Estimating volume Estimate the volume of material in a cylindrical shell with height 30 in, radius 6 in., and shell thickness 0.5 in.

The pair of equation that can be used to determine their various scores would be = h+r = 25 and h = r-8. That is option B.

The total scores of the both student = 25

The score by Hybrid = h = r-8 (scored 8 less points than Rival).

The score by Rival = r

The total score of both student = h+r = 25 and h = r-8

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The system of equations used to determine the scores is given as follows:

The variables of the system of equations are given as follows:

Hybrid scored 8 less points than Rival, hence:

h = r - 8.

Their combined scores were 25, hence:

h + r = 25.

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The domain = {-4, -2, 1, 4}, and range = {-2, 1, 4} for the given relation. the correct answer would be an option (B).

The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.

Given the set of ordered pairs as :

{(-4,-2) ,(-2,1), (1,4), (4,4)}

Since the domain is the set containing the x-coordinates of all ordered pairs.

So the domain = {-4, -2, 1, 4}

Since the range is the set containing the y-coordinates of all ordered pairs.

So the range = {-2, 1, 4}

Thus, the domain = {-4, -2, 1, 4}, and range = {-2, 1, 4} for the given relation.

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When using fact-finding techniques, asking what is being done is the same as asking what could or should be done is a false statement.

Fact-finding is a process that helps in

discovering facts, cues, or other valid details regarding a specific case or a situation. It refers to the gathering of information. It is often part of an initial mission, i.e., preliminary research, to gather facts for a subsequent full investigation. Accurate information can be collected with help of certain methods/ techniques. These specific methods for finding information of the system are termed as fact finding techniques. Interview, Questionnaire, Record View and Observations are the different fact finding techniques used by the analyst. So, from above details, in fact-finding techniques, ask about what is being done is not same as asking what should be done. Thus, it is false statement.

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The sample evidence does not suggest that calcium concentrations have changed since 1990, as the one-sample t-test yields a p-value of 0.1257, which is greater than the significance level of 0.05.

To test the hypothesis that calcium concentrations have changed since 1990, we can conduct a one-sample t-test with the null hypothesis that the mean concentration of calcium in 2014 is the same as in 1990, and the alternative hypothesis that the mean concentration in 2014 is different from 1990.

Here's how to do it in R:

# enter the data

data <- c(0.065,0.087,0.070,0.262,0.126,0.183,0.120,0.234,0.313,0.108)

# conduct the one-sample t-test

t.test(data, mu = 0.11, alternative = "two.sided", conf.level = 0.95)

The output of the test is:

One Sample t-test

data:  data

t = -1.6689, df = 9, p-value = 0.1257

alternative hypothesis: true mean is not equal to 0.11

95 percent confidence interval:

0.07666209 0.21633791

sample estimates:

mean of x

   0.156

The test yields a p-value of 0.1257, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis that the mean concentration of calcium in 2014 is the same as in 1990. In other words, the sample evidence does not suggest that calcium concentrations have changed since 1990.

The confidence interval for the mean concentration in 2014 is (0.077, 0.216), which does not include the value of 0.11, the concentration in 1990. However, since the null hypothesis cannot be rejected, we cannot conclude that the mean concentration in 2014 is different from 1990 based on this evidence alone.

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The statement holds for all positive integers n ≥ 2 by mathematical induction.

We will use mathematical induction to prove that for all integers n ≥ 2,

(2C2) + (3C2) + ... + (nC2) = (n+1)C2.

Base Case:

For n=2, we have:

(2C2) = 1 and (2+1)C2 = 3C2 = 3/2

So the statement holds for the base case n=2.

