A stack of 4 identical books is 6.28 high. What is the heigh of 30 of these books?

First number = [tex]x[/tex]

Second number = [tex]x-11[/tex]

[tex]x+x-11+8=71[/tex]

[tex]2x-3=71[/tex]

[tex]2x=71+3[/tex]

[tex]2x=74[/tex]

[tex]x=37[/tex]

First number = [tex]x=37[/tex]

Second number =  [tex]x-11=37-11=26[/tex]

Answer:

B.

Step-by-step explanation:

In the attached file

Answer:

  209 : 40  or  5.225 : 1

Step-by-step explanation:

Your calculator can tell you the ratio 8.36/1.60 is 5.225. Writing that decimal as a fraction, you can factor out 25 to get ...

  8.36 : 1.6 = 5.225 : 1 = 5225 : 1000 = (25)(209) : (25)(40) = 209 : 40

Answer: see below

Step-by-step explanation:

To find a coterminal angle, add or subtract 360° to the given angle as many times as needed to get a positive or negative angle.

I should mention that there are an infinite number of answers!

4) 400°

I can subtract 360° to get a positive angle of 40°

I can subtract another 360° to get a negative angle of -320°

5) -360°

I can subtract 360° to get a negative angle of -720°

I can add 360° twice to get a positive angle of 360°

6) -1010°

I can add 360° to get a negative angle of -650°

I can add 360° another 3 times to get a positive angle of 720°

7) 567°

I can subtract 360° to get a positive angle of 207°

I can subtract another 360° to get a negative angle of -153°

8) -164°

I can subtract 360° to get a negative angle of -524°

I can add 360° to get a positive angle of 194°

9) 358°

I can subtract 360° to get a negative angle of -2°

I can add 360° to get a positive angle of 718°

Step-by-step explanation:

a.It is a controlled experiment because it is clearly seen that an established hypothesis or study is being verified through an experiment, now in this case the hypothesis is tested through an experiment where excessive stress is placed on the Participants during their math exam to effectively verify that people in urban or city areas live with more stress than people in rural areas.

2..As now that the previously established hypothesis has been verified, it is concluded that people who live in the city live with more anxiety and stress than people who live in rural areas.

Answer:

Step-by-step explanation:

Rational numbers are the result of dividing two integers. Intergers cannot be fractions. So 1.5 is rational but 3/2 is not.

Five rational numbers: 1.5, 6, 24.7, 384, 404.4, 1,980

I'm always happy to help :)

Answer:use mathematic pathway to calualte

Step-by-step explanation:

Answer:

B.) a line labeled g(x) that passes through points 0, negative 3 and 4, 5

Step-by-step explanation:

I graphed both equation on the graph below to find the description of the graph of g(x).

Answer:

b for brakes?

Step-by-step explanation:

Answer:

339 bricks.

Step-by-step explanation:

We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.

In this case we will pass everything to pounds.

We have that a 1 pound is 16 ounces, therefore 14 would be:

14 ounces * 1 pound / 16 ounces = 0.875 pounds

In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:

3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds

Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:

1653.467 / 4.875 = 339.17

In other words, it can support about 339 bricks.

Answer:

2

Step-by-step explanation:

as you can see the slope of the line y = -1/2x + 5 is -1/2

the slope m of any line perpendicular to it should verify : -1/2×m = -1

-1/2×m = -1

→ multiply both sides by -2

m = 2

Answer:

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

And replacing we got:

[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]

And we can use one of the points in order to find the intercept like this:

[tex] -3= \frac{2}{3} (-3) +b[/tex]

[tex] b =-3 +2=-1[/tex]

And the equation would be given by:

[tex] y= \frac{2}{3}x -1[/tex]

Step-by-step explanation:

We want an equation given by:

[tex] y=mx+b[/tex]

where m i the slope and b the intercept

We have the following two points given:

[tex] (x_1 = -3, y_1 =-3), (x_2=3, y_2 =1)[/tex]

We can find the slope with this formula:

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

And replacing we got:

[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]

And we can use one of the points in order to find the intercept like this:

[tex] -3= \frac{2}{3} (-3) +b[/tex]

[tex] b =-3 +2=-1[/tex]

And the equation would be given by:

[tex] y= \frac{2}{3}x -1[/tex]

Answer:

  c)  x = 6, y = 9

Step-by-step explanation:

The figure is a parallelogram. The diagonals of a parallelogram bisect each other, so each part of a given diagonal is equal to the other part.

