Answer:
There exists a relationship between interpersonal violence and health.
Step-by-step explanation:
The relationship between interpersonal violence and health :
The null hypothesis will be ; the is no relationship between interpersonal violence and health while the alternative will negate the Null ;
If no relationship exists, correlation Coefficient = 0 and if a relationship exists, then correlation Coefficient is not = 0
H0 : ρ = 0
H1 : ρ ≠ 0
α = 0.05
Reported Pvalue = 0.016
Decison region :
Reject H0 ; If Pvalue < α
Therefore, Since Pvalue < α ; we reject H0 and conclude that there exists a relationship between interpersonal violence and health.
what is the value of -2(7-15)/4
Allen is looking through his weekly local grocery store newspaper ads he notices that Costco is advertising a pack of 60 eggs for $9.35 Safeway is advertising a dozen eggs for $4.79 and Trader Joe's is advertising a pack of 18 eggs for $6.18 which store is offering the better deal?
Answer:
Costco
Step-by-step explanation:
We find the cost per egg for each of the three stores.
Costco:
$9.35/(60 eggs) = $0.15583/egg
Safeway:
$4.79/(12 eggs) = $0.39917/egg
Trader Joe's:
$6.18/(18 eggs) = $0.34333/egg
The best deal is Costco.
Answer:
Costco
Step-by-step explanation:
[tex]\frac{60}{9.35}: \frac{1}{y}[/tex]
60 × y = 1 × 9.35
60y = 9.35
60y ÷ 60 = 9.35 ÷ 60
[tex]y=\frac{187}{1200}[/tex]
[tex]\frac{12}{4.79}: \frac{1}{y}[/tex]
12 × y = 1 × 4.79
12y = 4.79
12y ÷ 12 = 4.79 ÷ 12
[tex]y=\frac{479}{1200}[/tex]
[tex]\frac{18}{6.18}: \frac{1}{y}[/tex]
18 × y = 1 × 6.18
18y = 6.18
18y ÷ 18 = 6.18 ÷ 18
[tex]y=\frac{103}{300}=\frac{412}{1200}[/tex]
A decorative wall in a garden is to be built using bricks that are 5 1/2 inches thick and mortar joints are 1/4 inch thick. What is the height of the wall?
Step-by-step explanation:
how many layers of bricks are used ?
also, I assume, the thickness of bricks means actually their height when laid.
but still, I cannot answer that, as nothing indicates if there is only one layer of bricks or 2 or 3 or 4 or ...
Each student at some college has a mathematics requirement M (to take at least one mathematics course) and a science requirement S (to take at least one science course). A poll of 150 sophomore students shows that: 60 completed M, 45 completed S, and 25 completed both M and S
Find the number of students who have completed
(a) At least one of the two requirements
(b) Exactly one of the two requirements
(c) Neither requirement.
all students = 150
M = 60
S = 45
M and S = 25
(a) At least one of the two requirements:
M or S = M + S - (M and S) = 60 + 45 - 25 = 80
(b) Exactly one of the two requirements:
(M or S) - (M and S) = 80 - 25 = 55
(c) Neither requirement:
(all students) - (M or S) = 150 - 80 = 70
A radio transmission tower is 180 feet high. How long should a guy wire be if it is to be attached to the tower 11 feet from the top and is to make an angle of 45° with the ground?
Answer:
Step-by-step explanation:
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout($) 2 46 8 10
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]
The expected payout is
2 × 0.5 + 4 × 0.2 + 6 × 0.15 + 8 × 0.1 + 10 × 0.05
= 1 + 0.8 + 0.9 + 0.8 + 0.5
= 4
The expected value of the winnings from this game is $3.90.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To find the expected value of the winnings, we multiply each possible payout by its probability and then sum these products.
So,
Expected Value = (2 x 0.5) + (4 x 0.2) + (6 x 0.15) + (8 x 0.1) + (10 x 0.05)
Expected Value = 1 + 0.8 + 0.9 + 0.8 + 0.5
Expected Value = 3.9
Therefore,
The expected value of the winnings from this game is $3.90.
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PLEASE HELP I WILL MARK YOUR ANSWER AS BRAINLIEST PLEASE BE CORRECT BEFORE ANSWERING
LOOK AT THE BOTTOM
9514 1404 393
Answer:
y = 2
Step-by-step explanation:
The figure must be flipped top-to-bottom, so the line of reflection must be a horizontal line. Point B must be reflected to itself, so it is on the line of reflection. That means the line of reflection is y = 2.
__
You can draw the line of reflection using any two points that have y-coordinates of 2, for example, (0, 2) and (2, 2).
