Assume that you have a sample of n1=7, with the sample mean X1=45, and a sample standard deviation of S1=6, and you have an independent sample of n2=17 from another population with a sample mean of X2=37 and the sample standard deviation S2=5.

1.What is the value of the pooled-variance tstat test for testing H0:\mu1=\mu

The garden will be in the shape of rectangle with length=18feet, breadth=12feet or length=20 feet, breadth=10 feet.

What is a rectangle?

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.

For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.

Perimeter of a Rectangle:-

The perimeter of a rectangle is defined as the total distance covered by the outer boundary of the rectangle. It is measured in unit length. The formula of perimeter is given by:

Perimeter, P = 2 (Length + Width)

Now,

Total fencing available=60feet

that means perimeter should be 60 feet of the garden.

Hence,

two dimensions of the rectangle could be length=18feet, breadth=12feet or length=20 feet, breadth=10 feet.

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Answer:

4.712 radians

Step-by-step explanation:

Answer:

$64,082.25

Step-by-step explanation:

$205,375-16,050=189,325

189,325×33% (or .30)=62,477.25

16,050×10% (or .10)=1,605

1,605+62,477.25=$64,082.25

Chance is a term used to represent the percentage of time a specific result is expected to occur when the same basic procedure is repeated over and over again, where each repetition is independent.

Chance is a term that is used to describe the probability that a certain outcome will occur given a set of fundamental instructions repeated again with each repetition being independent.

Ultimately, this means the number of times a result of an event occurs when repeated over a number of times is chance.

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Answer:

\(\dfrac{n^2}{n+1}\)

Step-by-step explanation:

Let's break this apart by numerator (N) and denominator (D) and see if we can spot a pattern:

Don't see it? Let's write it another way:

The numerator always seems to be the number of the term squared, while the denominator is the number of the term plus 1. Putting things back in fraction form, we can say that

Answer:

A

Step-by-step explanation:

(8-3^2)*9-6

8-9*9-6

-1*9-6

-9-6

-15

Step-by-step explanation:

a, 3

b,

draw lines through the corresponding corners of each shape  These lines will cross at the centre of enlargement O

Data:

Manoj did 1/10

Kumar did 1/8

Kiran did 1/20

How much work did they finish working together?

Add the fractions as follow:

If the remaining part of the work is finished by Arun, what part of work is done by Arum?

Takes the total work as a unit (1), then subtract 11/40 from 1:

Then, Arum needs to do 29/40 part of the work to finish it,

To find the limit of (1 - sin(θ))/(1 + cos(6θ)) as θ approaches π/2, we can apply a trigonometric identity:

1 - sin(θ) = cos(θ)

1 + cos(6θ) = 2cos^2(3θ)

Substituting these expressions into the original limit, we have:

lim (1 - sin(θ))/(1 + cos(6θ)) = lim cos(θ)/(2cos^2(3θ))

Now, as θ approaches π/2, the denominator 2cos^2(3θ) approaches 0, so we can apply L'Hospital's rule to the limit:

lim cos(θ)/(2cos^2(3θ)) = lim -sin(θ)/(12cos(θ)sin(3θ))

Applying L'Hospital's rule again, we take the derivative of the numerator and denominator separately with respect to θ:

= lim -cos(θ)/(12cos(θ)cos(3θ) + 3sin(θ)sin(3θ))

= lim -1/(12cos(3θ) + 3tan(θ))

Substituting θ = π/2, we have:

lim -1/(12cos(3π/2) + 3tan(π/2)) = lim -1/0

Since the denominator approaches 0 and the numerator is negative, the limit approaches negative infinity.

Therefore, the limit of (1 - sin(θ))/(1 + cos(6θ)) as θ approaches π/2 is negative infinity.

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The volume of the cylnder is  9,728.5 ft³

For a cylinder of radius R and height H, the volume is given by:

V = pi*R^2*H

Where pi = 3.14

Here we know that the height is.

H = (20 + 1/2) ft = 20.5 ft

And the diameter is (1 + 1/5) times the height, then:

D = (1 + 1/5)*(20 + 1/2) ft = (1.2)*(20.5)ft = 24.6ft

And the radius is half of that, so:

R = 12.3ft

Then the volume is:

V = 3.14*(12.3ft)^2*20.5ft = 9,728.5 ft³

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Answer: A

Step-by-step explanation: -----------------

Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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Answer:

he got 210 dollars in interest

Step-by-step explanation:

The value of N when t=4 is: N = 300 + 450 = 750.

To evaluate the solution at the specified value of the independent variable, we need to find the relationship between N and t. Given the information, we have two points: (0, 150) and (1, 300).

