterals is same ⇒quadrilateral ABCD and quadrilateral EFCD are congruent.

Thus corresponding parts of congruent triangles are equal, corresponding angles will be equal.

Hence the measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).

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The value of x in the equation 1 1/5 - x/3 = 9/10 is 9/10

1 1/5 - x/3 = 9/10

- x/3 = 9/10 - 1 1/5

- x/3 = 9/10 - 6/5

-x/3 = 9-12 / 10

-x/3 = -3/10

x = -3/10 ÷ - 1/3

= -3/10 × -3/1

x = 9/10

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VARIABLE is a symbol which is used for representation in a  math.

According to the statement

we have to explain about the what is a variable.

So, VARIABLE is a symbol which is used for representation in a  math.

It represent the so many things like Algebra, Matrix,Vector etc. and also so many things.

A variable may also be called a data item.

It is used to represent a data like country name, name, age, date of birth etc.

we know that the every thing is changeable. So, like ther things variables are also changeable.

The changing of variable parameters is called as variation. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value.

So, VARIABLE is a symbol which is used for representation in a  math.

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The value of sample proportion is found to be 0.253.

The sample proportion [tex]\hat{p}[/tex] indicates the percentage of people in a sample who exhibit a particular quality or attribute.

Divide the number of individuals (or items) who possess the desired attribute by the overall sample size to obtain the sample proportion.

Now, according to the question;

The 90% confidence interval for a proportion is found to be (0.22,0.28).

The confidence interval for the sample is given as-

Confidence interval = Sample proportion ± Margin of Error

Let [tex]\hat{p}[/tex] be the sample proportion.

The level of significance = 1 - 0.90

                                         = 0.10 (10%)

From z-value table, at a significance level of 5% (two-sided), z has a critical value of 1.645.

90% confidence interval = [tex]\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Thus,                       0.22 = [tex]\hat{p} - 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex], and

                               0.28 = [tex]\hat{p} + 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Covert both equation in the form of [tex]\hat{p}[/tex] and equating to each other.

[tex]\begin{aligned}&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22\\&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06\\&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645}\\&\sqrt{\frac{\hat{\nu}(1-\hat{p})}{n}}=0.02\end{aligned}[/tex]

Take square root,

[tex]\begin{gathered}\frac{\hat{p}(1-\bar{p})}{n}=0.0004 \\n=\frac{\hat{p}(1-\bar{p})}{0.0004}\end{gathered}[/tex]

Substituting the value of 'n' in the receptive equation to get the value of [tex]\begin{aligned}0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{p(1-\hat{p})}} \times 0.0004 \\0.22 &=\hat{p}-1.645 \times \sqrt{0.0004} \\0.22 &=\hat{p}-(1.645 \times 0.02) \\0.22 &=\hat{p}-0.033 \\\hat{p}=& 0.22+0.033=0.253\\\end{aligned}[/tex]

Therefore, the value of sample proportion is 0.253.

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Answer:

C.  All real numbers.

Step-by-step explanation:

The domain is the set of all x values that are used by points on the graph.  This is a sine wave, and we assume it extends infinitely far to the left and right.  Even without that assumption, you can eliminate the other answers.

A. This describes the numbers on the x-axis between 0 and 5, inclusive.  But the graph includes many more points with x-coordinates beyond that interval.

B. The same sort of thing: the graph extends well beyond the interval of x values between -5 and 5, inclusive.

D.  This would mean the graph has only points with positive x-coordinates, but there are many with negative (or 0) x-coordinates.

The ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.

The number of flowers in the vase = 12 flowers

The number of roses in the vase = 5 roses.

Therefore, the number of daisies in the vase = The number of flowers in the vase - The number of roses in the vase,

or, the number of daisies in the vase = 12 - 5 = 7.

Thus, the number of daisies in the vase = 7.

We are asked to find the ratio of the total number of flowers in the vase, to the number of daisies in the vase.

Thus, the ratio = The number of flowers in the vase/The number of daisies in the vase,

or, the ratio = 12/ = 12:7.

Thus, the ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.

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