An annulus is the region between two concentric circles. The area of the annulus shown in the figure is R² - ².
R
(a) Factor this expression. (Factor your answer completely.)
I

The volume of the solid is approximately equal to 441.75 π cubic units.

The volume of the solid can be found using the disk method of integration. To set up the integral, consider a disk of height 'h' and radius 'r' at position y. The volume of this disk is given by πr^2h, and the radius 'r' is equal to 9 - y. Therefore, the volume of the solid is given by the following triple integral:

[tex]V = \int\{\pi(9 - y)^2dy} \int\,dh \int\,dx[/tex]

Where the limits of integration are:

So, the final expression for the volume is:

[tex]V = \int\limits^{9}_{y=0} \int\limits^{x}_{h=0} \int\limits^{9}_{x=0} \pi (9 - y)^2 dh dx dy[/tex]

Evaluating the integral gives:

[tex]V = \pi \int\limits_{y=0}^{9} (9 - y)^2dy \int\limits_{h=0}^{x} dh \int\limits_{x=0}^{9} dx[/tex]

[tex]= \pi \int\limits_{y=0}^{9} (81 - 18y + y^2)dy \int\limits_{h=0}^{x} dh \int\limits_{x=0}^{9} dx[/tex]

[tex]= \pi \int\limits_{y=0}^{9} (81 - 18y + y^2)dy (x^2/2) dx[/tex]

[tex]= \pi /2 \int\limits_{y=0}^{9} (81 - 18y + y^2)dy (x^2) dx[/tex]

[tex]= 441.75 \pi[/tex]

Hence, the volume of the solid is approximately equal to 441.75 π cubic units.

Learn more about the disk method of integration here:

https://brainly.com/question/13993335

#SPJ4

The constant of proportionality is 7.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

A four-sided figure is resized to create a scaled copy.

The proportional relationship between any given side length in the original figure f, and the corresponding side length in the scaled copy, s, can be represented by the equations s=1/7f.

To find the constant of proportionality from side lengths in the original figure to side lengths in the scaled copy

The equation we get as, f=7s

Therefore, the constant of proportionality is 7.

To learn more about the proportional relationship visit:

brainly.com/question/12917806.

#SPJ1

Kelvin's solution is correct because he multiplies the base of the triangle by the height of the triangle.

Area of triangle= base × height

The base of the triangle= 5 in

The height of the triangle = 8 in

Area of triangle= base × height

= 5 in × 8 in

= 40 square inches

Consequently, the area of the triangle as calculated by kelvin is correct.

Read more on area of triangle:

https://brainly.com/question/17335144

#SPJ1

A and B are each represented by an oval:IV LT III regions make up

the answer is (d) II.

What is Venn diagram ?

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.

The set (A union B) complement is defined as the set of all elements in the universal set that are not in A union B. In set notation, it can be expressed as (A union B)^c = U - (A union B), where U is the universal set and c represents the complement.

In a Venn diagram, the complement of a set is represented by the region outside of the set. In the given Venn diagram, the region outside of A and B is represented by region IV, so (A union B) complement = IV.

Therefore, A and B are each represented by an oval:IV LT III regions make up the answer is (d) II.

To learn more about Venn diagram visit : brainly.com/question/29301560

#SPJ4

The simplified value of the expression - 10 + 1 + (- 6). - (15 - 17 - 35) is 20.

PEMDAS rule states the correct order of simplifying an expression is as follows -: Parenthesis, exponents, multiplications, divisions, additions, and, subtractions.

Given, An expression - 10 + 1 + (- 6). - (15 - 17 - 35).

Now, If any of the arithmetic operations are not present we'll simply do the next and we'll also distribute the negative and positive signs.

- 10 + 1 + (- 6). - (15 - 17 - 35).

= - 10 + 1 - 6 - 15 + 15 + 35.

= - 9 - 21 + 50.

= - 30 + 50.

= 20.

learn more about the PEMDAS rule here :

https://brainly.com/question/20876480

#SPJ1

The system is stable since the magnitude of its impulse response is 0.25, which is a finite number that is less than any M.

