Identify a pair of vertical angles in the figure
A. Angle ADE and Angle ADB
B. Angle EDC and angle DBA
C. angle ADE and angle EDC
D. Angle ADE and angle BDC

Answer:

(a)[tex]R(x)=-0.02x^2+610x[/tex]

(b)[tex]R'(x)=-0.04x+610[/tex]

(c)R'(5400)=$394

Step-by-step explanation:

Given that x is the quantity demanded and the speaker's unit price (in dollars) is p where:

p = −0.02x + 610 (0 ≤ x ≤ 20,000)

(a)Revenue function R.

Revenue = Price X Quantity Demanded

Therefore:

R(x)=xp

[tex]=x(-0.02x + 610)\\R(x)=-0.02x^2+610x[/tex]

(b)Marginal revenue function R'(x)

If [tex]R(x)=-0.02x^2+610x[/tex]

Then, the marginal revenue function

[tex]R'(x)=-0.04x+610[/tex]

(c)We want to compute R'(5,400)

[tex]R'(5400)=-0.04(5400)+610\\R'(5400)=394[/tex]

From the above, we can infer that the revenue that will be generated on the sales of the 5401st item is $394.

Answer:

c

Step-by-step explanation:

plato

Answer:

a). Horizontal distance = 11.1 m

b). Maximum height = 6.2 m

c). Firefighter is 13.7 m from the house

Step-by-step explanation:

Given question is incomplete; find the complete question in the attachment.

Height of the water can be determined by the expression,

h(x) = -0.026x²+ 0.577x + 3

Here x = Horizontal distance of the from the firefighter

a). Since the stream of the water will follow a parabolic path, maximum point of the parabola will be = Vertex of the parabolic path

Horizontal distance from the firefighter at which the water achieves the maximum height = -[tex]\frac{b}{2a}[/tex]

From the quadratic function,

h(x) = -0.026x²+ 0.577x + 3

a = -0.026

b = 0.577

Therefore, the horizontal distance = [tex]-\frac{0.577}{2\times (-0.02612)}[/tex] = 11.05 m

                                                         ≈ 11.1 meters

b). By putting x = 11.1 in the quadratic equation,

    h(x) = -0.02612(11.1)²+ 0.577(11.1) + 3

           = -3.2182 + 6.4047 + 3

           = 6.18 m

           ≈ 6.2 m

c). For h(x) = 6 m

    6 = -0.02612x² + 0.577(x) + 3

    0.02612x² - 0.577x + 3 = 0

    From quadratic formula,

    x = [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

    x = [tex]\frac{0.577\pm \sqrt{(-0.577)^2-4(0.02612)(3))}}{2(0.02612)}[/tex]

    x = [tex]\frac{0.577\pm\sqrt{0.019489}}{0.05224}[/tex]

    x = [tex]\frac{0.577\pm0.1396}{0.05224}[/tex]

    x = 13.7 m, 8.37 m

Therefore, the farthest distance of the firefighter from the house will be 13.7 m

Answer:

1st Graph

Step-by-step explanation:

Step 1: Find the inverse

y = 2x - 2

x = 2y - 2

x + 2 = 2y

y = (x + 2)/2

Step 2: Graph the inverse

Simply use a graphing calculator and we should see our answer is the top left graph.

Answer:

56 ft

Step-by-step explanation:

Because the bedroom is similar to the bed we can write that

7 : 15 = 6 : x

x = 15*6/7 ≈ 12.86 ft

Perimeter of the bedroom is

15*2 + 12.86 *2 ≈ 56 ft

Answer:

24 feet.

Step-by-step explanation:

The side  of the square = √36 = 6 feet.

The square has 4 equal sides so the perimeter = 4*6 = 24 feet.

Answer:

Step-by-step explanation:

Given system of equations in the question are,

-3x + y = -6

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

We can rewrite these equation as,

-3x + y = -6

y = 3x - 6 ------(1)

Table of input-output values for this equation will be,

x       0      1        2         3          4

y      -6     -3       0         3          6

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

Table for this equation will be

x        0        2         4         6         8

y        -1        0         1          2         3

By plotting these points on the graph we find (2, 0) is a common point in both the tables,

Therefore, (2, 0) is the only one solution of the given system of equations.

Answer:

The margin of error is of 0.038 = 3.8%.

Step-by-step explanation:

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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 320, \pi = \frac{70}{320} = 0.21875[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The margin of error is:

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

[tex]M = 1.645\sqrt{\frac{0.21875(1-0.21875)}{320}}[/tex]

[tex]M = 0.038[/tex]

The margin of error is of 0.038 = 3.8%.

