An aquarium at a zoo is shaped like a cylinder. it has a height of 5 ft and a base radius of 3.5 ft. its being filled with water at a rate of 12 gallons per min. if one cubic foot is about 7.5 gallons, how long will it take to fill

The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.

According to the question we will set up Hypothesis

Null,  H0: U=26

Alternate, H1: U<26

Test Statistic

Population Mean(U)=26

Sample X(Mean)=24.4

Standard Deviation(S.D)=9.2

Number (n)=25

we use Test Statistic (t) = x-U/(s.d/√(n))

to =24.4-26/(9.2/√(25))

to =-0.87

| to | =0.87

Critical Value

The Value of |t α| with n-1 = 24 d.f is 1.711

We got |to| =0.87  & | t α | =1.711

According to this, we have to make a decision

Hence Value of  |to | < | t α |

P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658

Hence Value of P0.05 < 0.19658

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Answer: 17 years

Step-by-step explanation:

Exponential equation for compund amount( compunded continuously):

\(A=Pe^{rt}\) , where P= Principal value , r= rate of interest , t= time.

Given: A= 2P

r =4%= 0.04

To find : t

Substitute all values in the formula , we get

\(2P=Pe^{0.04t}\\\\\Rightarrow\ 2=e^{0.04t}\)

Taking natural log on both sides

\(\ln2=\ln e^{0.04t }\\\\\Rightarrow\ 0.693147=0.04t\\\\\Rightarrow\ t=\dfrac{ 0.693147}{0.04}\\\\\Rightarrow\ t=17.3286\approx17\)

hence, it will take 17 years (approx).

a) Two equivalent expressions to model the purchase made by Mrs. Singh, who bought 9 folders and 9 notebooks at the cost of each folder $2.50 and each notebook $4.00 respectively, are:

b) The total cost of the purchase by Mrs. Singh is $58.50.

Algebraic expressions involve the combination of variables, numbers, constants, and values using mathematical operands (addition, subtraction, division, and multiplication).

The unit cost of folders = $2.50

The unit cost of notebooks = $4.00

The number of folders bought = 9

The number of notebooks bought = 9

Let the number of folders bought = x

Let the number of notebooks bought = y

Folders: 2.50x

Notebooks: 4.00y

Folders: 2.50x = $22.50 ($2.50 x 9)

Notebooks: 4.00y = $36.00 ($4 x 9)

Total costs = $58.50

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I) f is continuous at x=2

II) f is differentiable at x=2

These both f (function ) are true

The given limit can be recognized as the definition of the derivative of f at x=2. Specifically, it states that the derivative of f at x=2 is equal to 5.

Using this information, we can make the following conclusions:

I) We cannot say for sure whether f is continuous at x=2 based on the given limit alone. While a function being differentiable at a point implies that it is also continuous at that point, the converse is not necessarily true. Therefore, we would need additional information to determine whether f is continuous at x=2.

II) The given limit implies that f is differentiable at x=2, since the limit exists and is finite. Specifically, we can say that the derivative of f at x=2 exists and is equal to 5.

III) The given limit also implies that the derivative of f is continuous at x=2. This is because the limit defines a continuous function at x=2, and it is well-known that if a function is differentiable at a point, then it is also continuous at that point.

Therefore, the correct answers are II and III.

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Answer:

true

Step-by-step explanation:

Answer:

x ≥ -6

Step-by-step explanation:

The arrow is directing towards the right, in which the line contains number greater than -6. Moreover the circle on top of -6 is closed, proving that it is 'greater than or equal to'. (if it was greater than, the circle on top of the number would be open; the inner part of the circle wouldn't be shaded)

The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

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Easy s pie

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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Answer:

2) 3&5 are the same side interior angle

Answer:

When a problem has infinite solutions, you'll end up with a statement that's true no matter what. For example: 3=3 This is true because we know 3 equals 3, and there's no variable in sight. Therefore we can conclude that the problem has infinite solutions. You can solve this as you would any other question.

Step-by-step explanation:

Hope this helped.

Answer:

20

Step-by-step explanation:

Area of one trapezoid is 10 so double that is 20

i think thats the answer im not 100% sure but i hope this helps :)

Answer:

Group 1:   -1, 3, 4

Group 2:   -2, 2, 3

Step-by-step explanation:

First, I separated -12 into two numbers by dividing. Then, I took one of those numbers and divided it again, leaving me with three numbers.

Answer:

it describes the proportion of individuals in a sample with a certain characteristic or trait

Step-by-step explanation:

to find sampling proportion, u have to divide the number of people or items who have the characteristic of interest by the total number of people/items in the sample.

It describes the percentage of people in a sample who possess a particular quality or attribute.

What is a sampling proportion?

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

Formula to calculate sampling proportion

p′ = x / n

where,

x: the number of successes

n: the sample size

p′:  sample proportion

Hence, it describes the percentage of people in a sample who possess a particular quality or attribute.

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The correct answer will be c. computing the average distance between every pair of observations between two clusters

What is Cluster Analysis?

