Find the product. Simplify your answer.
(m+2)(3m+2)

The definition of the set E gives you a natural choice for the limits in the integral:

[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x \int_{x-y}^{x+y} y \, dz \, dy \, dx[/tex]

Computing the integral, we get

[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x y ((x+y)-(x-y)) \, dy \, dx = 2 \int_0^6 \int_0^x y^2 \, dy \, dx[/tex]

[tex]\displaystyle \iiint_E y \, dV = 2 \int_0^6 \frac13 (x^3 - 0^3) \, dx = \frac23 \int_0^6 x^3 \, dx[/tex]

[tex]\displaystyle \iiint_E y \, dV = \frac23 \cdot \frac14 (6^4 - 0^4) = \boxed{216}[/tex]

The evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216

Triple integral integrates the integrand over three dimensions.

Given that:

E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}

Evaluating the integral:

[tex]I = \int \int \int _E y \: dV[/tex]

[tex]I = \mathlarger{\int_0^6 (\int_0^x (\int_{x-y}^{x+y} y\: dz)dy)dx}\\\\I = \int_0^6 (\int_0^x [yz]_{z=(x-y)}^{z=(x+y)}dy)dx\\\\I = \int_0^6 (\int_0^x y( (x+y) - (x-y)) \: dy)dx\\\\ I = \int_0^6 (\int_0^x y(2y) \: dy)dx\\\\I =2 \int_0^6 \left [\dfrac{y^3}{3}\right ]_{y=0}^{y=x} dx\\\\I = 2 \int_0^6 (x^3/3) dx\\\\I = \dfrac{2}{3} \left[\dfrac{x^4}{4} \right]_{x=0}^{x=6} = \dfrac{2}{3} \times \dfrac{6^4}{4} =216[/tex]

Thus, the evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216

Learn more about triple integral here:

https://brainly.com/question/17206296

Using the z-distribution and the formula for the margin of error, it is found that:

a) A sample size of 54 is needed.

b) A sample size of 752 is needed.

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].

Item a:

The estimate is [tex]\pi = 0.213 - 0.195 = 0.018[/tex].

The sample size is n for which M = 0.03, hence:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2[/tex]

[tex]n = 53.1[/tex]

Rounding up, a sample size of 54 is needed.

Item b:

No prior estimate, hence [tex]\pi = 0.05[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]

[tex]n = 751.7[/tex]

Rounding up, a sample of 752 should be taken.

A similar problem is given at https://brainly.com/question/25694087

Answer:

-1.36

Step-by-step explanation:

(-4^2/0.8-3)/10×-4/5=-1.36

Answer:

The equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.

A linear equation is in the form:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

For line s, using the points: (-5, 4) and (4, 22). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-4=\frac{22-4}{4-(-5)} (x-(-5))\\\\y-4=2(x+5)\\\\ y=2x+14[/tex]

Line T passes through the points (-4, 14) and (5, -4). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-14=\frac{-4-14}{5-(-4)} (x-(-4))\\\\y-14=-2(x+4)\\\\ y=-2x+6[/tex]

Hence the equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.

Find out more at: https://brainly.com/question/13911928

Answer:

Step-by-step explanation:

1. When the number of kilograms of paper is doubled, the points will be doubled

2. 300÷ 5 = 60

They have to collect 60 Kg of papers to earn 300 points.

3) P = 5*n

P = 5n

4) We are not only reducing the waste, the collected paper can be reused  or can be sent to recycling centers.

Answer: the answer is d hope this helps if not i'm sorry

Answer:

12/9+3 4/3 = 5 2/3 or 17/3

Step-by-step explanation:

Answer:

its 16/12 all together but if you do simplify its 0.75 hope this helped (❁´◡`❁) LOL.

Step-by-step explanation:

Sarah hanged 12/9 Ornaments on the Christmas tree but tom only hanged 3 4/3 Ornaments. how many Ornaments did both hanged on the tree altogether

Answer:

5 minimum 32 maximum

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

slope is y2-y1/x2-x1

-3-4=-7

-1-4=-5

now that you have -7/-5, or negative seven fifths, simplify.

you get -0.4, or -2/5 as your slope

Hope this helps!!

Answer:

hey there!

Step-by-step explanation:

FIRST QUESTION

3.75

10%= 0.375

20%= 0.75

3.75 + 75 = 4.50

$4.50

SECOND QUESTION

18/100 = X/154

X/154 = 18/100

X*154/154 = 18*154/100

X = 2772/100

X = 27.72

154- 27.72 = 126.28

$126.28

Answer:

16 points.

Step-by-step explanation:

24*2/3 = 16.

Hope this helped!

*Sorry if I'm wrong, though I think I'm correct.*

Enjoy the rest of your day.

Answer:16

Step-by-step explanation: 24 divided by 3 because it is for every 3 questions. You get 8. He gets 2 points for every 3 questions so 8 times 2 is 16.

[tex]\stackrel{\textit{something added to it}}{\boxed{\cfrac{}{} \qquad }+\cfrac{2}{7}}\implies \stackrel{\textit{will be greater than }\frac{2}{7}}{\cfrac{2}{7}+\textit{that something}}[/tex]

The given bar graph shows the number of years that each president served in office, and the presidents of the United States are represented by the width of the bar graph.

A bar graph is one way of representing data, The height of the bar graph represents relative frequencies and the width of the bar graph represents

it's class width or an interval.

The height given bar graph represents no. of years each president lasted

and the width of the bar graph represents the Presidents of the United States.

R-Republican lasted the most no.of years which is 18 years and U-Union lasted the least no of years which is one.

learn more about bar graphs here :

https://brainly.com/question/13298277

#SPJ1

Step-by-step explanation:

Given function:

See the graph below

According to the graph we see that

The minimum is (-4, -1) and zero's are (-5, 0) and (-3, 0)

Function is positive:

Negative:

Increasing:

Decreasing:​

Answer:

800 i think

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

10% of 300 = 300/10 = 30

50% of 20 = 20/2 = 10

30+10=40

Answer:

x is 4, and y is 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

17

343.23 /18 is 19.0683333333

so the closest number to that is 17, if not try 23!

Answer:

x=6

y=9

Step-by-step explanation:

Answer:

3x8m= 14 is the equation that matches the description.

Step-by-step explanation:

It is simply the number three, multiplied by eight with the variable m, and is equal to the number 14.

Answer:

The last one

Step-by-step explanation:

-4 1/3 is less than -1 3/4 because its farther on the negative side and -1 3/4 is closer to the positive side

Answer:

The answer is in the above attachment.

Answer:

we need 6 cups of cranberry juice for 12 gallons of punch

Answer:

Step-by-step explanation:

A' = (-1 + 4, 2 + 6) = (3, 8)

B' = (-2 + 4, -3 + 6) = (2, 3)

A' = (-5 + 4, -1 + 6) = (-1, 5)

Answer:

23

Step-by-step explanation:

First, divide the figure into a large rectangle (2 * 5), a small rectangle (3 * 2), and a quarter circle with a radius of 3. Adding the areas of the 3 shapes together we get 10 + 6 + 7 = 23.

[LARGE RECTANGLE]

A = w * l = 2 * 5 = 10 ([tex]units^{2}[/tex])

[SMALLER TRIANGLE]

A = w * l = 3 * 2 = 6 ([tex]units^{2}[/tex])

[QUARTER CIRCLE]

A * [tex]\frac{1}{4}[/tex] = πr² * [tex]\frac{1}{4}[/tex] = 3 * 3 * π * [tex]\frac{1}{4}[/tex]  = 7 ([tex]units^{2}[/tex])