We find that the surface integral evaluates to 54π. the surface integral ∫∫S (x^2 + y^2 + z^2) dS,
where S is the part of the cylinder x^2 + y^2 = 9 that lies between the planes z = 0 and z = 3, together with its top and bottom disks, evaluates to 54π.
To evaluate the surface integral, we can use the formula ∫∫S f(x, y, z) dS, where f(x, y, z) is the integrand and dS represents the surface element.
In this case, the integrand is (x^2 + y^2 + z^2) and the surface S is defined by the equation x^2 + y^2 = 9 and bounded by the planes z = 0 and z = 3, including the top and bottom disks.
We can express the surface integral as the sum of three parts: the lateral surface of the cylinder and the two disk surfaces. The lateral surface can be parameterized as x = 3cosθ, y = 3sinθ, and z ranges from 0 to 3. The two disk surfaces have their own parameterizations.
By performing the calculations, integrating over each surface element, and summing the results, we find that the surface integral evaluates to 54π.
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You have 7 balls that are each a different color of the rainbow. in how many distinct ways can these balls be ordered? a. 1 b. 7 c. 49 d. 343 e. 5,040
Answer:
5040 ways
Step-by-step explanation:
here we need to find the number of permutations of the 7 balls :
= 7!
= 7×6×5×4×3×2×1
= 5 040
What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%?
a. z = 0.52
b. z = 0.84
c. z = -0.84
d. z = -0.52
Using the normal distribution, the value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is:
z = -0.52.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is is the 30th percentile, which is Z with a p-value of -0.3, hence z = -0.52.
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What is the minimum point on the graph of the equation y=f(x)+5 ?
Answer:
Step-by-step explanation:
This function will have a minimum point only if f(x) has one.
Examples:
y = x + 5: straight line with no minimum
y = x^2 + 5: parabola that opens up and has vertex at (0, 5); thus, the minimum is (0, 5)
What f(x) did you have in mind? Please share it.
Billy is hiking in Colorado. He walks eastward four miles, then turns $60$ degrees northward and walks six miles. How far is he from his starting point
He is 2√19 miles far way from starting point.
Suppose Billy starts at point A, turns at point B, and ends at point D, as shown below.
If Billy turns 60◦ northward and walks six miles, then we can draw a 30 − 60 − 90 triangle whose hypotenuse is 6 miles
It follows that Billy traveled 6/2 = 3 miles eastward during these 6 miles, and that he traveled 3√3 miles northward during these 6 miles. In total, Billy traveled 4 + 3 = 7 miles eastward and 3√ 3 miles northward.
By the Pythagorean Theorem, the distance from his starting point is q:
(7)2 + (3√3)2
=√49 + 27
= √76
= 2√19 .
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The graphs below have the same shape. What is the equation of the red
graph?
Answer:
[tex]G(x) = x^{3} -1[/tex]
Step-by-step explanation:
The red graph is the blue graph translated 1 unit down, so the answer is A.
Which polynomial is a quintic trinomial?
A. -x^4-5x^2
B. x^3+2x^2−8x+16
C. x² + 4
D. 3x^5+7x^2−9x^4
Answer:
D
Step-by-step explanation:
a quintic polynomial is a polynomial of degree 5
A is a polynomial of degree 4 (- [tex]x^{4}[/tex] term )
B is a polynomial of degree 3 (x³ term )
C is a polynomial of degree 2 ( x² term )
D is a polynomial of degree 5 ( 3[tex]x^{5}[/tex] term )
Suppose the scores of students on an exam are normally distributed with a mean of 382 and a standard deviation of 97. According to the empirical rule, what percentage of students scored between 285 and 479 on the exam
If the mean is 382 and standard deviation is 97 then according to empirical rule 50% students scored between 285 and 479 on the exam.
Given mean of 382 and standard deviation of 97.
We have to calculate the percentage of students scored between 285 and 479 on the exam.
