Which numbers are divisible by 5?

1: 124, 333, 315, 266, 391
2: 135, 205, 330, 275, 365
3:135, 211, 330, 274, 252
4:232, 250, 365, 225, 210​

The first rider the displacement is, 17 km.

And the 2nd river the displacement is 20.22 km.

What is right triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

It is asked in this problem is who's displacement is greater (not distance) it means that the shortest distance of starting and ending point with direction from start and end.

Here we have two triangle with two arm know for both.

So we have to find the 3rd arm for both triangle.

Now we have for a right triangle

a^2 + b^2 = c^2

For other triangle we know the cosine law of triangle is,

a^2 + b^2 - 2ab cosθ = c^2

θ is the opposite angle of c

For the first rider the displacement is,

c = \(c = \sqrt{a^2 + b^2} = \sqrt{8^2 + 15^2} = 17 km\\\)

For the 2nd river the displacement is

\(c = \sqrt{a^2-b^2 -2abcosheta}\),  θ = 120°

\(c = \sqrt{8^2 + 15^2 - 2ab cos(120)} \\c = \sqrt{289 - 240cos(120)} \\c = \sqrt{289 - (-120)} \\c = \sqrt{289 + 120}\\ c = \sqrt{409} \\c = 20.22km\)

Hence, the first rider the displacement is, 17 km.

And  the 2nd river the displacement is 20.22 km.

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Answer:

(1,4.5)

(\(\frac{5+(-3)}{2} ,\frac{3+6}{2}\))

The point forecasts and conditional variances computed above, we have 95% interval forecast for [13.22, 17.18]

To compute point forecasts for each of the next 3 days' temperature, we use the formula Yt+h|t = Wt+h|t + â(Yt − Wt|t), where Yt+h|t is the point forecast for temperature h days ahead given information up to time t, Wt+h|t is the unconditional forecast, Yt is the temperature at time t, and â is the estimated coefficient.

Using yesterday's temperature of 92 degrees as Yt, we have:

Yt+1|t = Wt+1|t + â(Yt − Wt|t) = 4 + 0.4(92 − 76) = 15.2

Yt+2|t = Wt+2|t + â(Yt+1|t − Wt+1|t) = 4 + 0.4(15.2 − 76) = -16.32

Yt+3|t = Wt+3|t + â(Yt+2|t − Wt+2|t) = 4 + 0.4(-16.32 − 15.2) = -17.72

Therefore, the point forecasts for each of the next 3 days' temperature are 15.2, -16.32, and -17.728 degrees Fahrenheit.

To compute point forecasts for each of the next 3 days' conditional variance, we use the formula Var(Yt+h|t) = W + â2 Var(Yt+h-1|t), where Var(Yt+h|t) is the conditional variance of temperature h days ahead given information up to time t, W is the unconditional variance, â is the estimated coefficient, and Var(Yt+h-1|t) is the conditional variance of temperature h-1 days ahead given information up to time t.

Using the given values of W = 1 and â = 0.4, we have:

Var(Yt+1|t) = 1 + 0.4^2 Var(Yt|t) = 1 + 0.4^2 (0.01) = 1.0016

Var(Yt+2|t) = 1 + 0.4^2 Var(Yt+1|t) = 1 + 0.4^2 (1.0016) = 1.00064

Var(Yt+3|t) = 1 + 0.4^2 Var(Yt+2|t) = 1 + 0.4^2 (1.00064) = 1.000256

Therefore, the point forecasts for each of the next 3 days' conditional variance are 1.0016, 1.00064, and 1.000256.

To compute the 95% interval forecast for each of the next 3 days' temperature, we use the formula Yt+h|t ± zα/2 σt+h|t, where zα/2 is the 95% critical value of the standard normal distribution, σt+h|t is the square root of the conditional variance of temperature h days ahead given information up to time t, and Yt+h|t is the point forecast for temperature h days ahead given information up to time t.

Using the given values of z0.025 = 1.96 and the point forecasts and conditional variances computed above, we have:

95% interval forecast for Yt+1|t: 15.2 ± 1.96(1.0016) = [13.22, 17.18]

95%

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A. The point forecasts for each of the next 3 days' temperature are: Day 1: Y₁ = 4, Day 2: Y₂ = 4 + 0.05 x E₁, and Day 3: Y₃ = 4 + (-0.03) x E₂

B. Var(Y₁) = 1 + 0.4 x 76 x 76, Var(Y₂) = 1 + 0.4 x Y₁ x Y₁, and Var(Y₃) = 1 + 0.4 x Y₂ x Y₂

(a) To compute point forecasts for each of the next 3 days' temperature, use the given model:

Yt = 4 + Et x Et-1

Et ~ N(0, 0.01)

Given that yesterday's temperature was 92 degrees, use this as the starting point for the forecast.

