he parent function f(x) = x3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C.

Graph B represents the function g(x) =
.

Graph C represents the function h(x) =
.

Answer:

Part A)

2048π/3 cubic units.

Part B)

8192π/15 units.

Step-by-step explanation:

We are given that R is the finite region bounded by the graphs of functions:

[tex]f(x)=4\sqrt{x}\text{ and } g(x)=x[/tex]

Part A)

We want to find the volume of the solid of revolution obtained when rotating R about the x-axis.

We can use the washer method, given by:

[tex]\displaystyle \pi\int_a^b[R(x)]^2-[r(x)]^2\, dx[/tex]

Where R is the outer radius and r is the inner radius.

Find the points of intersection of the two graphs:

[tex]\displaystyle \begin{aligned} 4\sqrt{x} & = x \\ 16x&= x^2 \\ x^2-16x&= 0 \\ x(x-16) & = 0 \\ x&=0 \text{ and } x=16\end{aligned}[/tex]

Hence, our limits of integration is from x = 0 to x = 16.

Since 4√x ≥ x for all values of x between [0, 16], the outer radius R is f(x) and the inner radius r is g(x). Substitute:

[tex]\displaystyle V=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} \displaystyle V&=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx \\\\ &=\pi\int_0^{16} 16x-x^2\, dx \\\\ &=\pi\left(8x^2-\frac{1}{3}x^3\Big|_{0}^{16}\right)\\\\ &=\frac{2048\pi}{3}\text{ units}^3 \end{aligned}[/tex]

The volume is 2048π/3 cubic units.

Part B)

We want to find the volume of the solid of revolution obtained when rotating R about the y-axis.

First, rewrite each function in terms of y:

[tex]\displaystyle f(y) = \frac{y^2}{16}\text{ and } g(y) = y[/tex]

Solving for the intersection yields y = 0 and y = 16. So, our limits of integration are from y = 0 to y = 16.

The washer method for revolving about the y-axis is given by:

[tex]\displaystyle V=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy[/tex]

Since g(y) ≥ f(y) for all y in the interval [0, 16], our outer radius R is g(y) and our inner radius r is f(y). Substitute and evaluate:

[tex]\displaystyle \begin{aligned} \displaystyle V&=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy \\\\ &=\pi\int_{0}^{16} (y)^2- \left(\frac{y^2}{16}\right)^2\, dy\\\\ &=\pi\int_0^{16} y^2 - \frac{y^4}{256} \, dy \\\\ &=\pi\left(\frac{1}{3}y^3-\frac{1}{1280}y^5\Bigg|_{0}^{16}\right)\\\\ &=\frac{8192\pi}{15}\text{ units}^3\end{aligned}[/tex]

The volume is 8192π/15 cubic units.

Answer:

a) 0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.

b) 0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.

c) 0.1777 = 17.77% probability he or she is a registered Independent.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

57% of 46%(democrats)

38% of 42%(republicans)

76% of 12%(independents)

So

[tex]P = 0.57*0.46 + 0.38*0.42 + 0.76*0.12 = 0.513[/tex]

0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.

Question b:

1 - 0.513 = 0.487

0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.

c. Suppose you find a voter at random who supports the tax increase. What is the probability he or she is a registered Independent?

Event A: Supports the tax increase.

Event B: Is a independent.

0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.

This means that [tex]P(A) = 0.513[/tex]

Probability it supports a tax increase and is a independent:

76% of 12%, so:

[tex]P(A \cap B) = 0.76*0.12[/tex]

Thus

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.76*0.12}{0.513} = 0.1777[/tex]

0.1777 = 17.77% probability he or she is a registered Independent.

Answer:

480 gallons.

Step-by-step explanation:

Given that in a mixture of 240 gallons, the ratio of ethanol and gasoline is 3: 1, if the ratio is to be 1: 3, to find the quantity of gasoline that is to be added the following calculation must be performed:

240/4 x 3 = Ethanol

240/4 = Gasoline

180 = Ethanol

60 = Gasoline

0.25 = 180

1 = X

180 / 0.25 = X

720 = X

720 - 180 - 60 = X

480 = X

Therefore, 480 gallons of gasoline must be added if the ratio is to be 1: 3.

Answer:

Ok... I hope this is correct

Step-by-step explanation:

Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x^(2)+y^(2)=16

Center:  ( 0 , 0 )

Vertices:  ( 4 , 0 ) , ( − 4 , 0 )

Foci:  ( 4 √ 2 , 0 ) , ( − 4 √ 2 , 0 )

Eccentricity:  √ 2

Focal Parameter:  2 √ 2

Asymptotes:  y = x ,  y = − x

Then 0≤z≤1, and a hemispherical cap defined by x^2+y^2+(z−1)^2=16, z≥1.

Simplified

0 ≤ z ≤ 1 , x ^2 + y ^2 + z ^2 − 2 ^z + 1 = 16 , z ≥ 1

For the vector field F=(zx+z^2y+4y, z^3yx+3x, z^4x^2), compute ∬M(∇×F)⋅dS in any way you like.