What is the product (4.42 x 103)(5 x 10^) written in
scientific notation?
Answer:
2.2763 x 10 to the power of 4
for some reason it doesn't let me put in the explanation
8th Grade Which expression is equivalent to 1/27
Answer:
[tex]( \frac{1}{3})^{3} [/tex]
Step-by-step explanation:
There are many expressions that can be equivalent to 1/27.
For example, 2/54, 3/81 etc
But I think the expression you are looking for is
[tex] \frac{1}{27} = \frac{1 \times 1 \times 1}{3 \times 3 \times 3} = \frac{ {1}^{3} }{ {3}^{3} } = ( \frac{1}{3} )^{3} [/tex]
Hope this is helpful
Suppose f(x,y,z) = x2 + y2 + z2 and W is the solid cylinder with height 7 and base radius 2 that is centered about the z-axis with its base at z = −2. Enter θ as theta.
A) As an iterated integral, ∭WfdV = ∫BA∫DC∫FE dzdrdθ with limits of integration.
B) Evaluate the integral.
In cylindrical coordinates, W is the set of points
W = {(r, θ, z) : 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π and -2 ≤ z ≤ 5}
(A) Then the integral of f(x, y, z) over W is
[tex]\displaystyle\iiint_W(x^2+y^2+z^2)\,\mathrm dV = \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
(B)
[tex]\displaystyle \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^2\int_{-2}^5(r^3+rz^2)\,\mathrm dz\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(zr^3+\frac13rz^3\right)\bigg|_{z=-2}^{z=5}\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(\frac{133}3r+7r^3\right)\,\mathrm dr \\\\\\= 2\pi \left(\frac{133}6r^2+\frac74r^4\right)\bigg|_{r=0}^{r=2} \\\\\\= 2\pi \left(\frac{110}3\right) = \boxed{\frac{220\pi}3}[/tex]
Assume that when blood donors are randomly selected, 45% of them have blood that is Group O (based on data from the Greater New York Blood Program).
1. If the number of blood donors is n = 16 equation, find the probability that the number with Group O blood is equation x = 6.
2. If the number of blood donors is n = 8, find the probability that the number with group O is x = 3.
3. if the number of blood donors is n = 20, find the probability that the number with group O blood is x = 16.
4. if the number of blood donors is n = 11, find the probability that the number with group O blood is x = 9.
Answer:
1. 0.1684 = 16.84%.
2. 0.2568 = 25.68%
3. 0.0013 = 0.13%
4. 0.0126 = 1.26%.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have blood that is Group O, or they do not. The probability of a person having blood that is Group O is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
45% of them have blood that is Group O
This means that [tex]p = 0.45[/tex]
Question 1:
This is P(X = 6) when n = 16. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{16,6}.(0.45)^{6}.(0.55)^{10} = 0.1684[/tex]
So 0.1684 = 16.84%.
Question 2:
This is P(X = 3) when n = 8. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{8,3}.(0.45)^{3}.(0.55)^{5} = 0.2568[/tex]
So 0.2568 = 25.68%.
Question 3:
This is P(X = 16) when n = 20. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 16) = C_{20,16}.(0.45)^{16}.(0.55)^{4} = 0.0013[/tex]
So 0.0013 = 0.13%.
Question 4:
This is P(X = 9) when n = 11. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{11,9}.(0.45)^{9}.(0.55)^{2} = 0.0126[/tex]
So 0.0126 = 1.26%.
You are designing an experiment using human subjects. The study will include 30 participants. Of these, 16 will be placed in the experimental group and the remaining 14 will be placed in the control group. In how many ways can you assign participants to the two groups?
Answer:
The participants can be assigned in 224 different ways.
Step-by-step explanation:
Given that you are designing an experiment using human subjects, and the study will include 30 participants, of which 16 will be placed in the experimental group and the remaining 14 will be placed in the control group, to determine in how many ways can you assign participants to the two groups the following calculation must be performed:
16 x 14 = X
224 = X
Therefore, the participants can be assigned in 224 different ways.
One urn contains 6 blue balls and 14 white balls, and a second urn contains 12 blue balls and 7 white balls. An urn is selected at random, and a ball is chosen from the urn. a. What is the probability that the chosen ball is blue? b. If the chosen ball is blue, what is the probability that it came from the first urn?
Answer:
a) 0.4658 = 46.58% probability that the chosen ball is blue
b) 0.322 = 32.2% probability that it came from the first urn
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
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.
a. What is the probability that the chosen ball is blue?
6/20 = 0.3 of 0.5(first urn)
12/19 = 0.6316 out of 0.5(second urn).
