A sphere has a Volume of 972 cubic feet. Find the radius of the sphere.

Answer:

The suit originally cost $200.

Step-by-step explanation:

In order to calculate the original price of the suit, you can use a rule of three considering that $116 represents 58% of the original price:

116 → 58%

x  ←  100%

x=(116*100)/58

x=200

According to this, the answer is that the suit originally cost $200.

The order of points is:

1. -33         5. -55         9. 2.4

2. -23        6. -2.6        10. 7.6

3. -11.5       7. -2.5        11. 9.3

4. -10         8. 2.33       12. 10.6

Given,

The equations:

1. y = (-2/3) × -16 = 10.66

2. y = (1/2) × -23 = -11.5

3. y = (3/2) × -22 = -33

4. y = (4/3) × -2 = -2.66

5. y = (1/3) × 23 = 7.66

6. y = (1/2) × -5 = -2.5

7. y = (-1/4) × 22 = -5.5

8. y = 1 × -23 = -23

9. y = (4/3) × 7 = 9.33

10. y = (1/3) × 7 = 2.33

11. y = -1 × 10 = -10

12. y = (-2/5) × -6 = 2.4

We have to order this from 1 to 12. That is ascending order:

Here is the equations:

1. y = (3/2) × -22 = -33

2. y = 1 × -23 = -23

3.  y = (1/2) × -23 = -11.5

4. y = -1 × 10 = -10

5. y = (-1/4) × 22 = -5.5

6. y = (4/3) × -2 = -2.66

7. y = (1/2) × -5 = -2.5

8. y = (1/3) × 7 = 2.33

9. y = (-2/5) × -6 = 2.4

10. y = (1/3) × 23 = 7.66

11.  y = (4/3) × 7 = 9.33

12. y = (-2/3) × -16 = 10.66

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Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

ii

350x + 200y - 4200 = 0

Therefore, the equation in standard form that models the number of funnel cakes, x, and the number of deep-fried Oreos, y, Francis can buy if he spends $42.00 is:

350x + 200y - 4200 = 0

To find the x-intercept, we set y to zero and solve for x:

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

Therefore, the x-intercept is 12. This means that if Francis only buys deep-fried Oreos (y = 0), he can buy 12 funnel cakes with $42.00.

Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

3.50x + 2.00y = 42.00

3.50x + 2.00y - 42.00 = 0

Multiplying both sides by 100 to eliminate the decimals, we get:

350x + 200y - 4200 = 0

x-intercept means what is x when y is 0

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

y-intercept means what is y when x is 0

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

To find the y-intercept, we set x to zero and solve for y:

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

Therefore, the y-intercept is 21. This means that if Francis only buys funnel cakes (x = 0), he can buy 21 deep-fried Oreos with $42.00.

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

Answer:

Associative property of addition

Step-by-step explanation:

The range of the graph is -∞ ≤ y ≤ ∞

A graph is  a pictorial representation of of information. Graphs are plotted after some analysis of the data and information are plotted to help under the relationship existing in the data by looking at the graph.

This is a term used mostly in Cartesian coordinates to represent the output values.

The output values is also the values plotted on the ordinates or y direction.

The graph shows that the  values on the ordinate has an arrow pointing up and down at both ends ;of the graph .

This arrow tells that the information in the ordinate is continuous and hence can be represented by positive and negative infinity

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To determine the range of sample sizes that can be taken from a population of 768 games without violating the conditions required for performing normal calculations with the sampling distribution of r, we need to consider the guidelines for the Central Limit Theorem.

The Central Limit Theorem states that the sampling distribution of a statistic (such as the correlation coefficient r) approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution, under certain conditions.

One of the conditions for the Central Limit Theorem to hold is that the sample size should be sufficiently large. While there is no exact cutoff for the sample size, a general guideline is that the sample size should be at least 30.

Given this information, the correct answer choice is (C) 30 < n < 77. This range ensures that the sample size is greater than 30 and less than the total population size of 768, satisfying the conditions required for performing normal calculations with the sampling distribution of r.

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Answer:

Option B is the correct option.

