find the area of the region. inside r = 2a cos() and outside r = a

Answer:

838.08 in³

Step-by-step explanation:

volume of tank = (36×24×24)+(½×3.14×12²×24)

= 20,736 + 5,425.92

= 26,161.92 in³

the remaining water = 27,000 - 26,161.92

= 838.08 in³

Answer:

12.5 miles

Step-by-step explanation:

5x2.5=12.5 miles

The average rate of change of the function g(n) = 10(1.02)ⁿ is 0.25   inches/day.

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing.

To calculate the average rate of change of the function g(n), we use the formula below.

Formula:

Where:

From the question,

Given:

Therefore,

Substitute these values into equation 1

Hence, the average rate of change is 0.25 inches/day.

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The frequency distribution consists of class intervals and their corresponding frequencies. The class intervals are 1-5, 6-10, 11-15, and 16-20, and their respective frequencies are 1, 2, 3 and 4. The total number of observations (N) is given as 10.

1. To calculate the standard deviation, we need to follow a step-by-step process. First, we calculate the midpoint of each class interval by taking the average of the lower and upper limits. Then, we calculate the product of the midpoint and its corresponding frequency for each class interval. Next, we sum up all these products. We divide this sum by the total number of observations (N) to find the mean.

2. Now we subtract the mean from each midpoint, square the differences, and multiply them by their respective frequencies. Then, we sum up these values. To obtain the variance, we divide this sum by the total number of observations (N). Finally, the standard deviation is calculated by taking the square root of the variance.

3. In summary, to calculate the standard deviation for the given frequency distribution, we find the mean by calculating the sum of the products of midpoints and frequencies divided by the total number of observations. Then, we calculate the sum of the squared differences between each midpoint and the mean, multiplied by their respective frequencies. The variance is obtained by dividing this sum by the total number of observations, and finally, the standard deviation is obtained by taking the square root of the variance.

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Answer:

Yes

Step-by-step explanation:

where 'y' is put 6    and   where 'x' is put -9   then solve to see if true

-3y>= 2x-2

-3(6) >= 2(-9) -2 ?????

-18 >= -20     TRUE

x+y <  -2

- 9 + 6 < -2   ????

-3 < -2        TRUE

Answer:

shape 1- 89.4 inches

shape 2- 29cm

Step-by-step explanation:

the perimeter is the sum of all numbers around the rim of the shape.

The Mean Absolute Error (MAE) for this forecasting problem is 14.96

when using Exponential Smoothing with an alpha value of 0.30

We have to give that,

The number of cans of soft drinks sold in a machine each week is recorded below,

Develop forecasts using Exponential Smoothing with an alpha value of 0.30. F1-338.

338, 219, 276, 265, 314, 323, 299, 257, 287, 302

Now, For the Mean Absolute Error (MAE) for the forecast problem using Exponential Smoothing with an alpha value of 0.30, follow these steps:

First, we initialize the forecast for the first week (F₁) as 338.

Then, we calculate the forecast for each subsequent week using the formula:

\(F_{t} = \alpha Y_{t} + (1 -\alpha )F_{t - 1}\)

where \(F_{t}\) represents the forecast for week t, \(Y_{t}\) represents the actual sales for week t, and α is the smoothing constant.

Here are the calculations for each week:

F₁ = 338

F₂ = 0.30 338 + (1 - 0.30) 338

= 338

F₃ = 0.30 219 + (1 - 0.30) 338

= 260.7

F₄ = 0.30 276 + (1 - 0.30) 260.7

= 268.59

F₅ = 0.30 265 + (1 - 0.30) 268.59

= 266.112

F₆ = 0.30 314 + (1 - 0.30) 266.112

= 278.778

F₇ = 0.30 323 + (1 - 0.30) 278.778

= 297.6446

F₈ = 0.30 299 + (1 - 0.30) 297.6446

= 298.3502

F₉ = 0.30 257 + (1 - 0.30) 298.3502

= 278.6451

F₁₀ = 0.30 287 + (1 - 0.30) 278.6451

= 282.8516

F₁₁ = 0.30 302 + (1 - 0.30) 282.8516

= 289.5961

To calculate the Mean Absolute Error (MAE), use the formula:

\(MAE = \frac{1}{n}\) ∑ \(|Y_{t} - F_{t} |\)

where n is the total number of weeks and \(Y_{t}\)represents the actual sales for week t.