For today (Day 1):

Y₁ = 4 + E₁ x E₀

Since E₀ is not given, assume it to be zero (as the previous day's error term is not availiable). Therefore, Y₁ = 4 + E₁ x 0 = 4.

For tomorrow (Day 2):

Y₂ = 4 + E₂ x E₁

To compute E₂, use the fact that Et follows a normal distribution with mean 0 and variance 0.01. Therefore, E₂ ~ N(0, 0.01), and sample a value from this distribution. Assuming E₂ = 0.05. Then, Y₂ = 4 + 0.05 x E₁.

For the day after tomorrow (Day 3):

Y₃ = 4 + E₃ x E₂

Similarly, sample E₃ from the normal distribution: E₃ ~ N(0, 0.01). Supposing we get E₃ = -0.03. Then, Y₃ = 4 + (-0.03) × E₂.

So, the point forecasts for each of the next 3 days' temperature are:

Day 1: Y₁ = 4

Day 2: Y₂ = 4 + 0.05 x E₁

Day 3: Y₃ = 4 + (-0.03) x E₂

(b) To compute point forecasts for each of the next 3 days' conditional variance, use the formula:

Var(Yt) = w + a x Yt-1 x Yt-1

Given that w = 1, a = 0.4, and h = 76 (mean temperature):

Var(Y₁) = 1 + 0.4 x 76 x 76

Var(Y₂) = 1 + 0.4 x Y₁ x Y₁

Var(Y₃) = 1 + 0.4 x Y₂ x Y₂

(c) To compute the 95% interval forecast for each of the next 3 days' temperature, apply the formula:

Yt ± 1.96 x √(Var(Yt))

Using the point forecasts and conditional variances from parts (a) and (b), calculate the interval forecasts.

For Day 1, Y₁ = 4:

Interval forecast: 4 ± 1.96 × √(Var(Y₁))

For Day 2, Y₂ = 4 + 0.05 × E₁:

Interval forecast: Y₂ ± 1.96 × √(Var(Y₂))

For Day 3, Y₃ = 4 + (-0.03) × E₂:

Interval forecast: Y₃ ± 1.96 × √(Var(Y₃))

(d) Regarding predicting the next spell of bad weather, the given model is specifically focused on forecasting temperature volatility rather than explicitly identifying bad weather spells. The model's purpose is to estimate the variability of temperature, not classify it as good or bad weather.

While it can provide forecasts of temperature volatility, it may not be able to accurately predict whether the upcoming period will be considered "bad weather" based on guests' preferences or activity popularity. Additional factors and models may be necessary to assess and predict such conditions accurately.

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Answer: 10

Step-by-step explanation:

if x=-5

y= |-5-5| + |-5 + 5|    add what's inside the absolute values first

y=|-10|            absolute value means just take the positive of what's inside, even if its' positive

y=10

Step-by-step explanation:

y = |x-5|+|x+5| when x = -5

y = |(-5)-5|+|(-5)+5|

y = |-10|+|0| note: |x| = positive

y = 10

Answer:

y=10x+150

Step-by-step explanation:

Answer:

y = 1x-5

Step-by-step explanation:

We know two points so we can find the slope

(0,-5) and (5,0)

m = ( y2-y1)/(x2-x1)

   = ( 0 - -5)/(5-0)

   (0+5)/(5-0)

    5/5

=1

We know the y intercept = -5

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 1x-5

Solution of exponential equation is , x =  \(800. 7^4\)

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as  \(a^x\) .

where, a = the base of function

           x = main expression

Mathematically, if  \(log_aN = x\) is an logarithmic function then, this can be converted to exponential function as  \(a^x = N\).

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

Some important formulas of exponential :

According to given statement,

\(7^{-4} x = 800\)

=> \(\frac{1}{7^4} x = 800\)

=> \(x = 800 . 7^4\)

Thus solution for this equation is x =  \(800. 7^4\)

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The complete question is :

What is the solution of each exponential equation? Check your answer.

a. 7⁻⁴x=800

b. 5.2³x=400

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

A. 34,900

Good Luck!!

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ 

Answer:

A) 34,900

Step-by-step explanation:

When rounding to the nearest hundred, look at the TENS DIGIT of the number.

If that digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

brainliest please

Using Scientific notation, the expression (6.1 * 10⁴) + (5.2 * 10⁴) can be written as;  11.3 * 10⁴

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 750,000,000 can be written in scientific notation as 7.5 × 10⁸.