Percentage is a number or ratio that is expressed in terms of 100.
We have to use z statistic in this question.
z=X-μ/σ
where μ is mean and
σ is standard deviation
from 285 to 382
z=285-383/97
=-1
p value =0.1587.
From 382 to 479
z=479-382/97
=97/97
=1
p value =0.3413
Total probability from 285 to 382 is 0.3413+0.1587=0.5
Percentage=5/10*100
=50%
Hence the percentage of students scored between 285 and 479 is 50%.
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Determine the value of x and y, show calculations
The value for x and y are 140° and 70° respectively.
How to solve Polygon QuestionThere are two ways to solve polygon question. Formula for the sum of interior angle and sum of the exterior angle of regular polygon.
Sum of the interior = (n - 2)180
Sum of the exterior = 360/n
Where n = number of sides of a polygon.
The regular polygon in which x is one of its angle is called decagon
Sum of the interior = (n - 2)180
n = 10
Substitute n into the formula
Sum of the interior angle = (10 - 2)180
Sum of the interior angle = (8)180
Sum of the interior angle = 1440
Each angle = 1400/10
x = 140°
For y, the three angles are similar.
sum of angle in a triangle = 180
Since the each triangle is an isoceles triangle, angle at each base will be y
40 + y + y = 180
2y = 180 - 40
2y = 140
y = 70°
Therefore, the value for x and y are 140° and 70° respectively.
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What equation shows that 9 is a factor of 72?
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
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A hypothesis test is conducted at the 0.05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, what conclusion should be drawn
3.60
t = r√n − 2/1 − √r2
= 0.6√25 − 2/√1 − 0.62
= 3.5969 t or about 3.60 rounded to two decimal places.
Hypothesis Testing:
Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H0.
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Find the present value of a loan with a maturity value of $15,000 for 9 months at 6%.
Present value of the loan amount is $[tex]27[/tex] with a maturity value of $[tex]15000[/tex] for [tex]9[/tex] months at [tex]6[/tex]%
How to find the present value of loan amount ?
We know that
Maturity value of loan amount [tex]= 15000[/tex]
Time period is [tex]=9[/tex] months
Rate (r)[tex]=6[/tex] %
Present value of loan amount=?
So we can use the formula of maturity level
[tex]MV=PV*(1+r*t)[/tex]
Substitute the values
[tex]15000=PV *(1+6*9)\\15000=PV(55)\\\frac{15000}{55} =PV\\27.27=PV[/tex]
So present value of the loan amount is $[tex]27[/tex] in round figure.
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Find the midpoint of points A(-9, -3) and B(1, 7) graphically.
Plot the line segment AB
Answer: (-4,2)
Step-by-step explanation:
To find the midpoint of AB, we have to find the mean of the x coordinates for the x coordinate of the midpoint and the mean of the y coordinates for the y coordinate of the midpoint
So the midpoint is ((-9+1)/2,(-3+7)/2) = (-4,2)
To plot the line AB, just find the points A and B on the graph and draw a straight line from A to B
y square plus 5y equals to 0
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5ordenada al origen 6 = paralela a la recta 2x+3y+4=0
La ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
¿Cómo determinar la ecuación de una recta?
En esta pregunta tenemos que derivar una ecuación de la recta a partir de una recta y un punto. Dos rectas bajo forma implícita son paralelas si y solo si comparten los mismos coeficientes dependientes, entonces tenemos que el coeficiente independiente de la recta es:
2 · 0 + 3 · 6 + k = 0
18 + k = 0
k = - 18
Por tanto, la ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
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As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when _____
As a rule of thumb, when each component is selected independently from the same population, the sampling distribution of the sample percentage may be estimated by a regular probability distribution.
