Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.The owner of a football team claims that the average attendance at games is over 523 , and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test to support this claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

Answer:

W = 15900 ft.lb

Step-by-step explanation:

From the given information.

Consider y to be the distance from the ground towards the bucket of the cement.

At height y, suppose the bucket is lifted by Δy.

Then, the workdone can be = 500Δy + 0.5(75 - y) Δy

where;

The bucket of the cement =  500Δy

The remaining of the rope =  0.5(75 - y) Δy

However; the workdone (W) can be calculated as:

\(W = \int^{30}_{0} \ 500 \ dy + \int^{30}_{0} \ 0.5 (75-y ) \ dy\)

\(W = 500 \times 30 + 0.5 \bigg(75 \times 30 - \dfrac{1}{2} \times 30^2 \bigg )\)

W = 15000 + 0.5 ( 2250 - 450)

W = 15000 + 900

W = 15900 ft.lb

The required work is \(15,900 \ ft-lb\).

Integral Calculus is the branch of calculus where we study integrals and their properties. Integration is an essential concept which is the inverse process of differentiation. Both the integral and differential calculus are related to each other by the fundamental theorem of calculus.

Let \(x\) be the distance from the ground to the bucket of cement.

At the height \(x\), if the bucket is lifted by \(\Delta x\), the work done is,

\(500\Delta x+0.5\left ( 75-x \right )\Delta x\).

(See the attached figure below).

The \(500\Delta x\) term is due to the bucket of cement; the \(0.5\left ( 75-x \right )\Delta x\) term is due to the remaining cable.

So, the total work, \(W\), required to lift the bucket is,

\(W=\int_{0}^{30}500dx+\int_{0}^{30}0.5\left ( 75-x \right )dx \\ =500.30+0.5\left ( 75.30-\frac{1}{2}30^{2} \right ) \\ =15,900 \ ft-lb.\)

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The ratios will be equal if the theorem that the product of the extremes equals the product means follows.

Let us understand the equality of ratios through example. The example ratio will be -

7:10 = 21:30

In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.

Product of extremes = 7 × 30

Extremes product = 210

Product of means = 21 × 10

Means product = 210

Since the products are equal, the ratios are also equal.

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The complete question is -

Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.

Ratio = 7:10 and 21:30.

Answer:

2.5 ft into the wall leaving 2.5 feet on both sides of the dry erase board

Step-by-step explanation:

9-4=5

5/2=2.5

2.5 ft in

Answer:

A= 1/2 base*height

Step-by-step explanation:

: )

The correct equation for calculating the area of a triangle is D = 1/2 base · height.

The equation for calculating the area of a triangle is D = 1/2 base · height. This formula represents the most commonly used method for finding the area of a triangle.

To use this formula, you multiply the base of the triangle by its corresponding height, and then divide the result by 2.

This is because the area of a triangle is equal to half the product of its base and height.

By dividing by 2, we account for the fact that a triangle is essentially half of a parallelogram.

Therefore, the correct equation for calculating the area of a triangle is D = 1/2 base · height.

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Answer:

\(V=\frac{1}{3}(2.5)(6)=5 \ in^{3}\)

The volume of the pyramid is 5 cubic inches.

Step-by-step explanation:

Assuming that the triangle base dimensions are 1 inche and 5 inches, and the height of the pyramid is 6 inches, the volume would be

\(V=\frac{1}{3}Bh\)

Where B is the area of the base (triangle) and h is the height.

\(B=\frac{1}{2}bh =\frac{1}{2}(1)(5)=2.5 \ in^{2}\)

Then,

\(V=\frac{1}{3}(2.5)(6)=5 \ in^{3}\)

Answer:

4

Step-by-step explanation:

2m−13=−8m+27

2m+8m=27+13

10m=40

m=40÷10

Therefore, m=4

Answer:

2m - 13 = -8m +27

2m + 8m = 27 + 13

10m = 40

m = 4

Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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Answer:

3.81 s

Step-by-step explanation:

Let's consider the following formula that represents the journey of a falling object.

d = 3 t + 5 t²

where,

We can find the time that it will take to travel 84 feet by replacing d = 84 in the equation.

84 = 3 t + 5 t²

5 t² + 3 t - 84 = 0

We have a = 5, b = 3 and c = -84. We apply the second grade solving formula.

\(x_{1,2} = \frac{-b \pm \sqrt{b^{2}-4ac} }{2a} = \frac{-3 \pm \sqrt{3^{2}-4(5)(-84)} }{2(3)}\)

x₁ = 3.81 and x₂ = -4.41

Since the time cannot be negative, the answer is t = 3.81 s

The slope and the y-intercept of the line y = 4x + 5 are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is given as follows:

y = 4x + 5.