The stability of a linear system can be determined by analyzing the magnitude of its impulse response −

|h[n]| ≤ M for some finite M

In this case, the impulse response is h[n] = 0.25nu[n], where nu[n] is the unit step function. Since the magnitude of h[n] is 0.25 for all n, the system is stable since 0.25 is a finite number that is less than any M.

To summarize, the system is stable since the magnitude of its impulse response is 0.25, which is a finite number that is less than any M.

Learn more about linear system here:

https://brainly.com/question/21404414

#SPJ4

The values of the letters are:

A =  $37.5

B = $16.95

C = 5

D = $15.34

A sales tax is a tax paid to the government for the sales of certain goods and services.

Total price = Quantity * Unit Price

Unit price = Total price / Quantity

Quantity = Total price / Unit price

A = Total price = 3 * 12.5 = $37.5

B = Unit price = 33.90 / 2 = $16.95

C = Quantity = 31.00 / 6.20 = 5

15% VAT = 15% of Total Price

D = 15/100 * 108.28 = $15.34

Learn more about sales tax on:

brainly.com/question/9437038

#SPJ1

Answer:

[tex]\boxed{21.691} \; feet[/tex]

Step-by-step explanation:

See attached figure

The power cable going south first by 50 feet and then going west by 30 feet form the legs of a right triangle.

The diagonal which is the shortest distance between start and end points can be computed by the Pythagorean theorem

[tex]c^2 = a^2 + b^2[/tex]

where c is the hypotenuse and a, b the other two sides

Plugging in values for a = 50 and b = 30 we get

[tex]c^2 = 50^2 + 30^2\\\\c^2 = 2500 + 900\\\\c^2 = 3400\\\\c = \sqrt{3400}\\\\c = 58.3095 \;feet[/tex]

The cable length if going south and then west will be 50 + 30  = 80 feet

So cable length saved = 80 - 58.3095 = 21.6905

Rounded to 3 decimal places this would be 21.691 feet

Answer:

By using the Pythagorean Theorem, we can calculate that the diagonal of the city block is approximately 58.3 feet long. This means that the power company could save 7.3 feet of powerline cable by running the powerlines across the diagonal of the city block, instead of around the south and west sides.

Answer:

f(x) = 100 (3)^x  <===> C

f(x) = 100 (3.5)^x  <===> B

f(x) = 100 (4)^x <===> A

Step-by-step explanation:

Since the base of each of the exponential functions is the same, the higher the base, the higher up the graph will be with respect to another base with a lower value

This can be easily determined by choosing a specific value for x for each equation and seeing what the f(x) value is

Let's choose x = 2

For f(x) = 100 (3)^x, at x = 2 we get f(2) = 100(3)^2 = 100 x 9 = 900

For f(x) = 100 (3.5)^x, at x = 2 we get f(2) = 100(3.5)^2 = 100 x 12.25 = 12.25

For f(x) = 100 (4)^x, at x = 2 we get f(2) = 100(4)^2 = 100 x 16 = 1600

So for a specific value of x, the higher the base, the higher the graph is relative to the x-axis

So the matches are:

f(x) = 100 (3)^x  <===> C

f(x) = 100 (3.5)^x  <===> B

f(x) = 100 (4)^x <===> A

The probability of the other child being a girl is 1/2

From the question, we have the following parameters that can be used in our computation:

Kids = 2

Girls = 1

The probability of the other child being a girl is calculated as

Probability = Girl/Kids

Substitute the known values in the above equation, so, we have the following representation

Probability = 1/2

Hence, the probability is 1/2

Read more about probability at

https://brainly.com/question/251701

#SPJ1

Answer:

52 cats

Step-by-step explanation:

Let d be the number of dogs, then c = 2d + 10 is the number of cats.

The total number of animals is 73, so we have d + c = 73.

Substituting c = 2d + 10 into this equation, we get d + 2d + 10 = 73.

Combining like terms, we get 3d + 10 = 73.

Solving for d, we have 3d = 63, so d = 21.

Thus, there are 21 dogs and 2 * 21 + 10 = 52 cats up for adoption.

The number of tones of the black plastic that is required here is 9567.3 tones .

