5x - 3x - 3 - 8 = 2x + 8 - 8

Minimizing the Sum of Squared Deviations

In statistics, the objective of many analyses is to identify the values of parameters that minimize the sum of squared deviations between observed and expected values. A common example of this is finding the mean (average) of a set of values. In this context, the deviations are calculated as the difference between each observed value and the mean.

In the problem stated above, we have a sum of squared deviations given by the expression (x_1 - c)^2. The goal is to find the value of c that minimizes this expression. To do this, we will take the derivative of the expression with respect to c, set it equal to 0, and solve for c.

Taking the derivative with respect to c:

The derivative of (x_1 - c)^2 with respect to c is 2 * (x_1 - c) * (-1) = 2 * (c - x_1). Setting this equal to 0 and solving for c:

2 * (c - x_1) = 0

c = x_1

So, the value of c that minimizes the expression (x_1 - c)^2 is equal to x_1.

Comparing Sum(x_i - mu)^2 and Sum(x_i - x_1)^2:

Now, let's consider the two quantities Sum(x_i - mu)^2 and Sum(x_i - x_1)^2. Assuming that mu is the population mean and x_1 is a sample mean, we can say that Sum(x_i - mu)^2 will always be equal to or larger than Sum(x_i - x_1)^2. This is because the sample mean is an unbiased estimator of the population mean and has a smaller variance than the population mean. In other words, the sample mean will be closer to the observed values, on average, than the population mean, leading to smaller deviations and a smaller sum of squared deviations.

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From the information given, it is found that the value of the test statistic is z = -11.97.

At the null hypothesis, it is tested if the proportion is of at least 95%, that is:

\(H_0: p \geq 0.95\)

At the alternative hypothesis, it is tested if the proportion is of less than 95%< that is:

\(H_1: p < 0.95\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}\)

In which:

\(\overline{p}\) is the sample proportion.

p is the value tested at the null hypothesis.

n is the sample size.

In this problem, we have that the parameters are:

\(\overline{p} = 0.87, p = 0.95, n = 1063\).

Thus, the value of the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}\)

\(z = \frac{0.87 - 0.95}{\sqrt{\frac{0.95(0.05)}{1063}}}\)

\(z = -11.97\)

The value of the test statistic is z = -11.97.

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The range in which 95% of the scores lie is between 75 and 95.

According to the Empirical Rule: For a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% of the data falls within 2 standard deviations of the mean, and approximately 99.7% of the data falls within 3 standard deviations of the mean.

So, about 95% of the scores lie between 75 and 95. T

This is because the mean score is 85 and one standard deviation is 5, so one standard deviation below the mean is 80 (85-5) and one standard deviation above the mean is 90 (85+5).

Two standard deviations below the mean are 75 (85-2*5) and two standard deviations above the mean is 95 (85+2*5).

Therefore, the range in which 95% of the scores lie is between 75 and 95.

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Answer: Slope = 2; 3-intercept=-1

Step-by-step explanation:

Answer:

\(y-14=3(x-4)\)

Step-by-step explanation:

Point slope form: \(y-y_1=m(x-x_1)\) when the given point is \((x_1,y_1)\)

Now, we can just plug in the given values (plug in m and the point coordinates).

\(y-y_1=m(x-x_1)\\y-14=3(x-4)\)

I hope this helps!

We can conclude that the triangle with sides 5, 13, and 15 is not a right triangle.

To determine whether the given triangle with sides 5, 13, and 15 is a right triangle or not, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the longest side (hypotenuse).

That is, if a, b, and c are the lengths of the sides of a triangle, with c being the longest side, then:

a² + b² = c²

In this case, we have:

5² + 13² = 25 + 169 = 194

15² = 225

Since 194 is not equal to 225, we can conclude that the triangle with sides 5, 13, and 15 is not a right triangle. Therefore, the angle opposite the longest side (15) is not a right angle (90 degrees).

We can also use the fact that in a right triangle, the longest side (hypotenuse) is always the side opposite the right angle. Therefore, if we can determine that no angle in the triangle is a right angle, we can conclude that it is not a right triangle. In this case, we can use the Law of Cosines to determine the measures of the angles in the triangle:

cos(A) = (b² + c² - a²) / (2bc)

cos(B) = (a² + c² - b²) / (2ac)

cos(C) = (a² + b² - c²) / (2ab)

Using the side lengths 5, 13, and 15, we get:

cos(A) = (13² + 12² - 5²) / (21315) = 0.767

cos(B) = (5² + 15² - 13²) / (2515) = 0.866

cos(C) = (5² + 13² - 15²) / (2513) = 0.258

None of these values is equal to zero, so none of the angles is a right angle. Therefore, we can conclude that the triangle with sides 5, 13, and 15 is not a right triangle.

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Answer: THE ANSWER IS -205

Step-by-step explanation:

IF IT IS ALREADY 462 FEET BELOW SURFACE, AND IT CLIMBS UP 257 FEET, IT IS STILL UNDER WATER. THE ANSWER WOULD BE NEGATIVE SINCE BELOW SURFACE IS NEGATIVE AND ABOVE SURFACE IS POSITIVE. SO THE EQUATION IS -462+257. MEANING THE ANSWER IS -205.

