find the missing side lengths​

Answer:

The volume of the resulting solid is π/2 cubic units.

Step-by-step explanation:

Please refer to the diagram below.

The shell method is given by:

[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]

Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.

From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:

[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]

The volume of the resulting solid is π/2 cubic units.

Answer:

pi/2

Step-by-step explanation:

I always like to draw an illustration for these problems.

For shells method think volume of cylinder=2pi×r×h

Integrate(2pi(2-x)(x-x^2) ,x=0...1)

Multiply

Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)

Combine like terms

Integrate(2pi(2x-3x^2+x^3) ,x=0...1)

Begin to evaluate

2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1

2pi(x^2-x^3+x^4/4), x=0...1

2pi(1-1+1/4)

2pi/4

pi/2

Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation:

A well formatted table of the distribution is attached below :

Answer:

0.124

0.733

0.408

Step-by-step explanation:

Using the table Given :

1.) P(AP Statistics) = 90 / 725 = 0.124

2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733

3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408

Answer:

4/27

Step-by-step explanation:

total number of marbles=9

probability of red=4/9

since you returned the first marble, the total number of marbles remains the same

prob(Blue)=(3/9)=1/3

P(red then blue)=(4/9)*(1/3)

=4/27

===============================================

Explanation:

Add up the values to get

1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54

Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.

So the mean is approximately 1.8876923

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

Now make a spreadsheet as shown below

We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.

After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.

That sum is approximately 0.04403076924

Next, we divide that over n-1 = 13-1 = 12

0.04403076924 /12 = 0.00366923077

That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.

sqrt(0.00366923077) = 0.06057417576822

This rounds to 0.061 which is the final answer.

Answer:

soory i dont know just report me if you angry

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

Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

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

Question a:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]

[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]

[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]

[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}}  + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]0A + 0B = 0[/tex]

[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.

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

Question b:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]A + B = 3 \rightarrow B = 3 - A[/tex]

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

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]7A - \frac{1}{2}B = -5[/tex]

Using [tex]B = 3 - A[/tex]

[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]

[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]

[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]

[tex]15A = -7[/tex]

[tex]A = -\frac{7}{15}[/tex]

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

Then, B is given by:

[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]

Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]

A similar problem is given at https://brainly.com/question/2456414

Answer:

Scheme a 45000 is the answer

Answer:

..... surface area = 16 km^2.

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent Atsu's current age. Then Agyappng is 3x. Three years ago the relationship was ...

  (3x -3) = 4(x -3)

  9 = x . . . . . . . . . . . . add 12-3x

Atsu is 9; Agyappng is 27.

Answer:

(-2,0)

Step-by-step explanation:

The x intercept is the value when it crosses the x axis ( the y value is zero)

x = -2 and y =0

(-2,0)

[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto m\approx0.5[/tex]

Answer:

[tex]m=\frac{1}{2}[/tex]

Step-by-step explanation:

The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-4}{10-4}[/tex]

[tex]m=\frac{3}{6}[/tex]

[tex]m=\frac{1}{2}[/tex]

[tex]m=0.5[/tex]

Answer:

582-600

1,234-1,200

640-600

770-800

1,104-1,100

Perimeter = Sum of all sides

Perimeter = 14cm + 8cm + 10cm + 5cm

Perimeter = 22cm + 15cm

Perimeter = 37cm

Step-by-step explanation:

hope it helps you

...

........

Answer:

82.8

Step-by-step explanation:

mean = sum of all points, over the total given number of points

84 * 26 = 2184

2184 + 69 + 66 = 2319

Now the total number of tests is 26 + 2 or 28

So divide 2319 by 28

2319/28 = 82.82142

rounded to the nearest tenth is 82.8

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

605 boys.

Step-by-step explanation:

5:7 means 5 parts consists of boys and 7 parts consist of girls.

Since 7 parts = 847, 1 part = 121 and 5 parts = 605

Hence there are 605 boys.

Hope you have a nice day :)

Answer:

[tex]f(x) = \sqrt{x} + 2 \\ \\ g(x) = {x}^{2} + 1 \\ \\ f{g(x)} = \sqrt{ {x}^{2} + 1 } + 2 \\ \\ g{f(x)} = {( \sqrt{x} + 2 )}^{2} + 1[/tex]

9514 1404 393

Answer:

  -8,257,536·u^5·v^10

Step-by-step explanation:

The expansion of (a +b)^n is ...