Why is it crucial to use the thumb rule?One of our primary, simple-to-learn ways to handle complexity is the rule of thumb. Real thumb rules take into account operating, security, and financial constraints. They inform us of the likely location of a practical solution. Additionally, they reveal which tactics are most prone to failure.What is sampling distribution?A statistic that is obtained by sampled data from a bigger population is known as a sampling distribution. It depicts an array of potential results that may result from a statistic, such as the mean or mode of a certain parameter because there is really a population.Therefore the main solution is- from the identical group, each component is individually chosen.
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The diameter of the earth
at the equator is about
8.000 mi.
Based on this figure, how
far is it around the earth?
Answer:
25,132.74 miles
Step-by-step explanation:
Hello!
We are basically asked to find the circumference of the Earth's cross-section.
Circumference: [tex]C = 2\pi r[/tex]
We can replace 2r with the diameter, because the diameter is 2 times the radius.
Multiply the Diameter by pi:
[tex]C = \pi D[/tex][tex]C = 8000\pi[/tex][tex]C = 25,132.7412287183 \approx 25,132.74[/tex]It is around 25,132.74 miles around.
Analyze the graph below to identify the key features of the logarithmic function.
A) The x-intercept is y = 7, and the graph approaches a vertical asymptote at y = 6.
B) The x-intercept is x = 7, and the graph approaches a vertical asymptote at x = 6.
C) The x-intercept is y = -7, and the graph approaches a vertical asymptote at y = -6.
D) The x-intercept is x = -7, and the graph approaches a vertical asymptote at x = -6.
Answer: B
Step-by-step explanation:
When y=0, x=7, so the x-intercept is at x=7.
Eliminate everything except for B.Answer:
b. The x‐intercept is x = 7, and the graph approaches a vertical asymptote at x = 6.
Step-by-step explanation:
I took the test and got it right
Can someone help me please and show work !!
Answer:
Step-by-step explanation:
Rectangles have 2 pairs of equal sides that means:
2(4x) and 2(3x+2)
8x and 6x+4
8x+ (6x + 4) = 14x + 4
prove that 3+2√5 is irrational
Step-by-step explanation:
To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.
Let us assume that 3 + 2√5 is a rational number with p and q as co-prime integers and q ≠ 0
⇒ 3 + 2√5 = p/ q
⇒ 2√5 = p/ q - 3
⇒ √5 = (p - 3q ) / 2q
⇒ (p - 3q ) / 2 q is a rational number.
However, √5 is an irrational number
This leads to a contradiction that 3 + 2√5 is a rational number.
Ab and ac are tangent to circle o. if ab measures 23 cm, what is the measure of ac?
Answer:
AC = 23
Step-by-step explanation:
Discussion
AB and AC start from the same point -- A.
That means that when speaking of tangents to a circle that AB = AC
Answer
AB = 23 in Given
AC = 23 2 tangents to a circle starting from the same point are =
Help please
9 2 7
X = 12 x 12
Answer:
x=12
Step-by-step explanation:
x^9=12^9
power of 9 cancel eachother at both sides of equation.
so
x=12
if three pies require 2 dozen apples, then four bird require ? dozen apples?
WILL MAKE BRAINLIEST!!Determine if the two triangles are congruent if they are state the postulate or theorem that provides they are congruent
Answer:
Yes they are congruent by SSS criterionStep-by-step explanation:
AC=DC. (Given in figure)
AB=BD. (Given in figure
BC=BC. (Common)
that means triangle BAC is congruent to triangle BDC by SSS criterion.
Which are the solutions of x² = -7x − 8? √17 7 √17 + 4 2 7 √17 2 4 1412 THE + 7-√17 7 + √17 2 2 O-7-√17 −7+ √17 2 4
Answer:
[tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]
Step-by-step explanation:
First, convert this into a quadratic, [tex]x^{2}+7x+8=0[/tex]. We can use the quadratic formula for this, [tex](-7[/tex]±[tex]\sqrt{7^{2}-4(1)(8)})[/tex][tex]/2(1)[/tex]. This becomes [tex](-7[/tex]±[tex]\sqrt{49-32})/2[/tex]. This is [tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]. This is your answer
How many different 4 digit numbers can be formed using only digits 1,2,3 and 4 given that they contain each of these digits as many times as you want?