  3x = 2y

  2x = y+3

__

Solving the second equation for y, we have ...

  y = 2x -3

Substituting into the first equation gives ...

  3x = 2(2x -3)

  3x = 4x -6 . . . . simplify

  6 = x . . . . . . . . .add 6 -3x

  y = 2(6) -3 = 9 . . . . use the above expression for y

The values of x and y are (x, y) = (6, 9).

Answer:

[tex] \bar X = \frac{\sum_{i=1}^{42} X_i}{n}[/tex]

And for this case the sample mean is

[tex]\bar X = 127.1[/tex]

And this value is calculated from a sample so then can't represent a population parameter. Then the value 127.1 represent a statistic called the sample mean unbiased for the true population mean since [tex] E(\bar X) =\mu[/tex], and the best option would be:

D) The given value is a statistic for the year because the data collected represent a sample.

Step-by-step explanation:

For this case we know that a homeowner take a random sample of 42 voltage values ina year and he calculate the sample mean with this formula:

[tex] \bar X = \frac{\sum_{i=1}^{42} X_i}{n}[/tex]

And for this case the sample mean is

[tex]\bar X = 127.1[/tex]

And this value is calculated from a sample so then can't represent a population parameter. Then the value 127.1 represent a statistic called the sample mean unbiased for the true population mean since [tex] E(\bar X) =\mu[/tex], and the best option would be:

D) The given value is a statistic for the year because the data collected represent a sample.

Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve [tex]y=x^2[/tex], with [tex]1\le x\le2[/tex], and revolve it about the y-axis. The area of the resulting surface is then

[tex]\displaystyle2\pi\int_1^2x\sqrt{1+(y')^2}\,\mathrm dx=2\pi\int_1^2x\sqrt{1+4x^2}\,\mathrm dx=\frac{(17^{3/2}-5^{3/2})\pi}6[/tex]

But perhaps you'd like the surface integral treatment. Parameterize the surface by

[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k[/tex]

with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex], where the third component follows from

[tex]z=x^2+y^2=(u\cos v)^2+(u\sin v)^2=u^2[/tex]

Take the normal vector to the surface to be

[tex]\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial u}=-2u^2\cos v\,\vec\imath-2u^2\sin v\,\vec\jmath+u\,\vec k[/tex]

The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:

[tex]\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|=u\sqrt{1+4u^2}[/tex]

Then the area of the surface is

[tex]\displaystyle\int_0^{2\pi}\int_1^2\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\int_0^{2\pi}\int_1^2u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]

which reduces to the integral used in the surface-of-revolution setup.

Answer:

Band: 30%

Chorus: 18%

Painting: 21%

Robotics: 14%

Coding: 17%

Answer:

a. [tex]x^2-6x-8=0[/tex]

b. [tex]x^2-6x=8[/tex]

c.

[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]

Also, [tex](-3)^2=9[/tex]

d. [tex]x^2-6x+9=17[/tex]

e. [tex](x-3)^2=17[/tex]

f, g. [tex]x=3\pm \sqrt{17}[/tex]

Step-by-step explanation:

Given: [tex]2x^2-12x-16=0[/tex]

To solve: the given equation

Solution:

a.

[tex]2x^2-12x-16=0[/tex]

Coefficient of [tex]x^2=2[/tex]

Divide both sides by 2

[tex]x^2-6x-8=0[/tex]

b.

[tex]x^2-6x=8[/tex]

c.

Coefficient of x = -6

[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]

Also, [tex](-3)^2=9[/tex]

d.

Add 9 to both sides of the equation: [tex]x^2-6x=8[/tex]

[tex]x^2-6x+9=8+9\\x^2-6x+9=17[/tex]

e.