  (c0)a^nb^0 +(c1)a^(n-1)b^1 +(c2)a^(n-2)b^2 +... +(ck)a^(n-k)b^k +... +(cn)a^0b^n

Then the k-th term is (ck)a^(n-k)b^k, where k is counted from 0 to n.

The value of ck can be found using Pascal's triangle, or by the formula ...

  ck = n!/(k!(n-k)!) . . . . where x! is the factorial of x, the product of all positive integers less than or equal to x.

This expansion has 11 terms, so the middle one is the one for k=5. That term will be ...

  5th term = (10!/(5!(10-5)!)(2u)^(10-5)(-4v^2)^5

  = (252)(32u^5)(-1024v^10) = -8,257,536·u^5·v^10

Answer:

Step-by-step explanation:

I assume the sequence is 0, 2, 4, 6

nth term = 2(n-1)

Solution :

Given information :

A sample of n = 10 adults

The mean failure was 24 and the standard deviation was 3.2

a). The formula to calculate the 95% confidence interval is given by :

[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]

Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]

                       = 2.145

Substitute the values

[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]

(26.17, 21.83)

When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]

b). The formula to calculate 95% prediction interval is given by :

    [tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]

   [tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]

   (31.13, 16.87)

Answer:

it simple as look

Step-by-step explanation:

He y I a m r a v I t ha n k S

Wowowowowowowowowk

Answer:

-52

Step-by-step explanation:

-4(x + 10) - 6 = -3(x - 2)

Distribute the left side to get:

(-4x + -40) - 6

Now distribute the right side to get:

-3x + 6

Arrange the equation as the following:

-4x - 40 - 6 = -3x + 6

Add the like terms on each side:

-4x - 46 = -3x + 6

Do the inverse operation of each term:

-x = 52

Now we need to get x to become a positive, so we just divide -x by -1 to get x.

And 52/-1 to get our final answer of -52.

Answer: -52

Step-by-step explanation:

-4(x + 10) - 6 = -3(x - 2)

Distribute the left side to get:

(-4x + -40) - 6

Now distribute the right side to get:

-3x + 6

Arrange the equation as the following:

-4x - 40 - 6 = -3x + 6

Add the like terms on each side:

-4x - 46 = -3x + 6

Do the inverse operation of each term:

-x = 52

Now we need to get x to become a positive, so we just divide -x by -1 to get x.

And 52/-1 to get our final answer of -52.

The system of inequalities that is graphed is:

y ≤ - (2/3)*x

y < x - 3

So the correct option is B.

First, we can see that for both of the inequalities the shaded part is below the lines.

You also can see that the solid line (correspondent to the symbol ≤) is the one with a negative slope, and the dashed line (correspondent with the line <) is the one with a positive slope.

Only with that, we conclude that the correct option is B.

y ≤ - (2/3)*x

y < x - 3

If you want to learn more about inequalities:

https://brainly.com/question/24372553

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Answer:

a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Step-by-step explanation:

Question a:

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]1-\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]1 - \frac{\alpha}{2}[/tex].

Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.

So 120 - 62 = 58 favored the Republican candidate, so:

[tex]n = 120, \pi = \frac{58}{120} = 0.4833[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001[/tex]

The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.

The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Answer:

I believe its  EG and NE but i might be wrong

Step-by-step explanation:

Answer:

1.083

Step-by-step explanation:

Exact form: 13/12

Decimal form: 1.083 (put a line above the 3)

Mixed number form: 1 1/12

Answer:

628 mi^3

Step-by-step explanation:

the volume of a cylinder is given by:

V = base area x height

thus,

V = (3.14)(5)^2(8)

V = (3.14)(25)(8)

V = 628 mi^3

the volume of the cylinder is 628 cubic miles

The volume of the cylinder is 628 cubic miles.

We have a cylinder of radius 5 mi and height 8 mi.

We have to find the volume of the figure and round it to nearest tenth.

The volume of cylinder is given by the formula -

Volume [tex]=\pi r^{2} h[/tex]

We can use the above formula to calculate the volume of cylinder. In our case -

r = 5 mi

h = 8 mi

Substituting the values in the formula -

Volume [tex]=\pi\times5^{2}\times 8\\\\[/tex] = 628 cubic miles.

Hence, the volume of the cylinder is 628 cubic miles.

To solve more questions on finding the volume of cylinder, visit the link below -

https://brainly.com/question/16134180?referrer=searchResults

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