Answer: 4
Step-by-step explanation:
yeh
what is the domain of f(x)=√11-x?
The domain of the function f(x) is:
11 ≥ x
What is the domain of the function f(x)?
Here we have the function:
[tex]f(x) = \sqrt{11 - x}[/tex]
Now, remember that the argument of a square root can only be a number equal to or larger than zero, so the domain of our function is defined by:
11 - x ≥ 0
Then, solving this for x, we get:
11 ≥ x
Concluding, the domain of the function f(x) is:
11 ≥ x
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In a survey of 456 residents, 279 were opposed to the use of the photo-cop for issuing traffic tickets. What is the best point estimate for the proportion () of all residents opposed to the photo-cop use
The best point estimate for the proportion of all the residents opposed to the photo cop use is 60% which is the fourth option.
Given that in a survey of 456 residents , 279 were opposed to the use of the photo cop for issuing traffic tickets.
We have to find the best point estimate for the proportion of all residents opposed to the photo cop use.
Total residents=456
Residents who opposed to the use of the photo cop for issuing traffic tickets=279
Proportion=number of residents who opposed/ total residents
=279/456
=0.611
=61.1%
The nearest option is fourth which is 60%.
Hence the best point estimate for the proportion for the proportion of all the residents opposed to the photo cop use is 60% which is option 4.
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Question is incomplete as it should include options which are :
1) 500
2)50%
3)300
4)60%
5)40%
A rectangle's area is given by the expression 6–² -- − n +9. The width of the rectangle is 3n². w = 3n² A = 6n² − n +9
The length of the rectangle = 2 - (1/3n) +(3/n²).
How to estimate the length of a rectangle?
The formula for the area (taking this exists as a rectangle)
Area = length ⋅ width
where A exists the area of the rectangle
l exists the length of the rectangle and w exists the width of the rectangle.
If Area of the rectangle = length ⋅ width
then length of the rectangle = area/ width
Area = 6n² − n +9
width = 3n²
Area = length [tex]*[/tex] width
length = area/ width
= (6n² − n +9)/3n²
= 2 - (1/3n) +(3/n²).
The length of the rectangle = 2 - (1/3n) +(3/n²).
Therefore, the correct answer is option A. 2 - (1/3n) +(3/n²).
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A data store system that collects and stores all of the learning experiences in the form of statements that can be organized and presented in a meaningful way is the
The learning records is the meaningful way in which all of the data of learning experiences is record in the form of statements.
According to the statement
we have to tell that the which record is used when A data store system that collects and stores all of the learning experiences in the form of statements that can be organized and presented in a meaningful way.
So, for find this data store way to record the data
We know that the
The Learning Record provides an architecture and process for documenting student progress and achievement, based on interviews, observations over time, samples of students' naturally-occurring work, and well-supported interpretations of learning across five dimensions.
we see that the these given conditions in statement are approved by the data store way named the learning records.
So, The learning records is the meaningful way in which all of the data of learning experiences is record in the form of statements.
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The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = startfraction 3 x 10 superscript 8 baseline over x endfraction what is the wavelength for radio waves with frequency 3 × 109?
The wavelength for radio waves with frequency 3 × 10⁹ Hz is 0.1 m.
What's the relation between frequency and wavelength of electromagnetic waves?For electromagnetic waves travelling in vaccum, the product of frequency and wavelength is the speed of light in vaccum.Mathematically, frequency × wavelength = 3×10⁸ m/s (which is speed of light)So, wavelength= 3×10⁸/ frequencyWhat's the wavelength of radio wave with frequency 3×10⁹ Hz ?Wavelength of the radio wave= 3×10⁸/3×10⁹ = 0.1 m
Thus, we can conclude that the wavelength of the radio wave with frequency of 3 × 10⁹ Hz is 0.1 m.
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