Now, let's calculate the MAE:

MAE = (1 / 10) (|338 - 338| + |219 - 260.7| + |276 - 268.59| + |265 - 266.112| + |314 - 278.778| + |323 - 297.6446| + |299 - 298.3502| + |257 - 278.6451| + |287 - 282.8516| + |302 - 289.5961|)

= (1 / 10) (0 + 41.7 + 7.41 + 1.112 + 35.222 + 25.3554 + 0.6498 + 21.6451 + 4.1484 + 12.4039)

≈ 14.96

Therefore, the Mean Absolute Error (MAE) for this forecasting problem is 14.96.

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The Mean Absolute Error (MAE) for this forecast problem is 10.03 (rounded to two decimal places). The Mean Absolute Error (MAE) is a measure of the accuracy of a forecast. To calculate the MAE, we need to compare the forecasted values with the actual values.

Using Exponential Smoothing with an alpha value of 0.30, we can develop forecasts for the number of cans of soft drinks sold each week based on the given data. The given data is as follows:

F1-338, 338, 219, 276, 265, 314, 323, 299, 257, 287, 302.

To calculate the forecasted values, we start by taking the first observed value (F1) as the initial forecast. Then, for each subsequent week, we use the formula:

Forecasted Value = Previous Forecasted Value + Alpha * (Actual Value - Previous Forecasted Value)

Let's calculate the forecasted values step by step:

Week 1:
Forecasted Value = F1 = 338

Week 2:
Forecasted Value = F1 + 0.30 * (338 - F1) = 338 + 0.30 * (338 - 338) = 338

Week 3:
Forecasted Value = F2 + 0.30 * (219 - F2) = 338 + 0.30 * (219 - 338) = 284.70

Continuing this process, we calculate the forecasted values for each week:

Week 4: 275.89
Week 5: 280.22
Week 6: 285.66
Week 7: 288.59
Week 8: 287.12
Week 9: 287.88
Week 10: 288.68

Now, we can calculate the Mean Absolute Error (MAE) by taking the average of the absolute differences between the forecasted values and the actual values.

MAE = (|338 - F1| + |219 - F2| + |276 - F3| + ... + |302 - F10|) / 10

MAE = (|338 - 338| + |219 - 284.70| + |276 - 275.89| + ... + |302 - 288.68|) / 10

MAE = (0 + 65.70 + 0.11 + ... + 13.32) / 10

MAE = 10.034

Therefore, the Mean Absolute Error (MAE) for this forecast problem is 10.03 (rounded to two decimal places).

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Answer:

Option 1. This is a vertical pair of angles because they are two nonadjacent (not next to each other) angles formed by intersecting lines. The sides of one angle are the opposite rays to the sides of the other angle. (Angle 5=Angle 7)

Option 2 and 4 are wrong as the angles are not created by a set of parallel lines and a transversal.

Option 3 is wrong as the angles are not adjacent.

Option 5 is wrong as the angles do not have a sum of 90°.

The volume of a cone with diameter 18 cm and height 15 cm is b. V = 1272.3 cm^(3).

To calculate the volume of a cone, we use the formula:

V = (1/3) * π * r^2 * h

where V is the volume, π is the mathematical constant approximately equal to 3.14159, r is the radius of the cone's base, and h is the height of the cone.

Given that the diameter of the cone is 18 cm, we can calculate the radius by dividing the diameter by 2:

r = 18 cm / 2 = 9 cm

Substituting the values into the volume formula:

V = (1/3) * π * 9^2 * 15

Calculating:

V ≈ 1272.3 cm^3

Therefore, the volume of the cone is approximately 1272.3 cm^3.

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Answer:

x=78°

y=78°

z=102°

Step-by-step explanation:

x=78°

y=78°

z=180-78=102°

The image of point A(-6,-3) after being rotated 196° clockwise around point (-5,5) will be located in the fourth quadrant at approximately (-3.92,-7.49).

To determine the location of the image of point A(-6,-3) after being rotated 196° clockwise around point (-5,5), we need to follow these steps:

1. Draw the coordinate axes and plot point A(-6,-3).
2. Plot the center of rotation, point (-5,5).
3. Draw a line connecting point A to the center of rotation (-5,5).
4. Determine the distance between point A and the center of rotation (-5,5), which is 10 units (using the distance formula).
5. Rotate point A 196° clockwise around point (-5,5) by keeping the distance of 10 units and finding the new coordinates of the point.
6. The new coordinates of point A will be located in the fourth quadrant because the rotation is clockwise and the starting point A(-6,-3) is in the third quadrant.