Answer:

The answer is C (j' 1,4). It is not B J'(4, 1) because the new coordinate is moving 90 degrees clockwise not 180 degrees.

Step-by-step explanation:

J' will have coordinates (1, 4) after  90° clockwise rotation

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Rectangle JKLM is rotated 90° clockwise about the origin.

On a coordinate plane, rectangle J K L M has points (-4, 1), (-1, 1), (- 1, - 1), (- 4, - 1).

After rotating the rectangle 90° clockwise about the origin, the point J(-4, 1) will be transformed to a new point J' with coordinates (y, -x).

Thus, J' will have coordinates (1, 4).

Therefore,  J' will have coordinates (1, 4) after  90° clockwise rotation

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Answer:B.

Step-by-step explanation: it is better to have empty seats than toforce people to give up their seats.

Answer:

A) 360

B) 360

Step-by-step explanation:

Part A)

Given that there are a total of 6 people and 4 person subcommittee is to be selected.

Number of ways to select 1st person = 6

Now, 1 person is selected, total persons left are 5

Number of ways to select 2nd person = 5

Now, 1 person is selected, total persons left are 4

Number of ways to select 3rd person = 4

Now, 1 person is selected, total persons left are 3

Number of ways to select 4th person = 3

So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360

Part B)

Given that there are a total of 6 people in the committee

Number of ways to select president  = 6

Now, 1 person is selected, total persons left are 5

Number of ways to select vice president = 5

Now, 1 person is selected, total persons left are 4

Number of ways to select secretary = 4

Now, 1 person is selected, total persons left are 3

Number of ways to select treasurer = 3

So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360

Answer:

EF ≈ 3.8

Step-by-step explanation:

Using the Sine rule in Δ DEF

[tex]\frac{EF}{sin75}[/tex] = [tex]\frac{DE}{sin50}[/tex] , that is

[tex]\frac{EF}{sin75}[/tex] = [tex]\frac{3}{sin50}[/tex] ( cross- multiply )

EF × sin50° = 3 × sin75° ( divide both sides by sin50° )

EF = [tex]\frac{3sin75}{sin50}[/tex] ≈ 3.8

━━━━━━━☆☆━━━━━━━

▹ Answer

r = 4

▹ Step-by-Step Explanation

15r - 6r = 36

Collect like terms

9r = 36

Divide

r = 4

Final Answer

r = 4

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer: The answer would be 4, which is B, hopefully this helps.

hello

[tex]A-B=\left[\begin{array}{cc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\\\=\left[\begin{array}{cc}4+2&2\\-10&8+1\\-5+3&-4\end{array}\right] \\\\=\left[\begin{array}{cc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]

hope this helps

Using matrices A  and B, the result of A-B is

[tex]A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]

Given :

Two matrices A  and B. We need to subtract both matrix

Lets find out A-B

Given matrices  A  and B  are

[tex]A=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] \\B=\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right][/tex]

When we subtract A-B  we need to subtract the corresponding elements in that matrix

[tex]A-B=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] -\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right]=\left[\begin{array}{ccc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]

The above is the resultant matrix .

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Answer:

B

D

A

Step-by-step explanation:

Given:

A. [tex]2x^3-x^{2} -6x[/tex]

B. [tex]2x^3+8x+4[/tex]

C. [tex]3x^4+x^{2} +x-7[/tex]

D. [tex]3x^4-3x^{2} +5x-7[/tex]

Now, let us evaluate the given expressions one by one.

[tex](4x^3-4+ 7x)-(2x^3-x-8)\\\Rightarrow 4x^3-4+ 7x-2x^3+x+8\\\Rightarrow 2x^3+8x+ 4[/tex]

It is equation B.

So, [tex](4x^3-4+ 7x)-(2x^3-x-8)[/tex] is equivalent to B.

[tex](-3x^2+x^4+x)+(2x^4-7+4x)\\\Rightarrow -3x^2+x^4+x+2x^4-7+4x\\\Rightarrow3x^4-3x^{2} +5x-7[/tex]

It is equation D.

So, [tex](-3x^2+x^4+x)+(2x^4-7+4x)[/tex]  is equivalent to D.

[tex](x^{2} -2x)(2x+3)\\\Rightarrow 2x^3-4x^{2} +3x^{2} -6x\\\Rightarrow 2x^3-x^{2} -6x[/tex]

It is equation A.

So, [tex](x^{2} -2x)(2x+3)[/tex] is equivalent to A.