Mean: to find the mean you add all the data and then divide into the number of data.

number of data: 8

Median: to find the meadian order the data from least to greather and then select the middle data (as the total of data is 8 you select the two data in the middle and calculate the average)

Data ordered:

Middle data: 11 and 11:

Mode: To find the mode you look for the data that repeat the most.

Range: To find the range of a data set you substract from the greatest value the least value:

Greatest value: 17

Least value: 6

To find the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing with 50 people, follow these steps:

1. Since winning more than one prize is allowed, the probability of Bo winning the first prize is 1/50.

2. Likewise, the probability of Colleen winning the second prize is also 1/50.

3. Similarly, the probability of Jeff winning the third prize is 1/50.

4. Finally, the probability of Rohini winning the fourth prize is 1/50.

5. Since these events are independent, we can multiply the probabilities together to find the overall probability of this specific  :

  Probability = (1/50) * (1/50) * (1/50) * (1/50)

6. Calculate the result:

  Probability ≈ 0.00000016

7. Round the answer to two decimal places:

  Probability ≈ 0.00

So, the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing with 50 people is approximately 0.00.

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Answer:

Area = 6.2 yards²

Step-by-step explanation:

area = bh

area = 2(3.1)

Answer:

6.2

Step-by-step explanation:

2x3.1=6.2

Answer:

Cost for 25 songs: $23.50

Cost for s songs: .50(s) + 11

Step-by-step explanation:

To solve this problem, we can make an equation in slope-intercept form:

y = mx + b

y represents the total amount of $.

m represents the cost of each song downloaded, or $.50

x represents the number of songs, or 's'

b represents the $11, or the constant.

We have the equation:

y = .50(x) + 11

If Angel downloaded 25 songs, we have the equation:

y = .50(25) + 11

We get y = $23.50

Hope this helps!

Answer:

Im not sure but dont pick d

Step-by-step explanation:

Whoever says d r wrong

Answer: its D

Step-by-step explanation: it d

The person can make 60 trips.

Let us say that A indicates the major sea Islands and B indicates the major lakes. Taking both the cases as events, we will use multiplication principle. Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.

Thus, A × B = 5 × 12

Performing multiplication on Right Hand Side of the equation to find the number of trips

Total number of trips = 60

Hence, there are 60 trips that could be made.

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Answer:

n ≤ 4

Step-by-step explanation:

Which means you should start at four (make sure it's a close circle) pointing to the left. I hope it helps.

Answer:

8784/61

144#

Mark as a brainlist

Answer:

144

Step-by-step explanation:

i did it

Answer

The equation of our line is y = 8x - 3

Explanation

The slope-intercept form of writing the equation of the straight line is given as

y = mx + c

where

y = y-coordinate of any point on the line

m = slope of the line

x = x-coordinate of the point on the line whose y-coordinate is y.

c = y-intercept of the line; the value of y when x = 0.

To write this equation, we first compute the slope of the line

The slope of a line with two points on the line with the coordinates (x₁, y₁) and (x₂, y₂) given is calculated as

For this question,

(x₁, y₁) and (x₂, y₂) is (1/2, 1) and (1, 5)

y₂ = 5

y₁ = 1

x₂ = 1

x₁ = (1/2) = 0.5

So, the slope of this line = 8

The equation of the line is then

y = 8x + c

We can now solve for the y-intercept by taking any of the two points given

Using (1, 5), x = 1, y = 5

y = 8x + c

5 = 8(1) + c

5 = 8 + c

c = 5 - 8 = -3

Hence, the equation of our line is y = 8x - 3

Hope this Helps!!!

The surface area of a cylinder is found using the following formula:

Replace for the given values of radius and height:

It means that the surface area of the cylinder is 622.

The correct answer is D. 622 sq units.

Answer:

x = -1.434, x = -0.232

Step-by-step explanation:

The mean commuting time for the particular train, assuming a uniform distribution between 20 and 50 minutes, is 35 minutes. This means that, on average, commuters can expect their commuting time to be around 35 minutes.

To calculate the mean commuting time, we need to find the average value of the uniformly distributed commuting time between 20 and 50 minutes.

In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. Since the distribution is uniform between 20 and 50 minutes, the PDF is constant over that interval.

The mean of a uniform distribution can be calculated using the formula:

Mean = (a + b) / 2

where 'a' is the lower limit of the distribution (20 minutes) and 'b' is the upper limit (50 minutes).

Plugging in the values into the formula, we get:

Mean = (20 + 50) / 2 = 70 / 2 = 35 minutes

The calculation is straightforward because in a uniform distribution, the mean is simply the average of the minimum and maximum values of the distribution.

In this case, the commuting time is equally likely to be any value between 20 and 50 minutes. So, on average, commuters can expect a mean commuting time of 35 minutes.

It is important to note that the mean represents the average value and may not necessarily reflect the most frequently occurring commuting time. In this case, there is an equal likelihood of any time within the given range.

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Answer:

Two figures that have the same shape are said to be similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles below are similar, compare their corresponding sides.