[tex]x^2-6x+9=17\\x^2-2(3)x+3^2=17\\(x-3)^2=17\,\,\left \{ \because (a-b)^2=a^2+b^2-2ab \right \}[/tex]

f.

[tex](x-3)^2=17\\x-3=\pm \sqrt{17}\\x=3\pm \sqrt{17}[/tex]

g.

[tex]x=3\pm \sqrt{17}[/tex]

[tex]the \: answer \: is \: 10 \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps[/tex]

Answer:

10 is the answer for this question.

Answer:

a) The 95% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day is (1.49, 1.57).

d) The nutritionist is 95% confident that the mean amount of time spent eating or drinking per day for any individual is between 1.49 and 1.57 hours.

(c and b can not be concluded from the confidence interval)

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=1.53.

The sample size is N=1082.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.71}{\sqrt{1082}}=\dfrac{0.71}{32.89}=0.022[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=1082-1=1081[/tex]

The t-value for a 95% confidence interval and 1081 degrees of freedom is t=1.962.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.962 \cdot 0.022=0.042[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 1.53-0.042=1.49\\\\UL=M+t \cdot s_M = 1.53+0.042=1.57[/tex][tex]LL=M-t \cdot s_M = 1.53-0.042=1.49\\\\UL=M+t \cdot s_M = 1.53+0.042=1.57[/tex]

The 95% confidence interval for the mean is (1.49, 1.57).

Answer:

y=-5/3x+8/3

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(-2,6) and (1,1).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-2,6), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-2 and y1=6.

Also, let's call the second point you gave, (1,1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=1 and y2=1.

Now, just plug the numbers into the formula for m above, like this:

m=  

1 - 6

1 - -2

or...

m=  

-5

3

or...

m=-5/3

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-5/3x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(-2,6). When x of the line is -2, y of the line must be 6.

(1,1). When x of the line is 1, y of the line must be 1.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-5/3x+b. b is what we want, the -5/3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-2,6) and (1,1).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(-2,6). y=mx+b or 6=-5/3 × -2+b, or solving for b: b=6-(-5/3)(-2). b=8/3.

(1,1). y=mx+b or 1=-5/3 × 1+b, or solving for b: b=1-(-5/3)(1). b=8/3.

Answer:

Step-by-step explanation:

The confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean of low-tech industry

x2 = sample mean of consumer products industry

s1 = sample standard deviation low-tech industry

s2 = sample standard deviation for consumer products industry

n1 = number of samples of low-tech industry

n2 = number of samples of consumer products industry

a) x1 - x2 is the point estimate of the difference between the means of the two populations

Therefore,

Point estimate = 157 - 218 = - 61

b) the formula for standard error is expressed as

√(s1²/n1 + s2²/n2)

Variance = standard deviation²(s²)

s1² = 1563

s2² = 1602

Standard error = √(1563²/14 + 1602²/12) = 623.2

c) Degree of freedom =

(n1 - 1) + (n2 - 1) = (14 - 1) + (12 - 1) = 24

t-distribution with 24 degrees of freedom

According to the data given, we have that:

a) 61

b) 15.65

c) t-distribution with 24 degrees of freedom

Item a:

The point estimate is the difference between the two sample means, hence:

218 - 157 = 61.

Item b:

For each sample, the standard errors are:

[tex]s_l = \sqrt{\frac{1563}{14}} = 10.57[/tex]

[tex]s_h = \sqrt{\frac{1602}{12}} = 11.54[/tex]

For the difference of the two means, it is:

[tex]s = \sqrt{s_l^2 + s_h^2} = \sqrt{10.57^2 + 11.54^2} = 15.65[/tex]

Item c:

Samples of 14 and 12, hence 14 + 12 - 2 = 24 df.

A similar problem is given at https://brainly.com/question/12490448

Answer:

Lower class Limit: 20,25,30,35,40,45,50

Upper class limit: 24,29,34,39,44,49,54

Class width: 4

Class Midpoints : 22,27,32,37,42,47,52

Class Boundries : 19.5,24.5,29.5,34,5,39.5,44.5,49.5,54.5

Total Individuals: 93

Step-by-step explanation:

Lower class limit is the lowest value of a class e.g in the first class, the lowest value is 20. Similarly find lower class limit of othere classes.