Vector:

csc ( x )  ,  x = π

cot ( 3 x )  ,  x = 2 π 3

cos ( x 2 )  ,  x = 2 π

Since  

( z x + z ^2 y + 4 y , z ^3 y x + 3 x , z ^4 x ^2 )  is constant with respect to  F , the derivative of  ( z x + z ^2 y + 4 y , z ^3 y x + 3 x , z ^4 x 2 )  with respect to  F  is  0 .

Answer:

5000 km

Step-by-step explanation:

We are given that

3 cm represents on a map of  a town=150 m

Distance between two points=1 km

We have to find the distance between two points on the map.

3 cm represents on a map of  a town=150 m

1 cm represents on a map of  a town=150/3 m

1 km=1000 m

1 m=100 cm

[tex]1km=1000\times 100=100000 cm[/tex]

100000 cm  represents on a map of  a town

=[tex]\frac{150}{3}\times 100000[/tex] m

100000 cm  represents on a map of  a town=5000000 m

100000 cm  represents on a map of  a town

=[tex]\frac{5000000}{1000} km[/tex]

100000 cm  represents on a map of  a town=5000 km

Hence, two points are separated by 5000 km on the map.

Answer:

Terms:

Like Terms:

Coefficients:

Constants:

You simplify the expression by combining like terms:

-5x + 4 - x - 1 = -6x + 5

(7b - 4) + (-2b + a + 1) = 7b - 4 - 2b + a + 1 = 5b + a - 3

Answer:

3x2−2x+6/x2

Step-by-step explanation:

have a great day <33333

Answer:

B

Step-by-step explanation:

When we reflect something across the y axis, the y axis stays the same but the x values change by a factor of -1.

B is the Answer

Answer:

c. switch the x-values and y-values in the table

Step-by-step explanation:

For any table or graph reflection over the line y=x

The rule is (x,y) ----> (y,x)

f(x) is reflected over the line y=x, so the coordinates of f(x) becomes

(-2,-31) becomes (-31,-2)

(-1,0) becomes (0,-1)

(1,2) becomes (2,1)

(2,33) becomes (33,2)

As per the rule, we switch the x-values and y-values in the table

For reflection over the line y=x , the coordinate becomes

(-31,-2)

(0,-1)

(2,1)

(33,2)

Answer:

?

Step-by-step explanation:

Answer:

A. 32

Step-by-step explanation:

If the center is (0, 0) and a point is (0, 4) then the distance from the center to that point is 4 units. That distance is the radius. If you are dilating by a factor of 4, multiply the radius by 4 and you get 16. The new radius is 16 and the diameter= radius*2.

16*2=32

Answer:

The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces

Step-by-step explanation:

To find the sample mean, we can find the mean of the confidence interval.

(15.875 + 16.595)/2 = 16.235

To find the margin of error, that is the difference between the mean and one of the edges of the confidence interval. 16.595 - 16.235 = 0.36

The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces

Answer:

C. We are 90% confident that the interval from 15.875 ounces to 16.595 ounces captures the true mean weight of bags of grapes.

Step-by-step explanation:

Answer:

Step-by-step explanation:

so let the equation equal 13

13 = 3[tex]x^{3}[/tex]-12x+13

so when ever 3[tex]x^{3}[/tex]-12x=0  then this is equation is true, soooo

x (3[tex]x^{2}[/tex] - 12) =0

so when x = 0  this is true, but also when

3[tex]x^{2}[/tex]-12=0   also

3[tex]x^{2}[/tex] = 12

[tex]x^{2}[/tex] = 4

x = 2

so when x = 2  or -2  or 0  ,  then this is true

Answer:

Point D

Step-by-step explanation:

The intersection(s) of lines represents where they cross or intersect. We can see that lines AD and DE cross or intersect as Point D, hence the answer being Point D.

Answer: Point D

Step-by-step explanation: The intersection of two figures is the set of points that is contained in both figures. In the diagram shown, D is the intersection of lines AD and DE because D is the point contained by both line AD and DE.

Answer:

The two lines meet at (-1,1)

Answer:

I think the answer is 100 because nothing greater than 200 if its rounded hope this helped if not sorry

Answer:

x = 2

Step-by-step explanation:

The minimum point of the curve is (2, 0). Hence, axis of symmetry is x = 2

Answer:

answer is 1 2 3 and 4 respectively of given match the following

Given:

The limit problem is:

[tex]\lim_{x\to -\infty}(-2x^5-3x+1)[/tex]

To find:

The value of the given limit problem.

Solution:

We have,

[tex]\lim_{x\to -\infty}(-2x^5-3x+1)[/tex]

In the function [tex]-2x^5-3x+1[/tex], the degree of the polynomial is 5, which is an odd number and the leading coefficient is -2, which is a negative number.

So, the function approaches to positive infinity as x approaches to negative infinity.