So, answer is:

B

D

A

Answer:

B D A

Step-by-step explanation:

Hope I Helped

Answer:

The new salary of that person (for the period of a year) would be [tex]\$ 16,\!275[/tex].

Step-by-step explanation:

Start by considering: what is the exact value (in dollars) of that "[tex]5\%[/tex] raise in salary"?

[tex]5\%[/tex] (five percent) is equal to [tex]\displaystyle \frac{5}{100}[/tex].

To find the value of [tex]5\%[/tex] of [tex]\$15,\!500[/tex], simply multiply [tex]\$15,\!500[/tex] by [tex]5\%[/tex]:

[tex]\begin{aligned}&5\% \times \$15,\!500\\ &= \frac{5}{100} \times \$15,\!500 \\ &= 5\times \$155 = \$775 \end{aligned}[/tex].

Add that to the original (one-year) salary of this person to find the new one-year salary:

[tex]\$15,\!500 + \$775 = \$16,\!275[/tex].

Answer:

The new salary is $16,725

Step-by-step explanation:

To find the new salary, multiply 5% and $15,500

5% * $15,500

First, convert 5% to a decimal. Divide 5 by 100 or move the decimal place 2 spaces to the left.

5/100=0.05

5.0 --> 0.5--> 0.05

0.05 * $15,500

Multiply

$775

The raise is equal to $775.

Next, add the raise to the salary.

raise + salary

The raise is $775 and the salary is $15,500

$775 + $15,500

Add

$16,275

The new salary is $16,275

Answer:

  (–ꝏ, 0) U (0, 5)

Step-by-step explanation:

The relation can be written as ...

  x³ < 5x²

  x³ -5x² < 0

  x²(x -5) < 0

This is not true for x = 0. It is true for x < 5, otherwise. Then the solution set is ...

  x ∈ {(–ꝏ, 0) U (0, 5)}

Answer:

C

Step-by-step explanation:

got it right on edge

Answer:

B / px= k

Step-by-step explanation:

B = kpx

Divide each side by px

B / px= kpx/px

B / px= k

Answer:

First option

Step-by-step explanation:

B=kpx

B=k*(px)

Then,

[tex]k = \frac{b}{px} [/tex]

Answer:

If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.

If the data is unsymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.

Step-by-step explanation:

An histogram for a symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.

An histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.

Answer:

i ama

Step-by-step explanation:

Answer:

Net sales is $ 504285.71

Step-by-step explanation:

We have the following:

Let net sales be x.

Net sales - Cost of goods sold = Gross profit

We replace and we are left with:

x - $ 353000 = x * 30%

x - $ 353000 = 0.30 * x

x - 0.30 * x = $ 353000

0.7 * x = $ 353000

x = $ 353000 / 0.7

x = $ 504285.71

Therefore, net sales is $ 504285.71

The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

We have,

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = X ± (Z * (σ/√n))

where:

CI is the confidence interval

X is the sample mean

Z is the critical value corresponding to the desired confidence level (90% confidence level corresponds to Z = 1.645 for a large sample size)

σ is the population standard deviation

n is the sample size

Given that the sample mean X of the net change in LDL cholesterol is 2.7, the standard deviation (σ) is 17.8, and the sample size (n) is 47, we can calculate the confidence interval as follows:

CI = 2.7 ± (1.645 * (17.8/√47))

Calculating the standard error (SE):

SE = σ/√n = 17.8/√47 ≈ 2.587

Substituting the values into the confidence interval formula:

CI = 2.7 ± (1.645 * 2.587)

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 2.7 + (1.645 * 2.587) ≈ 7.199

Lower bound = 2.7 - (1.645 * 2.587) ≈ -1.799

Therefore, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199.

Interpreting the confidence interval:

Since the confidence interval contains both positive and negative values, it suggests that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

The interval includes zero, indicating that there is a possibility that the mean net change in LDL cholesterol after the garlic treatment could be zero (no change).

However, it is important to note that further studies or a larger sample size may be needed to draw more definitive conclusions.

Thus,

The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

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The 90% confidence interval suggests that the true mean net change in LDL cholesterol after the garlic treatment lies between -1.57 and 6.97 mg/dL. Since the interval contains both positive and negative values, it indicates that the garlic treatment may or may not be effective in reducing LDL cholesterol.

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = mean ± (Z * (standard deviation / √n))

Here, n represents the sample size (47), Z is the critical value corresponding to a 90% confidence level (Z = 1.645 for a 90% confidence level), and the mean is 2.7 with a standard deviation of 17.8.