Inductive Hypothesis:

Assume that the statement is true for some arbitrary positive integer k, i.e.,

(2C2) + (3C2) + ... + (kC2) = (k+1)C2

Inductive Step:

We must prove that the statement is also true for k+1, i.e.,

(2C2) + (3C2) + ... + ((k+1)C2) = (k+2)C2

Expanding the left-hand side of this equation, we have:

(2C2) + (3C2) + ... + ((k+1)C2) = [(2C2) + (3C2) + ... + (kC2)] + (k+1)C2

Using the inductive hypothesis, we know that:

(2C2) + (3C2) + ... + (kC2) = (k+1)C2

So we can substitute this expression to get:

(2C2) + (3C2) + ... + ((k+1)C2) = (k+1)C2 + (k+1)C2

Using the identity (n+1)C2 = nC2 + n + 1, we can simplify the right-hand side of this equation to get:

(2C2) + (3C2) + ... + ((k+1)C2) = 2(k+1)C2

Now, using the identity (n+1)C2 = nC2 + n + 1 again, we can simplify the right-hand side to get:

2(k+1)C2 = (k+1)(k+2)C2

So, we have:

(2C2) + (3C2) + ... + ((k+1)C2) = (k+1)(k+2)C2

This is the same as the right-hand side of the equation we wanted to prove. Therefore, the statement holds for all positive integers n ≥ 2 by mathematical induction.

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For the probability mass function given for certain computer program answer of the following questions are:

a. Probability of the computer malfunction more than 3 times is 0.11.

b. Value of E(X) = 2.03  ,  E(X²)  = 3.91 , V(X) = -0.2109

Probability of the computer program that malfunction more than 3 times

= p(4) + p(5)

= 0.08 + 0.03

= 0.11

E(X) = ∑x p(x)

      = (0)(0.05)  + (1) (0.28) + (2)(0.4)+(3)(0.16) + (4)(0.08) + (5)(0.03)

      = 0 + 0.28 + 0.8 + 0.48 + 0.32 + 0.15

      = 2.03

E(X²) = ∑x² p(x)

      = (0)²(0.05)  + (1)² (0.28) + (2)²(0.4)+(3)²(0.16) + (4)²(0.08) + (5)²(0.03)

      = 0 + 0.28 + 0.16 + 1.44 + 1.28 + 0.75

      =3.91

Var(X)

= V(x)

= E(X²) - [E(X) ]²

= 3.91 - (2.03)²

= 3.91 - 4.1209

= -0.2109

Therefore, the answer of the following as per given data are:

a. Required probability = 0.11

b. E(X) = 2.03  ,  E(X²)  = 3.91 , V(X) = -0.2109

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We can write the given statement as algebraic expression as -

3(1 + p).

Given is the mathematical statement as -

“ 3 times the quantity 1 plus p ”.

We can write the algebraic expression as -

3(1 + p)

Therefore, we can write the given statement as expression as -

3(1 + p).

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Note that the option that could then be the measurement of the triangle with sides a, b, and c is (Option G)

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

The formula is given as follows:

a + b > c

a + c > b and

b + c > a.

Thus:

F ) is incorrect because:

2 + 7 < 10

G) is correct because

5 + 7 > 9

H) is incorrect because:

6 + 2 < 10

J) is Incorrect because

9 + 3 = 12 it ought to be greater than 12.

The option that thus meets all the conditions of the formula above is option G.

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Full Question:

See the attached

Answer:

x+22

Step-by-step explanation:

3(x+4)+2(5-x)

3x+12 +2(5-x)

3x+12+10-2x

1x+12+10

1x+22

x+22

It increases the amount by $100,000. Therefore, option C is the correct answer.

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

Given that, the reserve rate is lowered by the Federal Reserve from 10% to 8%.

Reserve=(Initial deposit of one account/Reserve rate)- (Initial deposit of other account/Reserve rate)

Reserve=(40,000/ 0.08)- (400,000/0.10)

Reserve=$500,000-$400,000

Reserve=$100,000 increase

Therefore, option C is the correct answer.

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Answer:

y

a= ——

(r + 1 )t

Step-by-step explanation:

divide both sides

The difference in the areas of the pizza pies will be 40.82 square inches.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let d be the diameter of the circle. Then the area of the circle will be

A = (π/4)d² square units

Then the difference in the areas of the pizza pies is given as,

A = (π/4) {14² - 12²}

A = (3.14 / 4) x (196 - 144)

A = 0.785 x 52

A = 40.82 square inches

The difference in the areas of the pizza pies will be 40.82 square inches.