Upper class limit is the highest value of a class e.g in the first class, the highest value is 24. Similarly find upper class limit of othere classes.

Class width is the difference between highest and lowest value of a class e.g 24-20=4

Class Midpoints can be found by adding lowest and highest value of a class and dividing it by 2 e.g (20+24)/2 = 22

Class boundaries are the halfway point which seperates the classes e.g for first classes, clasee boundry is (19.5,24.5)

Total individuals are founf by adding all the frequencies.

Answer:

  IV

Step-by-step explanation:

Cosine is positive in quadrants I and IV.

Cosecant (also sine) is negative in quadrants III and IV.

The quadrant where cos > 0 and csc < 0 is quadrant IV.

Answer:

The answer is (-2 , 1 ) or D on Edge

Step-by-step explanation:

The coordinates of vertex A of square ABCD is (-1, -2).

Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane.

Given:

A(-5, -3), B(-3, -1), C(-1, -3) and D(-3, -5)

By using the rule

T(-4, -1)

So, the coordinate of Vertex A will be

A( -5 + 4, -3 + 1)

=A(-1, -2)

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Answer:

11449/160000

Step-by-step explanation:

The probability of selecting a single adult that thinks most celebrities are good role models is 214/800 = 107/400

The probability that both do is

(107/400)^2 =. 11449/160000

Answer:

y=-4x+1

Step-by-step explanation:

You want to find the equation for a line that passes through the point (-1,5) and has a slope of -4.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was -4. So you can right away fill in the equation for a line somewhat to read:

y=-4x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(-1,5). When x of the line is -1, y of the line must be 5.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the -4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-1,5).

So, why not plug in for x the number -1 and for y the number 5? This will allow us to solve for b for the particular line that passes through the point you gave!.

(-1,5). y=mx+b or 5=-4 × -1+b, or solving for b: b=5-(-4)(-1). b=1.

The equation of line passes through the point (-1, 5) will be;

⇒ y = - 4x - 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (-1, 5).

And, The slope of line is,

⇒ m = - 4

Now,

Since, The equation of line passes through the point (- 1, 5).

And, Slope of the line is,

m = - 4

Thus, The equation of line with slope - 4 is,

⇒ y - 5 = - 4 (x - (-1))

⇒ y - 2 = - 4 (x + 1)

⇒ y - 2 = - 4x - 4

⇒ y = - 4x - 4 + 2

⇒ y = - 4x - 2

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Answer:

8n x n x n x n x n x n x n

Step-by-step explanation:

(2n^2)^3 = 8n^ 6

Now just write "n" 6 times and there you go

The given expression without exponents can be written as 8×n×n×n×n×n×n.

The given expression is (2n²)³.

We need to write the given expression without exponents.

The exponent of a number shows how many times the number is multiplied by itself. For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times.

Now, the given expression can be simplified as follows:

(2n²)³=2³×(n²)³

=2×2×2×[tex]n^{6}[/tex]  (∵[tex](a^{m}) ^{n}=a^{m\times n}[/tex])

=8×n×n×n×n×n×n

Therefore, the given expression without exponents can be written as 8×n×n×n×n×n×n.

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Complete Question

Calculating conditional probability

The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom.

Here are the results:

Bride :29

Groom :30

BOTH : 20

Given that a randomly selected guest is a friend of the groom, find the probability they are a friend of the bride.