Plugging in the values:

CI = 2.7 ± (1.645 * (17.8 / √47))

CI = 2.7 ± (1.645 * (17.8 / 6.856))

CI = 2.7 ± (1.645 * (2.596))

CI = 2.7 ± 4.270

CI = 2.7 + 4.270  ;  CI = 2.7 - 4.270

CI = 6.97             ;  CI = -1.57

Thus, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately (-1.57, 6.97).

The confidence interval suggests that the effectiveness of garlic in reducing LDL cholesterol is inconclusive. The interval spans both positive and negative values, indicating that the true mean change in LDL cholesterol could be anywhere within this range. Further research or a larger sample size might be needed to draw a more definitive conclusion about the effectiveness of garlic in lowering LDL cholesterol.

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Answer:

Its the first answer choice.

Step-by-step explanation:

Its open circle because the sign is just greater than. And since x is an absolute value, the negative sign doesnt matter so, it points to the right of 10 and to the left of -10.

Answer:

Polly can choose 33264 schedules.

Step-by-step explanation:

None of these sections interfere with each other, so:

For each statistics choice, there are 12 composition choices.

For each composition choice, there are 11 section of Ethics choices.

For each section of Ethics choice, there are 18 Physics choises.

There are 14 statistics choices.

From how many possible schedules can Polly choose?

14*12*11*18 = 33264

Polly can choose 33264 schedules.

Answer:

  y = √(900 -x²); see below for a graph

Step-by-step explanation:

The high point (30 ft) is the radius of the circle, so the equation is ...

  x² +y² = 30²

Subtract the x-term and take the square root to find y.

  y² = 30² -x²

  y = √(30² -x²) = √(900 -x²)

The graph is shown in the attachment.

_____

Comment on "how that website works"

We don't know what web site you're referring to, but the one I like is Desmos. It only takes a few minutes to learn to graph the equation here.

You don't even need to solve for y to get the desired graph. You can simply specify that y ≥ 0.

Answer:

For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:

[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]

Where x represent the net price. And if we solve for the value of x we got:

[tex] x= 100 *\frac{156}{88}= 177.273[/tex]

So then the net price for this case would be $ 177.273

Step-by-step explanation:

For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:

[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]

Where x represent the net price. And if we solve for the value of x we got:

[tex] x= 100 *\frac{156}{88}= 177.273[/tex]

So then the net price for this case would be $ 177.273

Answer:

true

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

Answer:

[tex] \dfrac{5x^2 + 5x + 3}{3x^2 + 3x} [/tex]

Step-by-step explanation:

[tex] \dfrac{2x + 3}{3x} + \dfrac{x}{x + 1} = [/tex]

[tex] = \dfrac{(x + 1)(2x + 3)}{(x + 1)(3x)} + \dfrac{(3x)(x)}{(3x)(x + 1)} [/tex]

[tex] = \dfrac{2x^2 + 3x + 2x + 3}{3x^2 + 3x} + \dfrac{3x^2}{3x^2 + 3x} [/tex]

[tex] = \dfrac{2x^2 + 5x + 3 + 3x^2}{3x^2 + 3x} [/tex]

[tex] = \dfrac{5x^2 + 5x + 3}{3x^2 + 3x} [/tex]

Answer:

Due to the higher z-score, David has the higher standardized score

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Which student has the higher standardized score

Whoever had the higher z-score.

David:

Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. So [tex]X = 52, \mu = 70, \sigma = 11[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{52 - 70}{11}[/tex]

[tex]Z = -1.64[/tex]

Steven:

Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. So [tex]X = 52, \mu = 64, \sigma = 6[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{52 - 64}{6}[/tex]

[tex]Z = -2[/tex]

Due to the higher z-score, David has the higher standardized score

Answer:

S = 2π/9 [³/₂√10 − ½ ln(-3 + √10)]

S ≈ 3.946

Step-by-step explanation:

For a curve rotated about the x-axis, the surface area is:

S = ∫ₐᵇ 2πy ds,

where ds = √(1 + (dy/dx)²) dx.

y = e⁻³ˣ

dy/dx = -3e⁻³ˣ

ds = √(1 + (-3e⁻³ˣ)²) dx

S = ∫₀°° 2πe⁻³ˣ √(1 + (-3e⁻³ˣ)²) dx

If u = -3e⁻³ˣ, then du = 9e⁻³ˣ dx, or du/9 = e⁻³ˣ dx.

When x = 0, u = -3.  When x = ∞, u = 0.