The volume of one meter of piping can be calculated as follows:

V = π * (r^2) * l

Where r is the radius of the pipe (6.5 mm), and l is the length (1 meter).

So, the volume of one meter of piping is:

V = π * (6.5^2) * 1 = 134.96 mm^3

Since 1 m^3 = 10^9 mm^3, the volume in m^3 of one meter of piping is:

V = 134.96 / 10^9 = 0.00013496 m^3

Therefore, the total volume of 81000 km of piping is:

V = 0.00013496 * 81000 * 10^3 = 11,124.16 m^3

And the total weight of the piping is:

W = V * 0.86 tones/m^3 = 9567.3 tones

So, 9567.3 tones of black plastic is required.

Learn more about tones of plastic:https://brainly.com/question/28504901

#SPJ1

Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.

Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.

It is used to know the result of the genotype of the offspring having either having single or multiple traits.

The correct answers are:

1.Option C. 0%

In the Punnett square the cross is between the purebred dominant and purebred recessive parent.

This will result in all the offspring having a heterogeneous genotype trait carrying purple color. Hence 0% will carry white color.

2. Option D. 25%

It can be explained as:

Due to the presence of heterogenous parent species. It will result in 25% of offspring carrying white color.

Therefore, in question 1, 0% of plants will be white while in another question 25% of the offspring will carry the white color trait.

To learn more about Punnett square refers to;

https://brainly.com/question/12039915

#SPJ4

The solutions to the equation |4 − 2x| + 6 = 18, in order from least to greatest, are:

x = -4 or x = 8

What is inequality?

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.

We can solve this absolute value equation by first isolating the absolute value term on one side of the equation and then solving for both possible cases. Here are the steps:

|4 − 2x| + 6 = 18

|4 − 2x| = 12 (subtract 6 from both sides)

Now we have an absolute value equation with no constant term. We can split this equation into two cases: one where the expression inside the absolute value is positive, and one where it is negative. For each case, we can solve for x:

Case 1: 4 - 2x > 0

If 4 - 2x is positive, then we can drop the absolute value bars and write:

4 - 2x = 12

-2x = 8

x = -4

So one solution is x = -4.

Case 2: 4 - 2x < 0

If 4 - 2x is negative, then we must flip the inequality when dropping the absolute value bars:

-(4 - 2x) = 12

-4 + 2x = 12

2x = 16

x = 8

So the other solution is x = 8.

Therefore, the solutions to the equation |4 − 2x| + 6 = 18, in order from least to greatest, are:

x = -4 or x = 8

To learn more about inequality visit,

https://brainly.com/question/25944814

#SPJ1

Answer: option b. 71%

Step-by-step explanation:

Total Utility of Harry remains the same and so he would indifferent to this exchange.

Now, According to the question:

MUa(H) = ∂UH/∂a = ∂(2ab)/∂a = 2b

MUb(H) = ∂UH/∂b = ∂(2ab)/∂b = 2a

"Information available from the question"

a = 3 apples  and b = 2 bananas

For a = 3 and b = 2

MUa(H) = 2b = 4; MUb(H) = 2a = 6

Total Utility(H) = MUa(H) + MUb(H) = 4 + 6 = 10

New distribution after exchange --> a = 2 and b = 3.

MUa(H) = 2b = 6; MUb(H) = 2a = 4

Total Utility(H) = MUa(H) + MUb(H) = 6 + 4 = 10

Total Utility of Harry remains the same and so he would indifferent to this exchange.

Learn more about Distribution at:

https://brainly.com/question/29062095

#SPJ4

The given quesion is incomplete, complete question is:

Tom, Jim , and Harry, the only three people on a desert island with two consumption goods, apples and bananas, have utility functions UT, UD, and UH, respectively, where:

UT(xa,xb) = 6xa+9xb

UD(xa,xb) = 8xa+12xb

UH(xa,xb) = xaxb2

a)Suppose harry has 3 apples and 2 bananas. would he be willing to trade an apple for a banana? show why or why not.

A domain of discourse for a domain integer statement is,

(a) True : x ≥ 0 and False x < 0

(b) True : x ≠ z ≠  y and False x ≠ y =  z

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

An integer, also called a "round number" or “whole number,” is any positive or negative number that does not include decimal parts or fractions. For example, 3, -10, and 1,025 are all integers, but 2.76 (decimal), 1.5 (decimal), and 3 ½ (fraction) are not.