The figures P, R, and S are similar to figure Q because the similar figures have the same shape but not the same size.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

It is given that:

Emily draws figures P, Q, R, and S. The center of dilation is point Z.

It is claimed that two figures are comparable if they share the same shape. The ratios of the lengths of the corresponding sides are equal when the two figures are comparable.

The similar figures P, R, and S are comparable to figure Q since they share the same shape but differ in size.

Thus, the figures P, R, and S are similar to figure Q because the similar figures have the same shape but not the same size.

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Answer:

13x + 14

Step-by-step explanation:

5x + 6 + 3x = 8x + 6.

8x + 6 + x + 1 + x + 1 + 2= 10x + 10

10x + 10 + (2²)(i think) = 10x + 14

10x + 14 + 3x = 13x + 14

final answer

Answer:

\(13x+14\)

Step-by-step explanation:

First take all the sides and add:

\(5x+6+3x+3x+2+2+2+x+1+x+1\)

Then Combine Like terms:

\(5x+3x+3x+x+x+6+2+2+2+1+1\)

There is your answer:

\(13x+14\)

(If I misunderstood the handwriting, please tell me, and I will fix my mistakes)

The required answer is  the strip of sheet metal 13 31 inches long.

To determine how many pieces 15/16 inch long can be cut from a strip of sheet metal 13 31 inches long, follow these steps:
1. Convert the mixed number 13 31 inches to an improper fraction:
  (13 * 32) + 31 = 447 inches

2. Divide the total length of the strip (447 inches) by the length of each piece (15/16 inches):
  447 inches ÷ (15/16 inches) = 447/1 * 16/15 = (447 * 16) / 15
We need to first convert the length of the sheet metal to the same unit as the length of the pieces we want to cut. Since both are in inches, we can proceed with the calculation. To calculate the number of pieces that can be cut, we need to divide the length of the sheet metal by the length of each piece.
3. Perform the multiplication and division:
  (447 * 16) = 7152
  7152 ÷ 15 ≈ 476.8

Since you can't have a fraction of a piece, you can only cut 476 whole pieces of 15/16 inch long from the strip of sheet metal 13 31 inches long.

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You get a pie chart to do percentages just so you dont cheat you still can do work y'know

Example of an undecidable problem is given by the problems in the system created by computer viruses.

According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.

A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.

whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.

If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.

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Answer:

12

Step-by-step explanation:

Looking for LCM of 4 2 and 3    <==== this is 12

To find all subgame perfect Nash equilibria (SPNE), we need to analyze each decision node in the game tree and determine the best response for each player at that node.

Starting from the final round (bottom of the tree) and working our way up:

At the node labeled "N", Player 1 has two options: "H" and "S". Player 2 has only one option: "h". The payoffs associated with each combination of choices are as follows:

(H, h): Player 1 gets a payoff of 3, Player 2 gets a payoff of 0.

(S, h): Player 1 gets a payoff of 2, Player 2 gets a payoff of 3.

Since Player 1's payoff is higher when choosing "H" rather than "S" and Player 2's payoff is higher when choosing "h" rather than "H", the subgame perfect Nash equilibrium for this node is (H, h).

Moving up to the next round, we have a decision node labeled "a". Player 1 has two options: "C" and "T". Player 2 has only one option: "h". The payoffs associated with each combination of choices are as follows:

(C, h): Player 1 gets a payoff of 4, Player 2 gets a payoff of 0.

(T, h): Player 1 gets a payoff of 5, Player 2 gets a payoff of 5.

Since Player 1's payoff is higher when choosing "T" rather than "C" and Player 2's payoff is higher when choosing "h" rather than "C", the subgame perfect Nash equilibrium for this node is (T, h).

Finally, at the topmost decision node labeled "S", Player 1 has only one option: "S". Player 2 has two options: "C" and "T". The payoffs associated with each combination of choices are as follows:

(S, C): Player 1 gets a payoff of 0, Player 2 gets a payoff of 2.

(S, T): Player 1 gets a payoff of 3, Player 2 gets a payoff of 3.

Since Player 1's payoff is higher when choosing "S" rather than "N" and Player 2's payoff is higher when choosing "C" rather than "T", the subgame perfect Nash equilibrium for this node is (S, C).

In summary, the subgame perfect Nash equilibria for this game are (H, h), (T, h), and (S, C).

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Answer:

63

Step-by-step explanation:
Do 180-90.
then ad 34+53.

The answer is 63.

Answer: cos 810 = 0

Step-by-step explanation:

Keep Subtracting 360 until you get your reference angle.  You can also look at the image and know that it will be 90°

810 -360 = 450

450 - 360 = 90

At 90°, use unit circle, your x is cos and your y is sin

cos 90 = 0

cos 810 = 0

Answer:

They make 200 pieces of caramel candies a day and 500 pieces of chocolate candies a day.

Step-by-step explanation:

Since the ratio is two to five, make it 2x + 5x = 700.

7x = 700

x=100

So, for caramel candies, 2 x 100 = 200

For chocolate candies, 5 x 100 = 500