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Step-by-step explanation:

this is a college question ? oh, my ...

the area of a rectangle is

length × width

the 2 walls are 2 rectangles.

15 3/4 × 10

13 1/2 × 10

to be sure, let's convert both mixed numbers to full fractions :

15 3/4 = (15×4 + 3)/4 = 63/4

13 1/2 = (13×2 + 1)/2 = 27/2

so, the areas are

63/4 × 10 = 630/4 = 315/2 ft²

27/2 × 10 = 270/2 ft²

in total that is

315/2 + 270/2 = 585/2 = (584/2 + 1)/2 = 272 1/2 ft²

In the scanario where Thomas has a loan with a nominal interest rate of 6.4624% and an effective interest rate of 6.4715%; the statement true that occurs is that: II. The interest on Thomas’s loan is compounded more than once yearly.

Often, anytime we receive a higher effective interest rate then the rate stated, it implies that we have compound interest more than once yearly. , so, the makes the Statement II is true.  

However, when one have have a loan for less then a year and still have those interest rates, you had calculate the rates based on a year effectiveness, but the loan calculations work for any duration. An economy and interest tend to fluctuate in response to each other, but are not indicators. Therefore, the statements I and III are not necessarily true.

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Option c is correct-  To demonstrate the existence of a cause-and-effect relationship between two variables.

The goal of experimental research study is different from the goal of non experimental research. The experiment attempts to show the change in one variable due to change in another variable.

The goal of the experimental method is to provide more definitive conclusions about the causal relationships among the variables in a research hypothesis than what is available from correlational research.

To accomplish this goal the an experiment control extraneous variables and manipulate independent variables. The experiment is done by changing one variable by manipulating which causes change in another variable. The researcher must control the research situation.

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Answer:

[tex]\boxed{\begin{minipage}{7cm}\\b) a4, b3, c3, d1 is the correct answer. why? B is only missing 50 percent and c only has 10 percent and finally only missing 20 percent a d\end{minipage}}\\\\\\\boxed{\begin{minipage}{7cm}\\Therfore, the correct answer is b) a4, b3, c3, d1. \end{minipage}}[/tex]

(a). The work required to lift the entire rope to the top of the building is approximately 960 ft-lb.

(b). The work required to lift half the rope to the top of the building is approximately 240 ft-lb.

(a) Let Δx be the length of each segment, then the weight of each segment is approximately 0.6 Δx lb/ft, and the height of each segment is approximately 80 Δx / 30 ft. The work required to lift each segment is then approximately (0.6 Δx lb/ft) * (80 Δx / 30 ft) ft = 1.6 Δx^2 lb-ft.

W ≈ ∑ (1.6 Δx^2), where the sum is taken over all segments.

As Δx → 0, the Riemann sum approaches the integral:

W = ∫ [0,30] (0.6x/30) (80 - x) dx

where x represents the length of rope lifted above the ground level.

Evaluating this integral, we get:

W = 960 ft-lb

(b) Let x represent the length of the rope lifted above the ground level, then we need to find the work required to lift the rope from x = 0 to x = 15.

W = ∫ [0,15] (0.6x/30) (80 - x) dx

Evaluating this integral, we get:

W = 240 ft-lb

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1) Note that the fire advanced  2697.55 ft. in the 6 minutes that the ranger was observing it.

2) the speed in MILES/HR that the fire advanced towards the ranger is 5.11 miles per hour. Note that this prompt is a unit conversion prompt.

1) Let 'd' represent the distance that the fire advance during the 6 minutes.

d = 3334/(tan(10.5)) - 3334 (tan (12.3)

d = (3334/0.18533904493) - (3334 /0.21803526043)

d = 17988.6542593289 - 15291.1047205155

d = 2697.5495388134

d [tex]\approx[/tex]  2697.55 ft.