Hence the slope and the intercept are given as follows:

The problem asks for the slope and the intercept of y = 4x + 5.

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Answer:

1. List (in order) the five phases a single 2 solar mass will go through in its life.

2. List (in order) the five phases a single 25 solar mass will go through in its life.

3. List (in order) the five phases a single 60 solar mass will go through in its life.

Phase options (can be used more than once, some may not be used at all):

Type II Supernova

Protostar

White Dwarf

Giant Phase

Main sequence

Neutron Star

Brown Dwarf

Black Hole

Type 1a Supernova

Planetary Nebula

Step-by-step explanation:

Answer:

The answer is 42 times.

Step-by-step explanation:

The probability of taking out the red bead from the bag every time is

P = 7 ÷ (7 + 8) = 7/15

So, The number of times she expects to take a red bead is 'n'

Therefore,

n = 90 × 7/15

n = 6 × 7 = 42

Thus, The number of times she expects to take a red bead is 42.

The solution that makes both expressions true is x = 8.55556 and y = 10.31746.

To solve for x and y, we need to use a system of equations involves finding the values of x and y that satisfy both equations simultaneously.

We can start by using the first equation to solve for x:

2x + 7x = 77

Combining like terms:

9x = 77

Dividing both sides by 9:

x = 8.55556 (rounded to six decimal places)

Now that we know the value of x we can use either equation to solve for y. Let's use the second equation:

5x + 7y = 115

Substituting x = 8.55556:

5(8.55556) + 7y = 115

Simplifying:

42.7778 + 7y = 115

Subtracting 42.7778 from both sides:

7y = 72.2222

Dividing both sides by 7:

y = 10.31746 (rounded to six decimal places)

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Answer:

m<ZXY - m<WXZ   = m<WXY  

Step-by-step explanation:

given:

point Z is in the interior of <WXY creating XZ.

if m<WXZ = 20

 m<WXY = 100

find:

what would equation would you set up to find the missing angle measure?

solution:

Since Z is interior of <WXY

m<ZXY - m<WXZ   = m<WXY

<WXY =  100  - 20  = 80°

therefore, the equation would be  m<ZXY - m<WXZ   = m<WXY  

Answer:

500 (or 5) is in the hundreds place, 30 (or 3) is in the tens place, and 8 is in the ones place.

Step-by-step explanation:

500 is five-hundred, 30 is a ten (10, 20, 30, 40...), and 8 is a one because it is a single digit number and no other numbers come before it, unless it is a decimal.

Answer:

$45,000 at 13% =  B-rated bond

$5,000 at 3% = CD

Step-by-step explanation:

Let us assume the x amount at 13% be 0.13x

And, y amount at 3% be 0.03x

Total interest = $6,000

The equation is

0.13x + 0.03x = $6,000 ................(1)

Now the total amount is $50,000

So

x + y = $50,000

y = $50,000 - x ................(2)

Now put the y value in the equation 1

So,

0.13x + 0.03 ($50,000 - x)  = $6,000

0.13x + $1,500 - 0.03x = $6,000

0.10x = $6,000 - $1,500

0.10x = $4,500

x = $4,500 ÷ 0.10

= $45,000 at 13%

now y value would be

= $50,000 - $45,000

= $5,000 at 3%

Answer:

Oh easy here is the answer m=21

Answer:

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

There is a difference between the means

Step-by-step explanation:

Step(i):-

Given that mean of the Population = 5.9pounds/square inch

Given mean of the sample = 6.0pounds/square inch

Given that variance of the Population = 0.36

The standard deviation of the Population = √0.36 =0.6

critical value (Z₀.₀₅)= 1.96

Step(ii):-

Null Hypothesis:H₀: x⁻ = μ

Alternative Hypothesis:H₁:  x⁻ ≠ μ

Test statistic

              \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

               \(Z = \frac{6.0-5.9 }{\frac{0.6}{\sqrt{160} } }\)

              Z  =  2.1097

Final answer:-

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means

From the resulting solution, the correct linear inequality graph is Graph C.

Given the inequality equation below:

2(2x-1)+7< 13 or -2x+5 ≤ -10.​

Simplify the expression

2(2x-1)+7< 13

Expand

4x - 2 + 7 < 13

4x + 5 < 13

4x < 13 - 5

4x < 8

x < 2

For the inequality -2x+5 ≤ -10.

-2x+5 ≤ -10

-2x  ≤ -15

x  ≥ 7.5

Hence the solution to the given system of inequalities are x < 2 and x  ≥ 7.5

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The solution is:

The inverse of the given equation is ±sqrt(x+1).