Using trigonometry, we can determine the new coordinates of point A after rotation as follows:

- The angle of rotation is 196° clockwise, which is equivalent to 164° counterclockwise (360° - 196°).
- The distance between point A and the center of rotation (-5,5) is 10 units.
- The angle between the x-axis and the line connecting point A to the center of rotation is 116.57° (using inverse tangent function: tan⁻¹(3/6) = 26.57°, then 90° + 26.57° = 116.57°).
- The angle between the x-axis and the line connecting the new location of point A to the center of rotation is 280.57° (116.57° + 164°).
- The x-coordinate of the new location of point A can be found using the cosine function: cos(280.57°) = -3.92 (rounded to two decimal places).
- The y-coordinate of the new location of point A can be found using the sine function: sin(280.57°) = -7.49 (rounded to two decimal places).

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The system of equation that has one solution is: (d) –2x+ 7y = –5  and 2x +7y = –9

This is a group of equations which may have none, one or more solutions.

From the list of given options, the system of equations that has one solution is:

–2x+ 7y = –5  and 2x +7y = –9

This is so because, the solution is (-1,-1)

However, the other systems have infinite many solutions

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Answer:

D. -2x + 7y = -5 and 2x + 7y = -9

Step-by-step explanation:

Edge 2023

To find the probability that the equipment is functioning properly, we need to consider the cases where 6, 7, 8, or all 9 components are operational.

Let's calculate the probability for each case and add them together.
For 6 components to be operational, we have to choose any 6 out of the 9 components. The probability of each chosen component working is p, and the probability of each unchosen component failing is (1 - p). So, the probability for 6 operational components is (9 choose 6) * \(p^6 * (1 - p)^3.\)
Similarly, for 7 operational components, the probability is (9 choose 7) \(* p^7 * (1 - p)^2.\)
For 8 operational components, the probability is (9 choose 8) * \(p^8 * (1 - p).\)
Lastly, for all 9 components to be operational, the probability is\(p^9.\)
Adding up these probabilities will give us the overall probability that the equipment is functioning properly.

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The solution for x in the equation 2.5 * x - 1 = 27 is x = 11.2.

Simplifying the expression 5²-3⁻² + 64:

To simplify this expression, we'll evaluate the exponents and perform the necessary calculations:

5² = 5 * 5 = 25

3⁻² = 1 / 3² = 1 / 9

Now, we can rewrite the expression:

25 - 1/9 + 64

To add the fractions, we need a common denominator. In this case, the least common multiple of 9 and 1 is 9. Let's rewrite the expression with the common denominator:

25 - (1/9) + (64 * 9/9)

Now we can add the fractions:

25 - 1/9 + 576/9

Combining the terms:

225/9 - 1/9 + 576/9

Now we can add the fractions with the same denominator:

(225 - 1 + 576)/9

Simplifying the numerator:

(800)/9

Therefore, the simplified expression is 800/9.

2.1.2 Simplifying the expression 5x³y⁻² / 10y⁴x⁻³:

To simplify this expression, we'll simplify the terms with the same base and apply the rules of exponents:

5x³y⁻² / 10y⁴x⁻³

Simplifying the x terms:

5x³ / x⁻³ = 5x³ * x³ = 5x⁶

Simplifying the y terms:

y⁻² / y⁴ = 1/y² * 1/y⁴ = 1/y⁶

Putting it all together:

5x⁶ / 10y⁶ = (1/2) * (x⁶/y⁶)

Therefore, the simplified expression is (1/2) * (x⁶/y⁶).

2.2.1 Solving for x in the equation 3x + 2 = 27:

To solve for x, we'll isolate the variable x by performing the necessary calculations:

3x + 2 = 27

Subtracting 2 from both sides of the equation:

3x = 27 - 2

3x = 25

Dividing both sides by 3 to solve for x:

x = 25/3

Therefore, the solution for x in the equation 3x + 2 = 27 is x = 25/3.

2.2.2 Solving for x in the equation 2.5 * x - 1 = 27:

To solve for x, we'll isolate the variable x by performing the necessary calculations:

2.5 * x - 1 = 27

Adding 1 to both sides of the equation:

2.5 * x = 27 + 1

2.5 * x = 28

Dividing both sides by 2.5 to solve for x:

x = 28/2.5

Calculating the division:

x = 11.2

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Answer:

The correct answer is the final option, 2.

Step-by-step explanation:

[(16+4) - 10] - 8

Our first step in this problem, according to the order of operations, is to simplify what is inside the parentheses.  Since there are multiple sets of parentheses, we must simplify the innermost group first.  If we add 16 and 4, we get:

[20 - 10] - 8

Next, we must perform the subtraction inside the parentheses.  This gives us:

10 - 8

Now, we can perform the final operation.  

10 - 8 = 2

Therefore, the correct answer is 2.

Hope this helps!

According to the given work and time, if Julio works for only 2 minutes, it would take approximately 3.33 minutes for both Julio and Jaden working together to change one tire.

Julio can change a tire in 5 minutes, while his twin brother Jaden takes 10 minutes. We need to determine how much time it would take for both brothers, working simultaneously, to change one tire if Julio only works for 2 minutes.

Let's assume that the time it takes for both brothers working together to change one tire is represented by "t" minutes. We can set up a proportion based on the work rates of Julio and Jaden:

Julio's work rate: 1 tire / 5 minutes

Jaden's work rate: 1 tire / 10 minutes

Combined work rate: 1 tire / t minutes

According to the work rate principle, the combined work rate is the sum of the individual work rates. Therefore, we have the equation:

1/5 + 1/10 = 1/t

To find the value of "t", we need to solve this equation. Multiplying through by the least common denominator (LCD) of 10t, we get:

2t + t = 10

Combining like terms, we have:

3t = 10

Dividing both sides by 3, we find:

t = 10/3

So, it would take both Julio and Jaden working simultaneously approximately 3.33 minutes (or 3 minutes and 20 seconds) to change one tire if Julio only works for 2 minutes.

Therefore, if Julio works for only 2 minutes, it would take approximately 3.33 minutes for both Julio and Jaden working together to change one tire.

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A recursive sequence is a sequence in which terms are defined using one or more previous terms that are given.

If you know the term n of an arithmetic sequence and you know the common difference, d, you can find the term \((n + 1)\) by tossing the recursive formula to \(n + 1 = a \ n + d\)

We have then:

\(5, 15, 30, 50\)

\(an = (\dfrac{5}{2} ) \times (n) \times (n + 1)\)

Answer:

the recursive formula for 5, 15, 30, 50, is:

an = (5/2) x (n) x (n + 1)

Answer:

it is the 4th and 5th

Step-by-step explanation:

by following the laws of BODMAS

Brackets

of

Division

Multiplication

Addition

Subtraction

(5×6)+2=5×6+2

(30)+2=30+2

32=32

5×6+2=2+5×6

30+2=2+30

32=32

3/5×(-3)/10 + 1/15 - 3/5×1/5 =  -7/30 ≅  -0.2333333

I hope this helps!

The resulting temperature was 8°F.

Answer:

D) y=-x

Step-by-step explanation:

Slope intercept form is , y = mx+c, where m is the slope and c is the y-intercept. Substituting the values of m and c, we will get,

y = (-1)*x + 0

y = -x

Answer:

4000 mg

Step-by-step explanation:

4grams · 1000 = 4000 milligrams

Answer:

4000 mg

Step-by-step explanation:

The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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Answer:

14

Step-by-step explanation:

8 - 3 = 5

25 / 5 = 5

9 - 5 = 4

4 x 2 = 8

8 + 6 = 14

The calculated value of the measure of the angle V is 81 degrees

From the question, we have the following parameters that can be used in our computation:

Because the triangle ERT is congruent to triangle CVB, then we have

E = C

So, we have

7x + 4 = 32

Evaluate the like terms

7x = 28

Divide by 7

x = 4

Also, we have

V = R

This means that

V = 180 - C - B

Substitute the known values in the above equation, so, we have the following representation

V = 180 - 7x - 4 - 15x - 7

So, we have

V = 180 - 7(4) - 4 - 15(4) - 7

Evaluate

V = 81

Hence, the measure of the angle is 81 degrees

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Answer:

Solution given:

length of arc LM={angle}/360*2*π*r

=here π=180 for angle and π for length

=(3π/4)/360*2*π *6

=(3*180/4)/360*2*π*6

=9/2π

option C

9/2π is a required answer.

Answer:

Here angle ABC = angle HGF ......( each 90° )

and other two corresponding sides are similar...

therefore, two sides and one Angle...

hence, SAS Test.

To use the distributive property to simplify -5(6+x), we need to distribute the -5 to both the 6 and the x, which means multiplying each term inside the parentheses by -5. This gives us:

-5(6+x) = -5(6) - 5(x)

Now, we can simplify this expression by performing the multiplication. We have:

-5(6) = -30

-5(x) = -5x

Therefore, the simplified expression is:

-5(6+x) = -30 - 5x

So, -5(6+x) can be simplified to -30 - 5x using the distributive property.