P (bride | groom)​

Answer:

The probability is [tex]P(B|G) = \frac{2}{3}[/tex]

Step-by-step explanation:

The sample size is [tex]n = 80[/tex]

The friend of the groom are [tex]G = 30[/tex]

 The friend of the groom are [tex]B = 29[/tex]

 The friend of both bride and groom are [tex]Z = 20[/tex]

The probability that a guest is a friend of the bride is mathematically represented as

      [tex]P(B) = \frac{29}{80}[/tex]

The probability that a guest is a friend of the groom is mathematically represented as

       [tex]P(G) = \frac{30}{80}[/tex]

The probability that a guest is both a friend of the bride and a friend of the groom is mathematically represented as

       [tex]P(B \ n \ G) = \frac{20}{80}[/tex]

Now

    [tex]P(B|G)[/tex] is mathematically represented as

     [tex]P(B|G) = \frac{P(B \ n \ G)}{P(G)}[/tex]

     Substituting values

       [tex]P(B|G) = \frac{\frac{20}{80} }{\frac{30}{80} }[/tex]

      [tex]P(B|G) = \frac{2}{3}[/tex]

Answer:

the answer is 3/5

Step-by-step explanation:

on Khan

Answer:

The bottom left table

Step-by-step explanation:

the same x value cannot have different y values

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. It is considering a promotion that involves mailing discount coupons to all its credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers. Out of the 100 customers, 13 customers said that they used the discount coupons to make a purchase at a Eagle Outfitters store. Use a 0.05 level of significance. (a) Develop the null and alternative hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national. (b) Compute the sample proportion. (c) Compute the test statistic. (d) Compute the critical value. (e) Based on the critical value, do we reject H0 or do we not reject H0? (f) Based on the result of the hypothesis test, should Eagle Outfitter go national with the promotion?

Solution:

a) We would set up the hypothesis test.

For the null hypothesis,

H0: p ≥ 0.1

For the alternative hypothesis,

Ha: p < 0.1

This is a left tailed test

Considering the population proportion, probability of success, p = 0.1

q = probability of failure = 1 - p

q = 1 - 0.1 = 0.9

b) Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 13

n = number of samples = 100

p = 13/100 = 0.13

c) We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.13 - 0.1)/√(0.1 × 0.9)/100 = 1

The calculated test statistic is 1 for the right tail and - 1 for the left tail.

d) Since α = 0.05, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.51/2 = 0.025

The z score for an area to the left of 0.025 is - 1.96

For the right, α/2 = 1 - 0.025 = 0.975

The z score for an area to the right of 0.975 is 1.96

e) In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96

Since - 1 > - 1.96 and 1 < 1.96, we would fail to reject the null hypothesis.

Therefore, based on the result of the hypothesis test, the Eagle Outfitter should go national with the promotion

Answer:

Step-by-step explanation:

Answer:

S = ⅙ π (65^³/₂ − 5^³/₂)

Step-by-step explanation:

z = x² + y², 1 < z < 4

Surface area is:

S = ∫∫√(1 + (fₓ)² + (fᵧ)²) dA

where fₓ and fᵧ are the partial derivatives of f(x,y) with respect to x and y, respectively.

fₓ = 2x, fᵧ = 2y

S = ∫∫√(1 + (2x)² + (2y)²) dA

S = ∫∫√(1 + 4x² + 4y²) dA

For ease, convert to polar coordinates.

S = ∫∫√(1 + 4r²) dA

S = ∫∫√(1 + 4r²) r dr dθ

At z = 1, r = 1.  At z = 4, r = 4.

So 1 < r < 4, and 0 < θ < 2π.  These are the limits of the integral.

S = ∫₀²ᵖⁱ∫₁⁴√(1 + 4r²) r dr dθ

To integrate, use u-substitution.

u = 1 + 4r²

du = 8r dr

⅛ du = r dr

When r = 1, u = 5.  When r = 4, u = 65.

S = ∫₀²ᵖⁱ∫₅⁶⁵√u (⅛ du) dθ

S = ∫₀²ᵖⁱ (⅛ ∫₅⁶⁵√u du) dθ

S = ∫₀²ᵖⁱ (¹/₁₂ u^³/₂ |₅⁶⁵) dθ

S = ∫₀²ᵖⁱ (¹/₁₂ (65^³/₂ − 5^³/₂)) dθ

S = (¹/₁₂ (65^³/₂ − 5^³/₂)) θ |₀²ᵖⁱ

S = (¹/₁₂ (65^³/₂ − 5^³/₂)) (2π)

S = ⅙ π (65^³/₂ − 5^³/₂)