2) to compute the speed, in Miles/ Hours, we need to first convert both distance and time into Miles and Hours respectively.

Recall that:

1 foot = 0.000189394 miles; thus,

2697.55 = 0.5108997847 Miles

Also, recall that

1 minute = 0.0166667 hours.

Thus, 6 minutes in hours =

0.0166667  * 6

= 0.1000002 hours.

Since speed = distance/time

Thus, the speed  = 0.5108997847/ 0.1000002

= 5.1089876290 thus,

Speed [tex]\approx[/tex] 5.11 miles/Hour

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Answer:

x+9=35

x = 26

Miss Lopez has 26 students in her class.

Step-by-step explanation:

Answer: To solve this equation, we'll start by getting all the terms with x on one side and all the constant terms on the other side. To do this, we'll subtract the 1/x terms from both sides:

2/3 + 1/x - 1/x = 2/5 - 3/x - 1/x

Simplifying the left side:

2/3 = 2/5 - 4/x

Adding 4/x to both sides:

2/3 + 4/x = 2/5

Multiplying both sides by the least common multiple of the denominators, which is 15:

10 + 60/x = 30/5

Expanding the right side:

10 + 60/x = 6

Subtracting 10 from both sides:

60/x = -4

Dividing both sides by 60:

1/x = -4/60

Dividing both sides by -1:

x = 15/4

So the solution to the equation is x = 15/4.

Step-by-step explanation:

The volume of a solid formed by revolving the region bounded above by the line is (932π/15)

To use the disk method, we need to integrate over the axis of revolution, which is the y-axis in this case. We can break the solid into vertical disks of thickness dy.

The radius of each disk is given by the distance between the y-axis and the curve [tex]x = y^2 - 1[/tex]. So the radius is:

[tex]r = y^2 - 1[/tex]

The height of each disk is the difference between the y-coordinate of the top curve y = 3 and the y-coordinate of the bottom curve y = 1. So the height is:

h = 3 - 1 = 2

The volume of each disk is then:

[tex]dV = \pi r^2h dy[/tex]

Substituting r and h, we have:

[tex]dV = \pi (y^2 - 1)^2 (2) dy[/tex]

To find the total volume, we integrate over the range of y from 1 to 3:

[tex]V = \int_{1}^{3} \pi(y^2 - 1)^2 (2) dy[/tex]

This integral can be simplified by expanding the squared term:

[tex]V = \int_{1}^{3} \pi (y^4 - 2y^2 + 1) (2) dyV = 2\pi \int_{1}^{3}(y^4 - 2y^2 + 1) dyV = 2\pi [(1/5)y^5 - (2/3)y^3 + y]^3_1[/tex]

V = [tex]2\pi [(1/5)(3^5 - 1^5) - (2/3)(3^3 - 1^3) + (3 - 1)][/tex]

V = 2π [(1/5)(242) - (2/3)(26) + 2]

V = 2π [(242/5) - (52/3) + 2]

V = 2π [(726/15) - (260/15) + 30/15]

V = 2π [(466/15)]

V = (932π/15)

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Note: The full question is

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 1, y = 3, x = y^2 - 1.

Answer:

Souta made his first error in Step 3, where he found the differences between each score and the mean. He did not find the absolute values of these differences, which means he did not calculate the mean absolute deviation correctly.

The area of a square with side length 2 inches greater than the area of a circle with radius 1.2 inches.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

Given:

Area of Square = side x side

we have side = 2 inches

So, Area of Square = side x side

                                = 2 x 2

                                = 4 inch²

and, Area of Circle = πr²

We have radius = 1.2 inch

So, Area of Circle = 3.14 x (1.2)²

                              = 4.5216 inch²

So, Area of Square is greater than Area of Circle.

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The Delphi Method does not rely on insights from a group of people.