Step-by-step explanation:

\( \sf{ \frac{3}{5} = \frac{x - 1}{8} }\)

Apply cross product property

⇒\( \sf{ 5(x - 1) = 3 \times 8}\)

Distribute 5 through the parentheses

⇒\( \sf{5x - 5 = 3 \times 8}\)

Multiply the numbers

⇒\( \sf{5x - 5 = 24}\)

Move 5 to right hand side and change it's sign

⇒\( \sf{5x = 24 + 5}\)

Add the numbers

⇒\( \sf{5x = 29}\)

Divide both sides of the equation by 5

⇒\( \sf{ \frac{5x}{5} = \frac{29}{5} }\)

⇒\( \sf{x = \frac{29}{5} }\)

Hope I helped!

Best regards!!

Answer:

x = 2

because we have the same question and i got it right its hard to explain but trust me its x = 2

The solution to the given equation is 2. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x/6 = 4/12.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, x/6 = 4/12

By cross multiplication, we get

12x=24

⇒ x=2

The solution to the given equation is 2. Therefore, option B is the correct answer.

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The process may not be in control. A histogram is a graphical representation of the distribution of data, and it is used to understand the shape and characteristics of the data. The correct answer is c.

A histogram is a graphical representation of the distribution of data, and it is used to understand the shape and characteristics of the data. In statistical process control, histograms are used to monitor the stability and consistency of a process.

If the shape of the histogram is not what is expected, it suggests that the process may not be in control, which means that the process is not operating in a stable and predictable manner. This could be due to common causes of variation, such as random fluctuations in the process, or special causes of variation, such as a change in the process inputs or equipment. However, the presence of a special cause cannot be concluded solely from the shape of the histogram, as other factors need to be considered. Therefore, option a is not the correct answer.

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The given array is 10 2 66 71 12 34 8 52. Selection sort is a simple algorithm that is used to sort an array in ascending or descending order.

Selection sort is performed by selecting the smallest (or largest) element from the unsorted subarray and placing it at the beginning of the array. Then, repeat this process until the entire array is sorted. Here's how to use selection sort to sort the given array in ascending order:                                                                                                                                       Step 1: Initialize the minimum value as the first element of the array.                                                                                                    Step 2: Compare this value with all of the other values in the array. If any value is less than the minimum value, assign that value to the minimum value.                                                                                                                                                              Step 3: Swap the minimum value with the first element of the unsorted subarray.                                                                                      Step 4: Repeat steps 1-3 for the remainder of the array until the entire array is sorted.                                                                            The sorted array is 2 8 10 12 34 52 66 71.                                                                                                                                                    The selection sort algorithm is a simple, easy-to-understand algorithm that sorts an array in ascending or descending order. This algorithm works by repeatedly selecting the smallest (or largest) element from the unsorted subarray and placing it at the beginning of the array. Then, the algorithm moves on to the next element of the unsorted subarray and repeats the process. This process is repeated until the entire array is sorted. One of the benefits of the selection sort algorithm is that it is easy to understand and implement. However, it is not very efficient, particularly for large arrays. This is because the algorithm has to scan the entire unsorted subarray for every element in the sorted subarray. As a result, the algorithm has a time complexity of O(n^2). Selection sort is not the best choice for sorting large arrays, but it can be useful for sorting small arrays or for educational purposes. The selection sort algorithm is a simple, easy-to-understand algorithm that can be used to sort an array in ascending or descending order. However, it is not very efficient for large arrays and has a time complexity of O(n^2).                                                                                                                         The algorithm that defines a two-dimensional array:                                                                                                                       Step 1: Start                                                                                                                                                                                           Step 2: Declare a two-dimensional array of m rows and n columns, where m and n are integers.                                                       Step 3: Initialize the array by assigning values to its elements. This can be done using nested loops that iterate over the rows and columns of the array.                                                                                                                                                   Step 4: Display the elements of the array. This can be done using nested loops that iterate over the rows and columns of the array.                                                                                                                                                                                         Step 5: End                                                                                                                                                                                                 The algorithm that finds the smallest element in a one-dimensional array:                                                                                      Step 1: Start                                                                                                                                                                                            Step 2: Declare an array of n elements, where n is an integer.                                                                                                                                                                                                           Step 3: Initialize the array by assigning values to its elements. This can be done using a loop that iterates over the array and reads in values from the user.                                                                                                                                               Step 4: Set the minimum value to the first element of the array.                                                                                                       Step 5: Compare the minimum value with each of the other elements in the array. If any element is less than the minimum value, assign that element to the minimum value.                                                                                                                     Step 6: Display the minimum value.                                                                                                                                                        Step 7: End                                                                                                                                                                                                 The given array is: 10 2 66 71 12 34 8 52                                                                                                                                                        Insertion sort is a simple algorithm that is used to sort an array in ascending or descending order. Insertion sort is performed by iterating over the array and inserting each element into its proper position in the sorted subarray. Here's how to use insertion sort to sort the given array in ascending order:                                                                                                  Step 1: Iterate over the array starting from the second element. This is because the first element is already considered sorted.                                                                                                                                                                                                     Step 2: Compare the current element with the elements in the sorted subarray. If any element is greater than the current element, move that element to the right to make room for the current element.                                                                              Step 3: Insert the current element into its proper position in the sorted subarray.                                                                                     Step 4: Repeat steps 1-3 for the remainder of the array until the entire array is sorted.                                                                    The sorted array is 2 8 10 12 34 52 66 71Q5.                                                                                                                                          The algorithm reads 2 integer numbers and finds their sum.                                                                                                                     Step 1: Start                                                                                                                                                                                            Step 2: Read the first integer number from the data medium and assign it to variable a.                                                                                           Step 3: Read the second integer number from the data medium and assign it to variable b.                                                                       Step 4: Add the values of a and b and assign the result to variable c. c = a + b                                                                                               Step 5: Display the value of c.                                                                                                                                                                 Step 6: End