Grouping "things" into "similar" groups is one of the most fundamental, straightforward, and frequently overlooked techniques (or processes) of comprehending and learning, on which cluster analysis is based. To create clusters of a particular type, this process uses a variety of different algorithms and techniques. It is also a component of data management in statistical analysis.

A multivariate data mining technique called cluster analysis aims to group things (such goods, responders, or other entities) based on a set of user-selected features or characteristics. Data compression, machine learning, pattern recognition, information retrieval, and other areas all use this essential and crucial phase of data mining, which is also a widely used method for statistical data analysis.

Here as per the given question, there are two clusters given.

Hence, computing the average distance between every pair of observations between two clusters.

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Answer:

$31728

Step-by-step explanation:

sorry if I'm wrong

The contrapositive statement is:

If x ≠ 2, then x^2 ≠ 4

And it is false.

First, we have two propositions:

p = "x^2 = 4"

q = "x = 2"

The contrapositive statement is:

¬q → ¬p

The negation of the propositions are:

¬q  = "x ≠ 2"

¬p = "x^2 ≠ 4"

Then the contrapositive statement with the given propositions is:

If x ≠ 2, then x^2 ≠ 4

Now, is this statement true?

No, because we can have:

x = -2 (which is different than 2, so the hypothesis is true)

and x^2 = (-2)^2 = 4

Then the conclusion is false, so the statement is false.

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The graph of the function f(x) = x² - 10x. and the graph of the function

g(x) = x² - 30x.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over the x-axis, (x, -y).

The graph of the first function is a quadratic function.

f(x) = (x - 0)(x - 10).

f(x) = x² - 10x.

Now, g(x) = (x - 0)(x - 30).

g(x) = x² - 30x.

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Answer:

As societies exchange ideas, globalization is unable to keep up with the speed at which culture has spread.

Answer:

A.) will be the correct answer to your problem

The number line which represents the solution set for the given inequality  -1/2 x ≥ 4 is the second graph which tends to left from -8.

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

Normally integers are placed on the number line.

Given inequality is,

-1/2 x ≥ 4

We have to find the solution first to find the graph.

Multiplying both sides by 2,

-x ≥ 8

Multiplying both sides by -1, inequality sign also changes.

x ≤ -8

So the graph will be something where the line tends to left from x = -8.

Hence the correct option is B.

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The given statement about the stake holders of DMAIC is false.

The term DMAIC stands for Define, Measure, Analyze, Improve, and Control and it represents the five phases that make the process,

Here we have given that generally, all stakeholders agree that there is a problem and on what the problem is before beginning the DMAIC process.

And we need to check whether the statement is true or not.

Here we know that in DMAIC process we have to follow the following steps they are listed as,

=> Define the problem

=> Improve activity

=> To determine opportunities for improvement

=> Identify the project goals

=> To analyze project goals and customer requirements.

Hence through this we have identified that the main purpose of DMAIC is to improve the effectiveness and efficiency of an organization's existing processes.

And here we have also know that DMAIC is a core data-driven improvement methodology of Six Sigma.

So, here the given statement is false.

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Answer: 72m

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(4x^2-16x-9.\\Writ -16x - as -a -difference\\ 4x^2 +2x-18x -9 \\Factor -out- common- terms\\2x(2x+1)-9(2x+1)\\ Factor -out (2x+1)\\(2x+1)(2x-9)\)

I Hope It Helps :)

Answer:

\( \boxed{\sf (2x - 9)(2x + 1)} \)

Step-by-step explanation:

\( \sf Factor \: the \: following: \\ \sf \implies 4 {x}^{2} - 16x - 9 \\ \\ \sf Factor \: the \: quadratic \: 4 {x}^{2} - 16 x - 9. \\ \sf The \: coefficient \: of \: {x}^{2} \: is \: 4 \: and \: the \: constant \\ \sf term \: is \: - 9. \: The \: product \: of \: 4 \: and \: - 9 \: is \\ \sf - 36. \: The \: factors \: of \: - 36 \: which \: sum \: to \\ \sf - 16 \: are \: 2 \: and \: - 18. \\ \sf So, \\ \sf \implies 4 {x}^{2} - (18 - 2)x - 9 \\ \\ \sf \implies 4 {x}^{2} - 18x + 2x - 9 \\ \\ \sf \implies 2x(2x - 9) + 1(2x - 9) \\ \\ \sf Factor \: 2x - 9 \: from \: 2x(2x - 9) + 1(2x - 9) : \\ \sf \implies (2x - 9)(2x + 1)\)

Answer:

2000

Step-by-step explanation:

larger sample sizes have more reliable results

The populations from which the samples are obtained must be normally distributed.

Sampling is done correctly. Observations for within and between groups must be independent.

The variances among populations must be equal (homoscedastic).

Data are interval or nominal.

By using any two of the points in the table, we will see that the slope is -2.

A general linear relationship is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if the line passes through (x₁, y₁) and (x₂, y₂), the slope is:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

Here we can use the first two points on the table:

(-4, 11) and (2, -1), so the slope is:

\(a = \frac{11 - (-1)}{-4 - 2} = 12/-6 = -2\)

Then the slope of the line is -2.

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