Step 1: Calculate the slope (m) between the two points.
m = (N2 - N1) / (t2 - t1) = (300 - 150) / (1 - 0) = 150

Step 2: Use one of the points (e.g., (0, 150)) and the slope to find the equation N = mt + b.
150 = 150 * 0 + b
b = 150

Step 3: Write the equation with the slope and intercept.
N = 150t + 150

Step 4: Evaluate the value of N when the specified value of the independent variable t = 4.
N = 150 * 4 + 150
N = 600 + 150
N = 750

The value of N when t = 4 is 750.

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In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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Answer:

3

Step-by-step explanation:

3 + 2 < 6

5<6

Therefore the answer should be 3

Answer:

Step-by-step explanation:

To represent the different crops in the simulation, we should use the values that correspond to the percentages mentioned in the problem.

According to the given information:

40% of the crop is carrots

40% of the crop is potatoes

20% of the crop is green beans

The option that correctly represents these percentages is:

Use number 0, 1, 2, and 3 to represent carrots, 4, 5, 6, and 7 to represent potatoes, and 8 and 9 to represent green beans.

Therefore, we should use number 0, 1, 2, and 3 to represent carrots, number 4, 5, 6, and 7 to represent potatoes, and number 8 and 9 to represent green beans in the simulation.

Answer:

$10087.5

Step-by-step explanation:

take $7,500× 3.45% = $258.75 ×10= 2587.5+ the 7500= 10087.5

Answer:

Step-by-step explanation:

This problem bothers on the mensuration of flat shapes, circles and square.

we know that the pizza has a  circular profile

and the place-mat has a square profile.

Step one:

let us solve for the radius of the pizza

\(area-of- pizzza= \pi r^2\\\\ 78.5= 3.142*r^2\\\\r^2= 78.5/3.142\\\\r^2= 24.98\\\\r= \sqrt{24.98} \\\\r=4.998\\\\r= 5 in\)

Step two:

from inspection we know that the width of the place-mat is same as the diameter of the pizza

hence diameter of pizza

= 2r

=2*5

=10 in

Given equation: y(t) = 51-47 sin t y∫_0^t y(τ-t) dτ 5 -4 sin r y(t).

Taking Laplace transform on both sides, we getL{y(t)} = L{51-47 sin t} + L{(y∫_0^t y(τ-t) dτ)} + L{5 -4 sin r } = 51L{1} - 47L{sin t} + L{y}L{∫_0^t y(τ-t) dτ} + 5L{1} - 4L{sin r}L{y}Let L{y} = Y(s).

Now, Y(s) = 51/s - 47(s/(s^2 + 1)) + Y(s)∫_0^t e^(-s(t-τ))Y(τ) dτ + 5/s - 4(s/(s^2 + r^2))Y(s)Rearranging the above equation, we getY(s)∫_0^t e^(-s(t-τ))Y(τ) dτ = 51/s - 47(s/(s^2 + 1)) + 5/s - 4(s/(s^2 + r^2)).

Taking inverse Laplace transform on both sides, we gety∫_0^t y(τ-t) dτ = 51 - 47 cos t + 5 - 4 cos rt∴ y(t) = (51 - 47 cos t + 5 - 4 cos rt)u(t)

Hence, the solution of the given integral equation is y(t) = (51 - 47 cos t + 5 - 4 cos rt)u(t).

which can be written as y(t) = 56 - 47 cos t - 4 cos rt for t >= 0.

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Research has shown that when administering a survey, respondents who are asked questions in which they have little or no knowledge are likely to respond with inaccurate or incomplete information.

This can happen due to several reasons, such as the respondents feeling embarrassed or ashamed of admitting their lack of knowledge, or simply guessing the answer to avoid appearing uninformed. Graeff's (2003) study highlights the importance of carefully designing survey questions to ensure that they are clear and easy to understand for all respondents, regardless of their level of knowledge on the topic. It is also important to provide respondents with options such as "I don't know" or "Not applicable" to encourage honest and accurate responses. Administering surveys can be a valuable tool for gathering information, but it is crucial to consider the limitations and potential biases that may arise. Conducting thorough research and using appropriate survey methods can help to ensure that the data collected is reliable and useful for making informed decisions.

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Answer:

1st they should multiply 2 and 4 first because you need to fallow order of operations you will get 8 then you add the 1 getting you 9 finally you subtracted 12 and 9 getting 3 so NO THE STUDENTS WORK WAS NOT DONE CORRECTLY

Given:

The volume of a cube = \((2+3p)^3\ \text{cm}^3\)

To find:

The total surface area of the cube in terms of p.

Solution:

Volume of a cube is:

\(V=a^3\)            ...(i)

Where, a is the side length.

It is given that,

\(V=(2+3p)^3\ \text{cm}^3\)         ...(ii)

On comparing (i) and (ii), we get

\(a=2+3p\text{ cm}\)

Now, the total surface area of a cube is:

\(A=6a^2\)

Where, a is the side length.

Putting \(a=2+3p\), we get

\(A=6(2+3p)^2\)

Therefore, the total surface area of the cube in terms of p is \(6(2+3p)^2\ \text{cm}^2\).