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Answer:

1/2 of a bale

Step-by-step explanation:

1/4 times 2 equals 1/2

Answer:

16

Step-by-step explanation:

if 18 dollars will get your 4, 4 times 18 is 72 so 16 is your answer

Answer:

y = 3x +26

Step-by-step explanation:

1. First find the slope. The formula for finding the slope is \(m=(y_{2}-y_{1})/(x_{2}-x_{1} )\).

\(m = (2-8)/(-8-(-6)) = -6/-2 = 3\)

2. Plug the slope value into the point-slope equation: y = mx + b.

\(y = 3x + b\)

3. In order to find b, plug one of the coordinates into the equation and solve for b.

\(2 = 3 (-8) + b\)

\(2=-24 +b\)

\(b = 26\)

4. Substitute the b value into the point-slope equation, and you will have

\(y=3x+26\)

I hope this helps!

Answer:

yes

Step-by-step explanation:

--

Answer:

Step-by-step explanation:

Length ( L ) = 8 cm

Perimeter of square = 4 L

( where L is the side of the square )

Plug the value of length

⇒\( \sf{4 \times 8}\)

Multiply the numbers

⇒\( \sf{32 }\) cm

Hope I helped!

Best regards!

Answer:

\(\huge \boxed{\mathrm{32 \ cm}}\)

Step-by-step explanation:

The formula to calculate the perimeter of a square is given as:

\(\sf Perimeter = 4 \times side \ length\)

The side length of the square is 8 centimeters.

\(P=4 \times 8\)

Solve for the perimeter.

\(P=32\)

The perimeter of the square is 32 centimeters.

Given: The Table of Values

To Find: The least-squares regression line for the data set in the table by using the desmos graphing calculator.

SolutionThe general form of least-squares regression line is: y = mx + b Where, m is the slope and b is the y-intercept.

Where, m is the slope and b is the y-intercept.By using the desmos graphing calculator, we get

m 2.55 b -6.435 Substitute these Values

y = (2.55)x + (-6.435)

y = 2.55x - 6.435

Answer: A

The expression to generate the parameters and statistics is y tilde m x plus b, the correct option is C.

Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that;

x subscript 2 baseline y subscript 2 baseline;

1 2

2 9

3 7

4 12

Now,

To find the least-squares regression line for a data set using Desmos, you need to follow these steps:

Enter the data as a table in Desmos. For example, type {1, 2, 3, 4} in the x column and {2, 9, 7, 12} in the y column.

Type y tilde m x plus b in the expression box. This tells Desmos to find the values of m and b that minimize the sum of squared errors between y and y tilde (the predicted values).

Click on the wrench icon next to the expression to see the parameters and statistics. You should see something like this:

m = 2.8 b = -1.6 r² = 0.84

This means that the equation of the least-squares regression line is:

y tilde = 2.8 x - 1.6

And that the coefficient of determination (r²) is 0.84.

Therefore, by expression the answer will be y tilde m x plus b.

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To find IUF and EF in different situations, you need to determine the values of "m", "px", and "py" for the given function. Then, plug those values into the respective formulas. The IUF represents the importance of the function, while the EF represents the expected value.

In order to find EF and IUF in different situations, you need to understand the formulas and when to apply them.

1. Formula for IUF (Importance-Utility Factor):
  - In the first example, where u(x,y)=X^(1/2)*Y^(1/2), the formula for IUF is v=m/√(4pxpy).
  - Here, "m" represents the value of the function (32), and "px" and "py" represent the partial derivatives of "u" with respect to "x" and "y" (both equal to 1).
  - So, in this case, you can calculate IUF as v=32/√(4*1*1)=32/2=16.

2. Formula for EF (Expected Factor):
  - Continuing with the first example, the formula for EF is m=v√(4pxpy).
  - Plugging in the values, EF=32*√(4*1*1)=32*2=64.

3. Formula for IUF and EF in the second example:
  - In the second example, where u(x,y)=Min(x,2y), the formula for IUF is v=2m/√(2px+2py), and the formula for EF is m=v(2px+2py)/2.
  - Here, "m" represents the value of the function (15), and "px" and "py" represent the partial derivatives of "u" with respect to "x" and "y" (both equal to 1).
  - Plugging in the values, IUF=2*15/√(2*1+2*1)=30/√4=30/2=15, and EF=15*(2*1+2*1)/2=15*4/2=30.

In summary, to find IUF and EF in different situations, you need to determine the values of "m", "px", and "py" for the given function. Then, plug those values into the respective formulas. The IUF represents the importance of the function, while the EF represents the expected value. Make sure to use the correct formulas based on the given function.

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The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).

It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):

1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).

To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.

2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.

In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.

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(a) The equation of the line in point-slope form is y + 1 = 2x + 6.

(b) The equation of the line in slope-intercept form is y = 2x + 5.

(a) To write the equation of the line in point-slope form, we use the formula:

y - y1 = m(x - x1),

where m is the slope and (x1, y1) is a point on the line.

Given that the slope (m) is 2 and the point is (-3, -1), we substitute these values into the formula:

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

Simplifying the equation gives:

y + 1 = 2(x + 3).

Thus, the equation of the line in point-slope form is:

y + 1 = 2x + 6.

(b) To convert the equation to slope-intercept form (y = mx + b), where b represents the y-intercept, we need to isolate y on one side of the equation.

Starting from the point-slope form equation:

y + 1 = 2x + 6,

we can subtract 1 from both sides:

y = 2x + 6 - 1.

Simplifying further gives:

y = 2x + 5.

Therefore, the equation of the line in slope-intercept form is:

y = 2x + 5.

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Answer:

\(slope=\frac{4}{5}\)

Step-by-step explanation:

\(y=\frac{4}{5} x-3\)

This is written in slope-intercept form:

\(y=mx+b\)

m is the slope and b is the y-intercept. x and y are the corresponding points (x,y).

Therefore, the slope is \(\frac{4}{5}\).

:Done

Answer:

The median of the data is 3.5

Answer:

A.  Correct

B.  Correct

C.  Not correct

D.  Correct

E.  Not correct

Step-by-step explanation:

We are told that Michael's race numbers are:

5.25 miles

45.75 minutes

Divide the miles by the minutes to get mIchael's running rate:

0.114754098 mi/min

This result matches option B. " Michael's average pace was about 0.11 miles per minute."