So
[tex]P(A) = 0.3*0.5 + 0.6316*0.5 = 0.4658[/tex]
0.4658 = 46.58% probability that the chosen ball is blue.
b. If the chosen ball is blue, what is the probability that it came from the first urn?
Event A: Blue Ball
Event B: From first urn
From item a., [tex]P(A) = 0.4658[/tex]
Probability of blue ball from first urn:
0.3 of 0.5. So
[tex]P(A \cap B) = 0.3*0.5 = 0.15[/tex]
Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.4658} = 0.322[/tex]
0.322 = 32.2% probability that it came from the first urn
Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour. What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ? (Hint: Think exponential.)
a) e e-2 = 0.1353
b) e-13/15 = 0.4204
c) e-1 = 0.3679
d) 1-2-1 = 0.6321
Answer:
0.4204 probability, option b.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour
13 arrivals during an hour, which means that the mean time between arrivals, in minutes is of [tex]\mu = \frac{13}{60} = 0.2167[/tex]
What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ?
This is P(X > 4). So
[tex]P(X > 4) = e^{-0.2167*4} = 0.4204[/tex]
So the correct answer is given by option b.
By visual inspection, determine the best-fitting regression model for the
scatterplot.
X
10
.
-10
A. No pattern
B. Exponential
C. Quadratic
D. Linear
Answer:
The answer is B since the chance is expontential since it gets bigger over time and each one is farther apart
The best-fitting regression model for the scatterplot is Exponential, the correct option is B.
What is fitting of curve for a data plot?When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve(exponential) on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.
We are given;
The graph representation
Now,
By visual inspection of the scatterplot, we can see that the points do not follow a clear pattern that suggests an exponential or quadratic relationship. However, there appears to be a linear relationship between the variables.
Therefore, the answer will be exponential.
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2(-x-4)+3=-7x+5+5x
Pls help!!!!!!!!
6. Aerial photography is to be taken of a tract of land that is 8 x 8 mi2. Flying height will be 4000 ft above average terrain, and the camera has focal length of 6 inches. If the focal plane opening is 9 x 9 in., and minimum side overlap is 30%, how many flight lines will be needed to cover the tract for the given data
Answer:
the number of flight lines needed is approximately 72
Step-by-step explanation:
Given the data in the question;
Aerial photography is to be taken of a tract of land that is 8 x 8 mi²
L × B = 8 x 8 mi²
Flying height H = 4000 ft = ( 4000 × 12 )inches = 48000 in
focal length f = 6 in
[tex]l[/tex] × b = 9 × 9 in²
side overlap = 30% = 0.3
meaning remaining side overlap = 100% - 30% = 70% = 0.7
{ not end to end overlap }
we take 100% { remaining overlap }
[tex]l[/tex]' = 9 × 100% = 9 in
b' = 9 × 70% = 6.3 in
Now the scale will be;
Scale = f/H
we substitute
Scale = 6 in / 48000 in = 1 / 8000
so our scale is; 1 : 8000
⇒ 1 in = 8000 in
⇒ 1 in = (8000 / 63360)mi
⇒ 1 in = 0.126 mi
so since
L × B = 8 x 8 mi²
[tex]l[/tex]' = ( 9 × 0.126 mi ) = 1.134 mi
b' = ( 6.3 × 0.126 mi ) = 0.7938 mi
Now we get the flight lines;
N = ( L × B ) / ( [tex]l[/tex]' × b' )
we substitute
N = ( 8 mi × 8 mi ) / ( 1.134 mi × 0.7938 mi )
N = 64 / 0.9001692
N = 71.0977 ≈ 72
Therefore, the number of flight lines needed is approximately 72
Ms. Ambrose paid $10 for 1.25 pounds of almonds. How much did the almonds cost per pound???
Consider the following game: You reach into a jar of money, and select a single bill at random to keep. There are 9 five-dollar bills, 5 ten-dollar bills, and 3 twenty-dollar bills in the jar. What should the cost of this game be in order for the game to be fair
Answer:
[tex]E(x)=\$9.118[/tex]
Step-by-step explanation:
From the question we are told that:
Available bills
[tex]\$5=N0 9\\\\\$10=N0 5[/tex]
[tex]\$20=N0 3[/tex]
Therefore
Total Bills
[tex]n=5+9+3[/tex]
[tex]n=17[/tex]
Probability of selecting each bill
[tex]For\$5[/tex]
[tex]P(\$5)=\frac{9}{17}[/tex]
[tex]For\$10[/tex]
[tex]P(\$10)=\frac{5}{17}[/tex]
[tex]For\$20[/tex]
[tex]P(\$20)=\frac{3}{17}[/tex]
Generally the equation for Expected winning is mathematically given by
[tex]E(x)=\sum(X)*P(X)[/tex]
[tex]E(x)=5*\frac{9}{17}+10*\frac{5}{17}+20*\frac{3}{17}[/tex]
[tex]E(x)=\$9.118[/tex]
If llm and m<6 = 4x - 15 and m<7 = x + 30, then m<6=
Answer:
Step-by-step explanation:
There are only 2 angle values that <1 to <8 can be. The two values add up to 180
In this case <6 and <7 are equal.