(a) ∀x∃y( [tex]y^{2}[/tex] ≥  x)

[tex]y^{2}[/tex] ≥ 0

When x ≥ 0 , [tex]y^{2}[/tex] = x is True.

When x < 0 , without  [tex]y^{2}[/tex] = x is True.

(b) ∀x∀y(x < y → ∃z(x < z < y)

When x ≠ z ≠  y ,  x < z < y is True.

When z = x or z = y , x < z < y is False.

When x = y and x = z , y = z

Therefore,

A domain of discourse for a domain integer statement is,

(a) True : x ≥ 0 and False x < 0

(b) True : x ≠ z ≠  y and False x ≠ y =  z

To learn more about Integer problems visit :

brainly.com/question/30410577

#SPJ4

The limit of f(x) as x approaches positive infinity and negative infinity is equal to 3/4, and the horizontal asymptote of the function is y=3/4.

The horizontal asymptote of a function is a horizontal line that the function approaches as x approaches infinity or negative infinity.

The function f(x) is given by

=> f(x)= 3x³ + 8/4x³ + √ 64x⁶⁴.

To evaluate the limits, we need to consider what happens as x approaches positive infinity and negative infinity.

In this case, as x approaches positive infinity or negative infinity, the x³ term in the numerator and denominator will dominate and the limit of the function will be equal to 3/4.

This means that the function has a horizontal asymptote of y=3/4.

To know more about function here.

https://brainly.com/question/28193995

#SPJ4

The heights of the bars of a histogram correspond to Frequency values.

A histogram is a type of graph used to show the distribution of a dataset. It is used to display the frequency of values within the data set by depicting the number of observations that fall within a set of ranges.

The heights of the bars of a histogram correspond to the frequency of values within the data set.

A histogram is used to illustrate the distribution of data within a set by showing the number of data points that fall within a specified range of values (called bins).

The height of each bar in the histogram represents the frequency of values within the bin range. A taller bar indicates that more data points fall within that range. The area of each bar is also proportional to the frequency of the values in the bin.

To know more about histogram, click on the link below:

brainly.com/question/30354484

#SPJ4

In order to determine the practical significance requires considering both the effect size measures and the context of the study

One way to determine practical significance is by using effect size measures. Effect size is a standardized measurement of the magnitude of a treatment or intervention.

A common equation used to calculate effect size is Cohen's d, which is the difference between the means of two groups divided by the standard deviation.

Another equation used is the odds ratio, which is the ratio of the odds of an event occurring in one group compared to another.

Additionally, it is important to consider the context of the study when evaluating practical significance.

To know more about ratio here

https://brainly.com/question/13419413

#SPJ4

sssssssssaStep-by-step explanation:

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

At the end of 46 week the city will have: 132 streetlight + (4 streetlight/ week * 46 weeks)

At the end of 46 week the city will have: 132 streetlight  + 184 streetlight

At the end of 46 week the city will have: 316 streetlight

232 streetlight at the end of the week = (232 streetlight - 132 streetlight) / 4 streetlight /week

232 streetlight at the end of the week = 100 streetlight /4 streetlight /week

232 streetlight at the end of the week = 25 weeks

Learn more about algebraic operations at: brainly.com/question/3927786

#SPJ4

Correctly written question:

A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed. The city will have (blank) streetlights at the end of 46 weeks. The city will have 232 streetlights at the end of (blank) week

The table that represents the equation of the proportional relationship is; Table 4

A proportional relationship is defined as a mathematical relationship that exists between two variables in which their ratio is always equal.

We have that the equation s equals three fourths times f. This is expressed as;

s = ³/₄f

where;

s is the amount of sugar

f is the amount of flour

Table 1;

when f = 1

s = ³/₄(1)

s = ³/₄

when f = 2

s = ³/₄(2)

s = 6/4

Thus, table 4 is correct

Read more about  proportional relationship at; https://brainly.com/question/12242745

#SPJ1

The convert acres to miles 0.0015625.