======

Check all the answer options:

A. Michael's unit rate of minutes per mile was about 8.7.  

  Take 0.11475409 mi/min and invert it to find min/mile:

      1/(0.11475409 mi/min) = 8.71 min/mile

This is a correct statement.

B. Michael's average pace was about 0.11 miles per minute.

From above:  This is a correct statement.

C. Michael's unit rate of minutes per mile was about 6.9.

Take the given numbers:   (45.75 minutes)/(5.25 miles) = 8.71 min/mile

This is not a correct statement.

D. Michael's average speed during the race was about 6.9 miles per hour.  

Take the calculated rate of 0.11475409 mi/min and covert it to miles/hour:

  Use the conversion factor (60 min/1 hr)

   (0.11475409 mi/min)*((60 min/1 hr)) = 6.89 miles/hr

This is a correct statement.

E.  Michael ran about 8.7 miles in 1 minute.

We know from above that he runs at 6.89 miles per hour.  Running 8.7 miles in 1 minute  would mean he is running at (8.7)*(60) = 413 miles/hour.    

Perhaps he had some good energy bars, but the data do not support this conclusion.

This is not a correct statement.

It took 15.03 seconds to fill the 67% larger than the 3-gallon bucket

Calculating the time required to fill the bucket:

To solve this problem, use the concept of proportionality to calculate the time required. Use the concept of percentage increase to find the volume of the larger bucket, which was 67% larger than the 3-gallon bucket.

Here we have

A hose fills a 3-gallon bucket in 9 seconds.

The volume of the bucket which is 167% more than 3 gallons

= 167% of 3 gallons = [167/100] × 3 = 5.01 gallons

It took 9 seconds to fill 3 gallons

The time required to fill 5.01 gallons = 9/3 × [5.01]

= 15.03 seconds

Therefore,

It took 15.03 seconds to fill the 67% larger than the 3-gallon bucket

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(a) Yes, the air in the house would exceed the long-term health standard if the groundwater is in equilibrium with the air in the house.

(b) The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT).

(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.

(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm.

(a) The Henry's Law constant for TCE is 0.4, which means that the concentration of TCE in air at equilibrium with water is 40% of the concentration in water. The groundwater concentration is 110 ppm, so the equilibrium air concentration would be 44 ppm. This exceeds the long-term health standard of 25 ppm.

(b) The flux of TCE through the floor is given by FT = k(c+ - CT), where k is a measured constant, c+ is the concentration of TCE in the groundwater, and CT is the concentration of TCE in the air in the house. The normal strategy for remediating vapor intrusion is to install fans in the house that ventilate the house with outside air. The outside ambient air has a concentration of ca. The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT), where dct/dt is the rate of change of the concentration of TCE in the house, k is the flux constant, c+ is the concentration of TCE in the groundwater, CT is the concentration of TCE in the air in the house, Q is the ventilation rate, and ca is the concentration of TCE in the outside air.

(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q, where Ah is the area of the house, k is the flux constant, and Q is the ventilation rate. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.

(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm. The difference is due to the fact that the groundwater concentration is much higher than the ambient air concentration.

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Step-by-step explanation:

Here ,

Length = 7 cm

breadth = 3 cm

height = 10 cm

Volume = ?

Now ,

Volume ( v ) = l × b × h

= 7 cm × 3 cm × 10 cm

\( = 210 {cm}^{3} \)

Answer:

Formula: divide the value in centimeters per second by 100 because 1 meter per second equals 100 centimeters per second. So, 9000 centimeters per second = 9000100 = 90 meters per second.

Step-by-step explanation:

Using it's concept, the percentile rank for a score of 85 on this test is the 50th percentile.

When a measure is in the xth percentile of a data-set, it is greater or equal than x% of the measures and lesser than (100 - x)%.

In this problem, there are 20 scores, and 85 corresponds to the 10th highest score, hence the percentile is given by:

p = 10/20 = 0.5 x 100% = 50th percentile.

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