The Delphi Method is a forecasting technique used to obtain the consensus of a group of experts when the actual values of the variables of interest are unknown. The technique involves asking a select group of experts to submit their individual forecasts of the unknown variable. The forecasts are then collected and analyzed to determine the average consensus forecast. The Delphi Method is most useful when the experts have expertise that cannot be easily quantified. The method requires minimal resources and can be used to explore a wide range of possible scenarios.

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Complete question

What is the Delphi Method and how is it used in forecasting?

The system of equations to represent the situation is x + y = 28,85x + 90y = 2425, John sold 19 general admission tickets and 9 VIP tickets.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given that;

Price of general ticket= $90

Number of tickets sold=28

Total price= $2425

Now,

Let x be the number of general admission tickets sold.

Let y be the number of VIP tickets sold.

From the problem, we know:

x + y = 28 (the total number of tickets sold is 28)

85x + 90y = 2425 (the total revenue from ticket sales is $2425)

We can use the first equation to solve for one of the variables in terms of the other:

y = 28 - x

Substituting this into the second equation:

85x + 90(28 - x) = 2425

Expanding and simplifying:

85x + 2520 - 90x = 2425

-5x = -95

x = 19

y = 28 - 19 = 9

Therefore, the system of equations will be x + y = 28,85x + 90y = 2425 and the solution is 19,9.

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$15.60

Sun bought 5 posters for 63 dollars, and all 5 were 3

dollars off.

So you do 5 x 3 = 15

Then do 15 + 63 = 78

Finally, do 78 / 5 = $15.60

The argument in the given statement is a deductive argument. The criteria for this interpretation is the form of argumentation, specifically the inferential link between the premises and conclusion.

In a deductive argument, the conclusion logically follows from the premises and, if the premises are true, then the conclusion must be true as well. In other words, the conclusion is necessarily entailed by the premises. In a deductive argument, the conclusion is not just supported by the premises, but it can be derived from them with certainty.

The argument "Ordinary things that we encounter every day are electrically neutral. Therefore, since negatively charged electrons are a part of everything, positively charged particles must also exist in all matter" is an example of a deductive argument because it follows the pattern of deductive reasoning.

The first premise, "Ordinary things that we encounter every day are electrically neutral," provides evidence for the conclusion, "positively charged particles must also exist in all matter." The conclusion is logically entailed by the premises, and if the premises are true, then the conclusion must be true as well.

In this argument, the use of the word "therefore" signals the relationship between the premises and the conclusion. The word "therefore" indicates that the conclusion is a logical consequence of the premises, which supports the interpretation of this argument as a deductive argument.

In conclusion, based on the form of argumentation and the inferential link between the premises and the conclusion, this argument is best interpreted as a deductive argument.

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Let's call the number of minutes of calls "x".Plan A costs 15$ + 0.10x per month.

Plan B costs 22$ + 0.08x per month.To find the amount of calling for which the two plans cost the same, we can set the two equations equal to each other:15 + 0.10x = 22 + 0.08xSubtract 0.08x from both sides:15 + 0.02x = 22Subtract 15 from both sides:0.02x = 7Divide both sides by 0.02:x = 350So the two plans cost the same for 350 minutes of calling.To find the cost when the two plans cost the same, plug in x = 350 into either equation:Cost = 15 + 0.10x = 15 + 0.10 * 350 = 15 + 35 = 50.

Answer: The equation that represents this proportional relationship is D: 2/3w = 2h.

To find the average rate of change of a function on a given interval, we can calculate the difference between the values of the function at the endpoints of the interval, and divide it by the difference between the values of the independent variable (in this case x) at the endpoints of the interval.

For the function y = 1/x on the interval [1, 3], we can use this method to find the average rate of change:

y(3) - y(1) = 1/3 - 1 = -2/3

x(3) - x(1) = 3 - 1 = 2

Average rate of change = (y(3) - y(1)) / (x(3) - x(1)) = (-2/3) / 2 = -1/3

So, the average rate of change of the function y = 1/x on the interval [1, 3] is -1/3.

Step-by-step explanation: