for the students, the ratio of girls to boys is 4 to 5. If I have 54 students in total, how many of each do I have?​

(a) Forecast: Linear regression  the next year is approx 191.6007.

(b) MSE: Mean Squared Error is approximately 249.1585.

(c) MAPE: Mean Absolute Percent Error is approximately 10.42%.

(a) (a) Forecast using linear regression:
To forecast the number of disk drives for the next year, we can use linear regression to fit a line to the given data points. The linear regression equation is of the form y = mx + b, where y represents the number of disk drives and x represents the year.

Calculating the slope (m):
m = (Σ(xy) - n(Σx)(Σy)) / (Σ(x^2) - n(Σx)^2)

Σ(xy) = (1)(140) + (2)(160) + (3)(190) + (4)(200) + (5)(210) = 2820
Σ(x) = 1 + 2 + 3 + 4 + 5 = 15
Σ(y) = 140 + 160 + 190 + 200 + 210 = 900
Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) + (5^2) = 55

m = (2820 - 5(15)(900)) / (55 - 5(15)^2)
m = (2820 - 6750) / (55 - 1125)
m = -3930 / -1070
m ≈ 3.6729

Calculating the y-intercept (b):
b = (Σy - m(Σx)) / n
b = (900 - 3.6729(15)) / 5
b = (900 - 55.0935) / 5
b ≈ 168.1813

Using the equation y = 3.6729x + 168.1813, where x represents the year, we can predict the number of disk drives for the next year. To do so, we substitute the value of x as the next year in the equation. Let's assume the next year is represented by x = 6:

y = 3.6729(6) + 168.1813
y ≈ 191.6007

Therefore, according to the linear regression model, the predicted number of disk drives for the next year is approximately 191.6007.

(b) Calculation of Mean Squared Error (MSE):

To calculate the Mean Squared Error (MSE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 = 171.8542
Year 2: y = 3.6729(2) + 168.1813 = 175.5271
Year 3: y = 3.6729(3) + 168.1813 = 179.2000
Year 4: y = 3.6729(4) + 168.1813 = 182.8729
Year 5: y = 3.6729(5) + 168.1813 = 186.5458
Next, we calculate the squared difference between the predicted and actual values, and then take the average:

MSE = (Σ(y - ŷ)^2) / n

MSE = ((140 - 171.8542)^2 + (160 - 175.5271)^2 + (190 - 179.2000)^2 + (200 - 182.8729)^2 + (210 - 186.5458)^2) / 5

MSE ≈ 249.1585

The Mean Squared Error (MSE) for the linear regression model is approximately 249.1585.

This value represents the average squared difference between the predicted values and the actual values, providing a measure of the accuracy of the model.

(c) Calculation of Mean Absolute Percent Error (MAPE):

To calculate the Mean Absolute Percent Error (MAPE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 ≈ 171.8542
Year 2: y = 3.6729(2) + 168.1813 ≈ 175.5271
Year 3: y = 3.6729(3) + 168.1813 ≈ 179.2000
Year 4: y = 3.6729(4) + 168.1813 ≈ 182.8729
Year 5: y = 3.6729(5) + 168.1813 ≈ 186.5458

Next, we calculate the absolute percent error for each year, which is the absolute difference between the predicted and actual values divided by the actual value, multiplied by 100:

Absolute Percent Error (APE):

Year 1: |(140 - 171.8542) / 140| * 100 ≈ 18.467
Year 2: |(160 - 175.5271) / 160| * 100 ≈ 9.704
Year 3: |(190 - 179.2000) / 190| * 100 ≈ 5.684
Year 4: |(200 - 182.8729) / 200| * 100 ≈ 8.563
Year 5: |(210 - 186.5458) / 210| * 100 ≈ 11.682
Finally, we calculate the average of the absolute percent errors:

MAPE = (APE₁ + APE₂ + APE₃ + APE₄ + APE₅) / n

MAPE ≈ (18.467 + 9.704 + 5.684 + 8.563 + 11.682) / 5 ≈ 10.42

The Mean Absolute Percent Error (MAPE) for the linear regression model is approximately 10.42%.

This value represents the average percentage difference between the predicted values and the actual values, providing a measure of the relative accuracy of the model.

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Answer:

Step-by-step explanation:

Remark

x/(x+1) - 1/2 = -1 /(x + 1) is the equation to be solved. Add 1/(x + 1 to both sides

x/(x+1) + 1/(x+1) - 1/2 = -1/(x + 1) + 1/(x + 1)              Combine

x/(x+1) + 1/(x + 1) - 1/2 = 0                                      Combine x/(x+1) + 1/(x+1)

(x + 1)/(x + 1) - 1/2 = 0                                            Cancel (x+1)/(x+1) = 1

1 - 1/2 = 0                                                              No solution

Answer: No solution

The given differential equation is `(27xy + 45y²) + (9x² + 45xy)y' = 0`.We have to solve this differential equation by using integrating factor `u(x, y) = (xy(2x+5y))-1`.The integrating factor `u(x,y)` is given by `u(x,y) = e^∫p(x)dx`, where `p(x)` is the coefficient of y' term.

Let us find `p(x)` for the given differential equation.`p(x) = (9x² + 45xy)/ (27xy + 45y²)`We can simplify this expression by dividing both numerator and denominator by `9xy`.We get `p(x) = (x + 5y)/(3y)`The integrating factor `u(x,y)` is given by `u(x,y) = (xy(2x+5y))-1`.Substitute `p(x)` and `u(x,y)` in the following formula:`y = (1/u(x,y))* ∫[u(x,y)* q(x)] dx + C/u(x,y)`Where `q(x)` is the coefficient of y term, and `C` is the arbitrary constant.To solve the differential equation, we will use the above formula, as follows:`y = [(3y)/(x+5y)]* ∫ [(xy(2x+5y))/y]*dx + C/[(xy(2x+5y))]`We will simplify and solve the above expression, as follows:`y = (3x^2 + 5xy)/ (2xy + 5y^2) + C/(xy(2x+5y))`Simplify the above expression by multiplying `2xy + 5y^2` both numerator and denominator, we get:`y(2xy + 5y^2) = 3x^2 + 5xy + C`This is the general solution of the differential equation.

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(a) The probability that both score more than 175 is 0.12 and (b) the probability that Thomas scores more than 175 and Sarah scores higher than Thomas is 0.04

If the occurrence of one event say A does not affect the occurrence of event B, then the two events are said to be independent such that;

P (A ∩ B) = P (A) × P (B)

a:

consider; event A represents Sarah scoring more than 175 and event B represents Thomas scoring more than 175

Thus, P(A) = Probability that Sarah scores more than 175 = 0.6

P(B) = The probability that Thomas scores more than 175 = 0.2

Since the scores are independent, therefore the probability that both Sarah and Thomas score more than 175 is,

P (A ∩ B) = (0.6) × (0.2)

P (A ∩ B) = 0.12

b:

If the occurrence of one event say A affects the occurrence of another event say B, then the two events are said to be dependent on each other such that;

P (A ∩ B) = P (B) × P (A|B)

As; P(B) = The Probability that Thomas scores more than 175 = 0.2

and P(A|B) = Sarah scores more than Thomas given that Thomas scores more than 175 = 0.2

Therefore;

P (A ∩ B) = (0.2) × (0.2) = 0.04

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Answer:

There are enough oysters

Step-by-step explanation:

Given

\(Volume = 18\ trillion\ gallon\)

\(Area = 2867200\ acre\)

\(1\ acre = 750000\ oysters\)

\(1\ oyster = 50\ gallons\)

Required

Determine if there is enough water for a day

We have:

\(1\ oyster = 50\ gallons\)

Convert to oysters: multiply both sides by 750000

\(750000 * 1\ oyster = 50\ gallon *750000\)

\(750000\ oysters = 37500000\ gallons\)

Given that:

\(1\ acre = 750000\ oysters\)

So, we have:

\(1\ acre= 37500000\ gallons\)

Convert to acre: Multiply by 2867200

\(2867200 * 1\ acre= 37500000\ gallons * 2867200\)

\(2867200\ acres= 107520000000000\ gallons\)

By comparison:

\(18000000000000\ gallons < 107520000000000\ gallons\)

i.e. the volume of water in the bay is less than the capacity of the oysters. Hence, there are enough oysters.

Answer:

To ensure that you have grabbed 250 balls of one color, you need to use the Pigeonhole Principle. The worst-case scenario is that you grab 249 balls of each color, totaling 996 balls. Therefore, the smallest amount of balls you need to grab is 997, which guarantees that you have grabbed 250 balls of one color.

To explain further, let's consider the worst-case scenario where you grab 249 red balls, 249 green balls, 249 blue balls, and 249 yellow balls. This totals to 996 balls. However, if you grab just one more ball, you will have a total of 997 balls, and since there are only four colors, at least one color will have 250 balls or more. Therefore, by grabbing 997 balls, you can be sure that you have grabbed at least 250 balls of one color.

Answer:

997

Step-by-step explanation:

I multiplied 249 by 4 first. This is because I wanted to find how many balls the person could grab in total without having 250 of the same color.

249*4= 996

However, the question wants to guarantee that one color has 250.

So I did 996+1=997. (which means there could be: 249 red, 249 yellow, 249 green, and 250 blue)

This means that every other color could be at 249, but one would guarantee to be at 250 with 997 pulls

Answer:

who's Whitney? And im gonna say 47

Step-by-step explanation:

Answer: I think 43 If it is whitner bulger you actually talking about.

Step-by-step explanation:

Answer:

Yes, sin (z) = 3/5

No,  sin (x) = 4/5

No, cos (z) = 4/5

Yes, cos (x) = 3/5

Step-by-step explanation:

sin (z) = 21/35 = 3/5

sin (x) = 28/35 = 4/5

cos (z) = 28/35 = 4/5

cos (x) = 21/35 = 3/5

Answer:

A. x = 4

I hope this helps!

Answer

put 1 on top and exo on bottom

Step-by-step explanation:

Answer:

cos 60° = 1/2

Step-by-step explanation:

\( \sin( \alpha ) = \cos(90 - \alpha ) \)

\( \sin(30) = \cos(90 - 30) \\ \sin(30) = \cos(60) \)

Answer:

528 cookies

Step-by-step explanation:

3 hours is 180 minutes

55 minutes - the 15 for preheating is 40 minutes

180 minutes + 40 minutes = 220 (total time she could've had cookies in the oven)

220 divided by 20 is 11 (total batches of cookies)

11 times 48 is 528

Sorry if my answer is confusing lol

The total number of cookies that Amy baked is 528 cookies.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

To solve this problem, we need to convert the total time the oven was on (3 hours and 55 minutes) into minutes.

Since there are 60 minutes in an hour, the total time the oven was on in minutes is : 3 hours x 60 minutes/hour + 55 minutes = 235 minutes.

We need to subtract the time the oven was preheating (15 minutes) from the total time the oven was on to get the time that was spent baking cookies. This gives us a total of 235 minutes - 15 minutes = 220 minutes of baking time.

Since each batch of cookies takes 20 minutes to bake, the number of batches of cookies that Amy baked is :

220 minutes / 20 minutes/batch = 11 batches.

Since each batch contains 48 cookies,

So, the total number of cookies that Amy baked is :

11 batches × 48 cookies/batch = 528 cookies.

Thus, Amy baked 528 cookies overall altogether.

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Answer:

6 gallons of gasoline

Step-by-step explanation:

1 gallon = 24 miles

you need to get 144 miles

144 divided by 24 = 6

there fore you need 6 gallons

hope it helps

The person that has the higher average speed is Teresa.

Average speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.

Therefore, Karl drove 40 miles in 50 minutes and Teresa drove 35 miles in 42 minutes.

The person that has the higher average speed can be calculated as follows;

average speed of Karl = distance / time

average speed of Karl = 40 / 50

average speed of Karl = 4 / 5 miles per minutes

average speed of Teresa = distance / time

average speed of Teresa = 35 / 42

average speed of Teresa = 5 / 6 miles per minutes

Therefore, Teresa had the higher average speed.

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Explanation

We are given the following:

We are required to determine the exact value of sin 2Θ.

We know that the trigonometric identity for sin 2Θ is thus:

Since Θ is between 180° and 270° as given above, we know that this angle falls in the third quadrant, and sine and cosine are negative in this quadrant.

Therefore, we have:

Now, we can determine the value of sin 2Θ as:

Hence, the answer is:

Answer:

Step-by-step explanation:

Slope is 2

solve into Ax+by=C

Y-y1=m(x-x1)

Y-(-4) = 2(x - (-5))

Y+4=2x+10

Y-2x =6

(0,6)

(-3,0)

Assuming there are only 6 seats in that row.

Case 1 : The father is sitting in neither of both ends.

-> There are only 3 possible seats left for the mother, as she cannot sit to either of the seats next to the father.

-> There are 4 x 3 x 4 x 3 x 2 x 1 = 288 possible ways.

Case 2 : The father is sitting at one end.

-> There are 4 possible seats for the mother (because there is only 1 seat next to the father).

-> There are 2 x 4 x 4 x 3 x 2 x 1 = 192 possible ways.

Altogether, there are 480 possible ways to arrange the family.

If the answer is wrong, please comment because I'm not too confident about this answer to be honest.

There are 480 ways in which this family of 6 can be seated in a row while the father and mother are not sitting together.

We will find the number of arrangements when the father and mother are sitting together (say N), then subtract it from the total number of arrangements.

Now, let us find the total number of arrangements

Total no. of arrangements = 6!

                                           = 720

Now, find the number of arrangements when the father and mother are sitting together. As father and mother are together, treat them as a single person. Now, there are 5 people.

A number of arrangements = 5! =120

but, father and mother can also change their places in 2 ways = 2!

So, N = 120 * 2 = 240

Subtract N from total arrangements, 720-240 = 480.

Therefore, the answer is 480.

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Answer:

13.1148770486

.....................,...

The Z score for the proportion of consumers who purchased milk chocolate, given a sample of 97 individuals where 52% purchased milk chocolate, is approximately -3.87.

To calculate the Z score, we need to compare the observed proportion (52%) with the expected proportion (79%) and account for the sample size. The formula for calculating the Z score for proportions is: Z = (p - P) / sqrt((P * (1 - P)) / n), where p is the observed proportion, P is the expected proportion, and n is the sample size.

Substituting the given values into the formula, we have: Z = (0.52 - 0.79) / sqrt((0.79 * (1 - 0.79)) / 97). Simplifying the equation further, we get: Z = (-0.27) / sqrt(0.1621 / 97).

Calculating the expression inside the square root, we have sqrt(0.1621 / 97) ≈ 0.040. Substituting this value back into the equation, we find: Z ≈ (-0.27) / 0.040 ≈ -6.75.

Rounding the Z score to two decimal places, we get approximately -3.87.

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Answer:B D

Step-by-step explanation:

I just got it right

Step-by-step explanation:

To dilate the figure by a factor of 2, I will multiply the x and y-value of each point by 2. I plotted all the new points to find the new triangle. To dilate the figure by a factor of 2, I will multiply the x-value of each point by 2.

Answer:

6y+4

Step-by-step explanation:

(−y^2+y+2)−(y^2−5y−2)

=-y^2+y+2-y^2+5y+2

=6y+4

Answer:

1/4

Step-by-step explanation:

Answer:

15/60 simplified equals:

1/4

Step-by-step explanation:

In the fraction 15/60, 15 is the numerator and 60 is the denominator.

When you ask "What is 15/60 simplified?", we assume you want to know how to simplify the numerator and denominator to their smallest values, while still keeping the same value of the fraction.

We do this by first finding the greatest common factor of 15 and 60, which is 15.

Then, we divide both 15 and 60 by the greatest common factor to get the following simplified fraction:

1/4

The solution is, 52 ft is the perimeter of the base of the pyramid.

Here, we have,

Given that:

We have an pyramid with square base.

Area of base of the square pyramid = 169

To find:

Perimeter of the base of pyramid = ?

Solution:

First of all, let us have a look at the formula of area of a square shape.

Area = side * side

Let the side be equal to  ft.

Putting the given values in the formula:

169 = a^2

so, a = 13 ft

Now, let us have a look at the formula for perimeter of square.

Perimeter of a square shape = 4  Side

Perimeter = 4 * 13 = 52ft

The solution is, 52 ft is the perimeter of the base of the pyramid.

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complete question:

A pyramid has a square base with an area of 169 ft2. What is the perimeter of the base of the pyramid? A pyramid has a square base with an area of 169 ft2. What is the perimeter of the base of the pyramid?

The maximum value of B is 80.

1. We are given the expression B = 5xy² and the constraint x + y² = 8.

2. We need to find the maximum value of B by optimizing the variables x and y.

3. To solve this problem, we can use the method of Lagrange multipliers.

4. Let's define the Lagrange function L(x, y, λ) as L(x, y, λ) = B - λ(x + y² - 8).

5. Taking the partial derivatives of L concerning x, y, and λ, we have:

  ∂L/∂x = 5y² - λ

  ∂L/∂y = 10xy - 2λy

  ∂L/∂λ = -(x + y² - 8)

6. Setting the partial derivatives equal to zero, we get the following equations:

  5y² - λ = 0    ...(1)

  10xy - 2λy = 0  ...(2)

  x + y² = 8     ...(3)

7. From equation (1), we can solve for λ in terms of y:

  λ = 5y²    ...(4)

8. Substituting equation (4) into equation (2), we have:

  10xy - 2(5y²)y = 0

  10xy - 10y³ = 0

  10y(x - y²) = 0

9. From the above equation, we have two possibilities:

  i) 10y = 0, which implies y = 0.

  ii) x - y² = 0, which implies x = y².

10. If y = 0, then from equation (3), we get x = 8.

11. If x = y², then substituting this into equation (3), we have:

   y² + y² = 8

   2y² = 8

   y² = 4

   y = ±2

   If y = 2, then x = (2)² = 4.

   If y = -2, then x = (-2)² = 4.

12. We have three potential solutions: (x, y) = (8, 0), (4, 2), and (4, -2).

13. Finally, substitute each of these solutions into the expression B = 5xy² and find the maximum value of B:

   B = 5(8)(0)² = 0

   B = 5(4)(2)² = 80

   B = 5(4)(-2)² = 80

14. Therefore, the maximum value of B is 80.

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Answer:

b

Step-by-step explanation:

because basically and so therefore yeah

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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Answer:

Bottom two

Step-by-step explanation:

The shapes that are rectangles are the two blue shapes on the right-hand side in the image attached.

A rectangle is a plane figure that comprises four side sides and it also has four right angles. The opposite sides of a rectangular shape are usually equal.

From the given image, the shapes that exhibit the rectangular shapes are the second and the fourth blue shapes which can be seen on the right-hand side in the image attached.

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