S = ∫₋₃⁰ 2π √(1 + u²) (du/9)

S = 2π/9 ∫₋₃⁰ √(1 + u²) du

S = 2π/9 [ ½ u √(1 + u²) + ½ ln|u + √(1 + u²)| ] |₋₃⁰

S = 2π/9 {[0] − [ -³/₂√10 + ½ ln(-3 + √10) ]}

S = 2π/9 [³/₂√10 − ½ ln(-3 + √10)]

S ≈ 3.946

The area of a surface is the amount of space it occupies.

The area of the resulting surface is [tex]3.947[/tex] square units

The infinite curve is given as:

[tex]y =e^{-3x},\ \ x \ge 0[/tex]

Integrate y, with respect to x

[tex]\frac{dy}{dx} = -3e^{-3x}[/tex]

The area of the curve about the x-axis is:

[tex]S = \int\limits^a_b {2\pi y} \, ds[/tex]

[tex]ds = \sqrt{(1 + (\frac{dy}{dx})^2)}\ dx[/tex]

Substitute [tex]\frac{dy}{dx} = -3e^{-3x}[/tex] in [tex]ds = \sqrt{(1 + (\frac{dy}{dx})^2)}\ dx[/tex]

[tex]ds = \sqrt{(1 + (-3e^{-3x})^2)}\ dx[/tex]

Let

[tex]u = -3e^{-3x}[/tex]

So:

[tex]\frac{du}{dx} = 9e^{-3x}[/tex]

Make [tex]e^{-3x}\ dx[/tex] the subject

[tex]e^{-3x}\ dx = \frac{du}9[/tex]

[tex]x \ge 0[/tex] means that, the value of x is: [tex][0,\infty][/tex]

When [tex]x = 0[/tex]

[tex]u = -3e^{-3x}[/tex]

[tex]u = -3 \times e^{-3 \times 0} = -3[/tex]

When [tex]x = \infty[/tex]

[tex]u = -3 \times e^{-3 \times \infty} = 0[/tex]

Recall that:

[tex]S = \int\limits^a_b {2\pi y} \, ds[/tex]

Substitute [tex]ds = \sqrt{(1 + (-3e^{-3x})^2)}\ dx[/tex] and [tex]y =e^{-3x}[/tex]

This gives

[tex]S = \int\limits^0_{-3} {2\pi (e^{-3x}) \sqrt{(1 + (-3e^{-3x})^2)}\ dx}[/tex]

Rewrite as:

[tex]S = \int\limits^0_{-3} {2\pi \sqrt{(1 + (-3e^{-3x})^2)}\ (e^{-3x})\ dx}[/tex]

Substitute [tex]u = -3e^{-3x}[/tex] and [tex]e^{-3x}\ dx = \frac{du}9[/tex]

[tex]S = \int\limits^0_{-3} {2\pi \sqrt{(1 + u^2)}\ \frac{du}9}[/tex]

This gives

[tex]S = \frac{2\pi}{9} \int\limits^0_{-3} {\sqrt{(1 + u^2)}\ du}[/tex]

Integrate with respect to u

[tex]S = \frac{2\pi}{9}[\frac 12 u\sqrt{(1 + u^2)} + \frac 12\ln|u + \sqrt{1 + u^2}|\ ]|\limits^0_{-3}[/tex]

Substitute 0 and -3 for u

[tex]S = \frac{2\pi}{9}([\frac 12\times 0 \times \sqrt{(1 + 0^2)} + \frac 12\ln|0 + \sqrt{1 + 0^2} ] - [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}([0] - [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}(- [\frac 12 \times (-3) \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}(- [\frac{-3}2 \times \sqrt{(1 + (-3)^2)} + \frac 12\ln|-3 + \sqrt{1 + (-3)^2} ] )[/tex]

[tex]S = \frac{2\pi}{9}( [\frac{3}2 \times \sqrt{10} - \frac 12\ln(-3 + \sqrt{10}\ )] )[/tex]

[tex]S = \frac{2\pi}{9}( [4.743 + 0.909] )[/tex]

[tex]S = \frac{2\pi}{9}( 5.652 )[/tex]

[tex]S = 3.947[/tex]

Hence, the area of the resulting surface is [tex]3.947[/tex] square units

Read more about areas at:

https://brainly.com/question/3547303

Answer:

1/20

Step-by-step explanation:

5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles

P( brown) = brown / total = 5/20 = 1/4

Replace

5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles

P( red) = red / total = 4/20 = 1/5

P( brown, replace, red) = 1/4 * 1/5 = 1/20