[tex]\lim_{x\to -\infty}(-2x^5-3x+1)=\infty[/tex]

Therefore, [tex]\lim_{x\to -\infty}(-2x^5-3x+1)=\infty[/tex].

Answer:

bottom graph

Step-by-step explanation:

f(x) = |3q-6|

because you have absolute value there are 2 possibilities

y= +(3q-6) and y= -(3q-6)

to find where the graph intersects the x-axis make y=0 because there the y coordinate is 0, so we have...

3q-6 =0 and -3q+6 =0

3q= 6 and -3q =-6

q=2 and q=2

the bottom graph has the intersection with x-axis only at 2, so is the correct one

9514 1404 393

Answer:

  bottom graph shown

Step-by-step explanation:

It can be helpful to rearrange the equation to either of the equivalent forms ...

  f(x) = |3(x -2)|

or ...

  f(x) = 3|x -2|

_____

The first of these forms represents a horizontal compression of the absolute value function by a factor of 3, then a right-shift by 2 units. This matches the bottom graph shown.

__

The second of these forms represents a horizontal right-shift by 2 units, and a vertical expansion by a factor of 3. This matches the bottom graph shown.

__

The attached graph shows the function given here along with the absolute value parent function.

_____

Additional comment

The transformations we're usually interested in are ...

g(x) = k·f(x) . . . . vertically scaled (stretched) by a factor of k

g(x) = f(kx) . . . . .horizontally compressed by a factor of k

g(x) = f(x) +k . . . shifted up by k units

g(x) = f(x -k) . . . . shifted right by k units

In many cases, as here, horizontal scaling and vertical scaling are indistinguishable as to which caused a given effect.

Answer:

The right solution is "0.5".

Step-by-step explanation:

According to the question,

P(pay with the sponsored credit card | order exceeds $110)

= [tex]\frac{P(Pay \ with \ the \ sponsored \ credit\ card\ and\ order\ exceeds\ 110)}{P(order \ exceeds \ 110)}[/tex]

= [tex]\frac{P(A \ and \ B)}{P(A)}[/tex]

By putting the values, we get

= [tex]\frac{0.17}{0.34}[/tex]

= [tex]0.5[/tex]

Thus, the above is the right solution.

Answer:

[tex]{ \tt{y = 8 - 3x}} - - - (i) \\ \\ = > 7x - 4(8 - 3x) = 6 \\ 7x - 32 + 12x = 6 \\ 19x - 32 = 6 \\ 19x = 38 \\ x = 2 \\ \\ = > y = 8 - 3(2) \\ y = 2[/tex]

Answer:

A. ¼

Step-by-step explanation:

Rate of change (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:

Where,

[tex] (4, 1) = (x_1, y_1) [/tex]

[tex] (-4, -1) = (x_2, y_2) [/tex]

Plug in the values

Rate of change (m) = [tex] \frac{-1 - 1}{-4 - 4} [/tex]

= [tex] \frac{-2}{-8} [/tex]

= [tex] \frac{1}{4} [/tex]

Rate of change = ¼

Given:

Net income = $19,090

Assets at the beginning of the year = $209,000.

Assets at the end of the year total = $264,000.

To find:

The return on assets.

Solution:

Formula used:

[tex]\text{Return of assets}=\dfrac{\text{Net income}}{\text{Average of assets at the beginning and at the end}}[/tex]

Using the above formula, we get

[tex]\text{Return of assets}=\dfrac{19090}{\dfrac{20900+264000}{2}}[/tex]

[tex]\text{Return of assets}=\dfrac{19090}{\dfrac{473000}{2}}[/tex]

[tex]\text{Return of assets}=\dfrac{19090}{236500}[/tex]

[tex]\text{Return of assets}\approx 0.0807[/tex]

The percentage form of 0.0807 is 8.07%.

Therefore, the return on assets is 8.07%.

Answer:

A

Step-by-step explanation: just divide 71 into 2 which gives you 35.5 making a your answer.

Answer:

the answer is -6. you just subtract 2 with 8

the answer Is 95.61465. If you approximate you get 10.

hope it helps.

Answer: look below

Step-by-step explanation:

A straight angle is 180

180-50=130

the opposite is also the same angle which is the same

180-50-50=80 and 80 + 2x =180

x=50

the angles are 50, 50, 50, 50, 80, 130 and 130 degrees respectively

The customer bought 8 pies.

To find the total amount of pies the customer bought, simply divide 64 by 8 to recieve your answer of 8 pies.

I hope this is correct and helps!

If the question meant that we should write a linear prediction function ;

Answer:

y = bx + c

Step-by-step explanation:

The equation for a linear regression prediction function is stated in the form :

y = bx + c

Where ;

y = Predicted or dependent variable

b = slope Coefficient

c = The intercept value

x = predictor or independent variable

Therefore, the Linear function Given represents a simple linear model for one dependent variable, x

b : is the slope value of the equation, whuch represents a change in y per unit change in x