<6 = 4x - 15
<7 = x + 30
4x - 15 = x + 30 Subtract x from both sides
4x-x - 15 = 30 Add 15 to both sides
3x = 30 + 15
3x = 45 Divide by 3
x = 45 / 3
x = 15
<6 = 4x - 15
<6 = 4*15 - 15
<6 = 60 - 15
<6 = 45
5/6 ÷ 1/3 - 2/3 (2/5)
Answer:
[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]
Step-by-step explanation:
5/6 ÷ 1/3 - 2/3 (2/5)
= 5/6 ÷ 1/3 - 2/3 × 2/5= 5/2 - 2/3 × 2/5= 5/2 - 4/15= 67/30 or 2 7/30Hope it helps you! ＼(^ᴥ^)／
Need the answers from a - e
Answer:
10
Step-by-step explanation:
Sorry. I needed to answer this question to get access.
In 2013, the Public Religion Research Institute conducted a survey of 1,033 adults, 18 years of age or older, in the continental United States. One of the questions on their survey was as follows:
Answer:
Probability[Number of people from church] = 0.26 (Approx.)
Step-by-step explanation:
Given:
Total number of adult in survey = 1,033
Missing information:
Number of people from church = 269
Find:
Probability[Number of people from church]
Computation:
Probability of an event = Number of favourable outcomes / Number of total outcomes
Probability[Number of people from church] = Number of people from church / Total number of adult in survey
Probability[Number of people from church] = 269 / 1,033
Probability[Number of people from church] = 0.2604
Probability[Number of people from church] = 0.26 (Approx.)
A three-dimensional object's measurement(s) include which of the following?
Check all that apply.
A. Width
B. Length
C. Height
D. None of these
Answer:
A.
B.
C.
Step-by-step explanation:
all three are used in 3 dimensional objects hence the name 3 dimensions.
From the table below, determine whether the data shows an exponential function. Explain why or why not.
x
3
2
1
–1
y
8
2
0.5
0.125
a. No; the domain values are at regular intervals and the range values have a common factor 0.25. b. No; the domain values are not at regular intervals although the range values have a common factor. c. Yes; the domain values are at regular intervals and the range values have a common factor 4. d. Yes; the domain values are at regular intervals and the range values have a common factor 0.25.
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Answer:
b. No; the domain values are not at regular intervals although the range values have a common factor.
Step-by-step explanation:
The differences between x-values are ...
-1, -1, -1, -2 . . . . not a constant difference
The ratios of y-values are ...
2/8 = 0.5/2 = 0.125/0.5 = 0.25 . . . . a constant difference
The fact that the domain values do not have a common difference renders the common factor of the range values irrelevant. The relation is not exponential.
Which rectangle has an area of 18 square units? On a coordinate plane, a rectangle is 2 units high and 7 units wide. On a coordinate plane, a rectangle is 2 units high and 6 units wide. On a coordinate plane, a rectangle is 3 units high and 5 units wide. On a coordinate plane, a rectangle is 3 units high and 6 units wide.
Answer:
On a coordinate plane, a rectangle is 3 units high and 6 units wide.
Answer:
option "B"
You Welcome
Step-by-step explanation:
I NEED HELP ILL MARK!!!
Answer:
c) tan
Step-by-step explanation:
For the 63-deg angle, YZ is the opposite leg. The unknown side, AY, is the adjacent leg. The trigonometric ratio that relates the opposite and adjacent legs is the tangent.
Answer: c) tan
For any real number √a²
a
- |al
lal.
-a
Answer:
|a|
Step-by-step explanation:
For any positive or negative a, when you square it, the answer is positive.
The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.
Answer: |a|
what is the slope of a line parallel to the line whose equation is 2x+5y=10
Answer:
1. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -1
Find the area of the surface generated when the given curve is revolved about the y-axis. The part of the curve y=4x-1 between the points (1, 3) and (4, 15)
Answer:
Step-by-step explanation:
Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.
Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1
4x = y + 1
[tex]x = \dfrac{y+1}{4}[/tex]
[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
By integration, the required surface area in the revolve is:
[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]
where;
g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]
∴
[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]
[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]
[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]
[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]