Here, we have,

given equation is :

y = x^2 -1

now, we have to find the inverse of the given equation

so, we have,

Exchange x and y, we get,

x = y^2 -1

Solve for y, we get,

Add 1 for each side

we get,

x+1 = y^2-1+1

x+1 = y^2

Take the square root of each side

we get,

±sqrt(x+1) = sqrt(y^2)

±sqrt(x+1) = y

The inverse is ±sqrt(x+1)

Hence, The solution is:

The inverse of the given equation is ±sqrt(x+1).

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complete question:

If f(x) = x^2 -1, what is the equation for f–1(x)?

As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.

Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

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Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

a) Probability of occurrence of evant A is equals to the 7/10.

P(not getting a white or a blue shirt), P(Aᶜ ) is equals the 3/10.

Probability of occurrence of evant B is equal to the 1/2.

b) The events A and B are not mutually exclusive

c) Mike's preference is to getting a white shirt with his size L.

We have a probabality based problem. Probability is defined as chance of occurrence of an event or result. It can be calculate as favourable outcomes divided by total possible outcomes. There is total number of avaliabile shirts = 20 i.e., total possible outcomes = 20

Mike is interested in getting a white or a blue shirt in size L. Let us consider two events :

A : Getting a white or a blue shirt

B: Getting a shirt in size L

a) Number of favourable outcomes to getting white or a blue shirt = 9 white or 5 blues

Probability ( Getting a white or a blue shirt) , P(A)

= 9/20 + 5/20 + 0 = 14/20 = 7/10

P(not Getting a white or a blue shirt), P(Aᶜ )

= 1 - P(A) = 1 - 7/10 = 3/10

ii) The number of favourable outcomes for event B, n(B) = 10

So, Probability of getting a shirt in size L, P(B)

= 10/20 = 1/2

b) Mutually exclusive events are defined as the events that can't happen at the same time. In other words AnB = 0 . Here, we see there is total 14 shirts which are in white or blue colors and 10 are in size L , So there is possibility that shirt is white or blue in colour and in size L , i.e, An B ≠0

So, events A and B are not mutually exclusive.

c) Event ,n( A u B )= n(A) + n(B) - n(A n B)

On the basis of all details, we conclude that Mike's preference is to choose white shirt with size L .

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Answer:

(a) Expanded form:

\(((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)\)

(b) The value of the expression: -21

Step-by-step explanation:

Given

\(\sum \limit^4_{i=1}\ ((X_i+X_iY_i) - X_iZ_i)\)

Solving (a): The expanded form:

This means that we substitute the values of i from 1 to 4 in the above expression.

So, the expression becomes:

\(((X_1 + X_1Y_1) - X_1Z_1) + ((X_2 + X_2Y_2) - X_2Z_2) + ((X_3 + X_3Y_3) - X_3Z_3) + ((X_4 + X_4Y_4) - X_4Z_4)\)

Solving (b): The value of the expression

To do this, we simply substitute the given values of X1, X2....... in the expression.

This gives:

So, the expression becomes:

\(((0 + 0*5) - 0*0) + ((1 + 1*26) - 1*-2) + ((12 + 12*-2) - 12*3) + ((-1 + -1*25) - -1*24)\)

Simplify each bracket

\(((0 + 0) - 0) + ((1 + 26) +2) + ((12 -24) - 36) + ((-1 -25) +24)\)

\(0 + 29 -48 -2\)

\(-21\)

Hence, the result of the expression is -21

Answer: Heyaa!~

                  - Write 63 as the product of prime factors -

              - Write the prime factors in ascending order -

         -   what's the highest common factor of 63 and 105   -

             Hopefully this helps you! ^^^

Answer:

f(x, y) = yx²/2 + 3x² + 4yx + 24x + K

Step-by-step explanation:

Given the expression dy/dx=xy+6x+4y+24

To find the solution, we are to make y the subject of the formula as shown

dy = (xy+6x+4y+24)dx

∫dy =∫(xy+6x+4y+24)dx

y = ∫(xy+6x+4y+24)dx

We are to integrate the function with respect to x keeping y constant. Since all constant are brought out if integral sign we will have;

y = ∫(xy)dx + ∫(6x)dx + ∫(4y)dx + ∫24dx

y = y∫xdx + 6∫xdx + 4y∫dx + 24∫dx

Integrate;

y = yx²/2 + 6x²/2 + 4yx + 24x + K

y = yx²/2 + 3x² + 4yx + 24x + K

Hence the solution to the differential expression is;

f(x, y) = yx²/2 + 3x² + 4yx + 24x + K

Where K is the constant of integration.