Answer: 0.05508474576

Step-by-step explanation:

The correct Answer is D

s1 = s2 and r1 = r2

The two data sets have the same range. The first data set has a range of 88 − 56 = 32, and the second data set has a range of 112 − 80 = 32.

This relationship is sometimes referred to as the range rule for standard deviation. The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s = (Maximum – Minimum)/4.

The standard deviation is a more effective measure of variation than the range. Range of the data is a measure of variation which gives the difference in the maximum and the minimum observation of the dataset. It is only based on two observations, the maximum and the minimum.

Alternatively, it can be seen visually that the ranges are the same because the two dot plots are aligned, the scales of the graphs are the same, and the graphs have the same width. The two data sets have different standard deviations. Both dot plots show distributions that have a mean near the center value of the dot plot. The first dot plot shows most values clustered near the mean, while the second dot plot shows most values farther from the mean. Therefore, the standard deviations of the two data sets are not equal—the data represented by the second dot plot has a greater standard deviation.

Choices A, B, and C are incorrect because they incorrectly assert either that the standard deviations are the same or that the ranges are different.

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The number of quarts of oil that should have been used for 980 oil changes is 6,076 quarts.

To calculate the number of quarts of oil that should have been used for 980 oil changes, we can use the given information. We know that on average, a typical oil change takes 24 minutes and 6.2 quarts of oil are used.
First, let's calculate the total number of minutes for the 980 oil changes.

We can multiply the average time per oil change (24 minutes) by the total number of oil changes (980):
Total minutes = 24 minutes/oil change × 980 oil changes = 23,520 minutes
Next, we can calculate the number of quarts of oil used for the 980 oil changes.

We can multiply the average quarts of oil used per oil change (6.2 quarts) by the total number of oil changes (980):
Total quarts = 6.2 quarts/oil change × 980 oil changes = 6,076 quarts
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Answer: The slope of the line passing through the points (1,-1) and (4,3) is 4/3

Explanation:

The two points marked on the green line are (1,-1) and (4,3)

Let's use the slope formula.

\((x_1,y_1) = (1,-1) \text{ and } (x_2,y_2) = (4,3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{3 - (-1)}{4 - 1}\\\\m = \frac{3 + 1}{4 - 1}\\\\m = \frac{4}{3}\\\\\)

The slope is 4/3

slope = rise/run = 4/3

rise = 4

run = 3

It means "go up 4 and to the right 3" so we can move from (1,-1) to (4,3).

Answer:

The answer is Quadratic

By providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship, we have

(i) \(3^{n/2}\) = O(2^n)

(ii) \(8^{\log n}\) = θ(\(n^2(\log n)^4\) ≤ 3n^3)

(iii) √n + (log n)^5 = O(\((2)^{1/2\times\log n}\))

We have to compare the following function pairs by providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship

i) The first function is \(3^{n/2}\) vs. 2^n

We can write  \(3^{n/2}\) as

\(3^{n/2}\) = \((\sqrt{3})^n\)

\(3^{n/2}\) = (1.732)^n

Clearly, we get for c = 1 and n ≥ 0, then

0 ≤ 1.732n ≤ 2n

Hence, \(3^{n/2}\) = O(2^n)

ii) The second function is \(8^{\log n}\) vs. n^2(log n)^4 + 2n^3

We can write it as

\(8^{\log n}\) = \(n^{\log 8}\)

\(8^{\log n}\) = \(n^{\log 2^3}\)

\(8^{\log n}\) = n^3

For n ≥ 0, c(1) = 1 and c(2) = 3, we have

0 ≤ n^3 ≤ \(n^2(\log n)^4\) ≤ 3n^3

Hence, \(8^{\log n}\) = θ(\(n^2(\log n)^4\) ≤ 3n^3)

iii) The third function is  \((\sqrt{2})^{\log n}\) vs. √n + (log n)^5

We can write \((\sqrt{2})^{\log n}\) as

\((\sqrt{2})^{\log n}\) =  \((2)^{1/2\times\log n}\)

For c = 2 and n ≥ 2, we have

0 ≤ √n + (log n)^5 ≤ \((2)^{1/2\times\log n}\)

Hence, √n + (log n)^5 = O(\((2)^{1/2\times\log n}\))

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The complete question is:

Show your complete work when comparing the following function pairs. provide the c and k values in the formal definition when asserting a big O, Ω or θ relationship(e.g. f(n) is O(g(n)) if there exists C>0 and k≥0 such that f(n)≤Cg(n) for all n≥k).

(i) \(3^{n/2}\) vs. 2^n

(ii) \(8^{\log n}\) vs. n^2(log n)^4 + 2n^3

(iii) \((\sqrt{2})^{\log n}\) vs. √n + (log n)^5

Step-by-step explanation:

The number which is repeated more times will be mode...

So...

11 is Answer