What is meant by miles ?

To learn more about miles refer to

https://brainly.com/question/25631156

#SPJ4

the data y = (y1,..., yn) are a sample from a normal distribution with unknown mean θ and known standard deviation σ = 2. Our prior distribution p(θ) is normal with mean 0 and standard deviation σ0.

y > 3/2, α² → 0 ⇒p(Ф=2Iy) → 1 y < 3/2, α² → 0 ⇒p(Ф=1Iy) → 1

We have two cases for Ф,

1.  Ф=1; it implies that Pr(Ф=1)=0.5, while y~N(1,α²)

2. Ф=2; it implies that Pr(Ф=2)=0.5, while y~N(2,α²)

Now,

For 1st case of α=2,

We have marginal probability density formula

p(y)=∑p(yIФ)p(Ф)

=p(yIФ=1)p(Ф=1)+p(yIФ=2)p(Ф=2)

=N(yI1,2²)(1/2)+N(yI2,2²)(1/2)

=(1/2)[N(yI1,2²)+N(yI2,2²)]

Now.

For Pr(Ф=1Iy=1) at α=2

We have,

=p(Ф=1Iy=1)

=[p(y=1,Ф=1)]/[p(y=1)]

=[p(y=1IФ=1)p(Ф=1)]/[p(y=1)]

={(1/)exp[(-1/(2*2²))(1-1)²(1/2)]}/{(1/)(1/2)[exp[(-1/(2*2²))(1-1)²]+exp[(-1/(2*2²))(1-2)²]}

=0.53 Answer

Now, to describe the changes in shape of Ф when α is increased and decreased deviation

The formula for posterioir density is p(ФIy)=p(yIФ)p(Ф)/p(y)

=exp[(-1/(2α²)(y-Ф)²]/{exp[(-1/(2α²)(y-1)²]+exp[(-1/(2α²))(y-2)²]}

Now at Ф=1 and solving the equation, we get

p(Ф=1Iy)=1 / {1+exp[(2y-3)/2α²]}

Similarly at Ф=1 and solving the equation, we get

p(Ф=2Iy)=1 / {1+exp[(2y-3)/2α²]}

Conclusion:

α² → ∞ ⇒p(ФIy) → p(Ф) = 1/2

α² → 0 ⇒ two cases

y > 3/2, α² → 0 ⇒p(Ф=2Iy) → 1

y < 3/2, α² → 0 ⇒p(Ф=1Iy) → 1

learn more about of deviation here

https://brainly.com/question/14669917

#SPJ4

No, u is not in the plane spanned by the columns of A.

To check if u is in the plane spanned by the columns of A, we first need to construct the augmented matrix of the system A · x = u, where x is the vector of unknowns. The augmented matrix is:

[−5 9 | 26 4 −2]

The reduced row echelon form of this augmented matrix is:

[1 0 | 2 -1]

This is an inconsistent system,the reduced row echelon form of the augmented matrix is , which is an inconsistent system so it does not have any solutions. This means that u cannot be written as a linear combination of the columns of A, so it is not in the plane spanned by the columns of A.

Learn more about augmented matrix here:

https://brainly.com/question/16796667

#SPJ4

Answer:

13.2cm

Step-by-step explanation:

The surface area of the sphere=4πr∧2

take r as radius, so you have to find the diameter. which means d/2=r

So,

4*22/7* (d/2)²=544

d=13.15

to the first decimal place= d= 13.2 cm.

Answer:$3.35

subtract 10.00 - 6.65

You will get $3.35

A distribution that has both mean and median of (-15) is referred to as a perfectly symmetrical distribution.

This is referred to as a type of distribution in which the values of the mean and the median are the same as they are the central component of inferential statistics.

In this scenario, we were given the mean and median to be of the same value which is (-15) which therefore denotes that the type of distribution is a perfectly symmetrical one.

Read more about Perfectly symmetrical distribution here https://brainly.com/question/29754111

#SPJ1

Answer:

Area of a circle= 1/4*π d^2

A=1/4*π*12^2=

A=1/4*π*144=113.1

Step-by-step explanation:

Hope this helps!! :)). Mark me brainliest! :))