Now, we want to use scientific notation to simplify;

(6.1 * 10⁴) + (5.2 * 10⁴)

Using distributive property of equality, we can say that the expression can be broken down as;

10⁴(6.1 + 5.2)

= 11.3 * 10⁴

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Answer:

5th term = 2*1st term + 3*2nd term

Step-by-step explanation:

z₁ : 1st term, z₂ : 2nd term

z₃ = z₁ + z₂

z₄ = z₃ + z₂ = z₁ + 2*z₂

z₅ = z₄ + z₃ = (z₁ + 2*z₂) + (z₁ + z₂) = 2*z₁ + 3*z₂

The probability of the second die landing on any number is 1/6. This is because there are six possible outcomes on a fair die (1, 2, 3, 4, 5, 6) and each outcome is equally likely. Therefore, the probability of the second die landing on any given number is 1/6.

To calculate the probability of the second die landing on a specific number, you can use the formula P(A) = number of favorable outcomes / number of possible outcomes. In this case, the number of favorable outcomes is 1 (since there is only one number that you want the second die to land on) and the number of possible outcomes is 6 (since there are six possible numbers that the second die can land on). Therefore, the probability of the second die landing on a specific number is 1/6.

In conclusion, the probability of the second die landing on any number is 1/6 and the probability of the second die landing on a specific number is also 1/6.

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Answer:

no

Step-by-step explanation:

Proportional must go through (0,0)

0 = 2(0) +7

0 = 7

This is not true so this is not proportional

Answer:

2.5x

Step-by-step explanation:

Given information for width:

Model: 10 in.

Real: 25 in.

Solve: How much times wider is real than model?

To find this, lets divide 25in. by 10in to find the scale factor.

25/10 = 2.5

2.5

We can verify this by multiplying 10 by 2.5

10 x 2.5 = 25

Answer:

\(\sqrt{74}\) units

Step-by-step explanation:

Hi there!

We can use the Pythagorean theorem to solve this question:

\(a^2+b^2=c^2\) where a and b are the two legs and c is the hypotenuse

Plug in the two legs 5 and 7 and solve for c, the hypotenuse:

\(5^2+7^2=c^2\\25+49=c^2\\74=c^2\\c=\sqrt{74}\)

Therefore, the length of the hypotenuse in radical form is \(\sqrt{74}\) units.

I hope this helps!

Answer:

1/5 is biggest fraction

Step-by-step explanation:

1/5 = 0.2

1/10 =0.1

⅕ > ⅒

The biggest fraction in between 1/5 and 1/10 is 1/5.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

We have the fractions:

1/5 and 1/10.

To find the biggest fraction:

Here, 1 is the numerator in both of the fractions.

So, 10 and 5 are the denominators.

And 5 < 10

That means, 1 is separated in 5 parts and 10 parts.

1/5 = 0.2

And 1/10 = 0.1

0.2 > 0.1

Therefore, the fraction 1/5 is bigger than 1/10.

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Answer:

\(\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}\)

Step-by-step explanation:

Setting the expression equal to zero to find the roots,

\(3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-\frac{2}{3}\\\\x=\pm i\sqrt{\frac{2}{3}}\)

This means that

\(3x^2 +2=\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}\)

Answer: x=17

Step-by-step explanation:

Simplifying

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

The value of x in the equation is 17 .

Given,

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

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In order to understand the relationships among the complexity classes of these functions, we can categorize them based on their growth rates. Here's a categorization of the given functions:

1. Constant time complexity: 10, 1
2. Logarithmic time complexity: logn, ln n, log(log n)
3. Polynomial time complexity:
  - Linear time complexity: nlogn, n1/k (k > 3)
  - Quadratic time complexity: n2
  - Cubic time complexity: n3
  - Sublinear time complexity: n1/2, n1/3, n1/2 logn, n1/3 logn
4. Exponential time complexity: 2n, 3n
5. Higher-degree polynomial time complexity: nk (k > 3)
6. Super-exponential time complexity: nn
7. Factorial time complexity: n!

These categories are arranged in increasing order of complexity, meaning that functions in higher categories have higher growth rates and belong to more complex complexity classes than those in lower categories.

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Tom's pencil is longer than Ellen's pencil with (3x+10)cm

Subtraction is one of the four arithmetic operation along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 minus 2 peaches, this means that 5 peaches with 2 taken away, resulting in a total of 3 peaches.

Ellen's pencils length = 2x+15

Tom's pencil length = 5x+25

Tom's pencil will be longer than Ellen's with;

(5x + 25 ) - (2x+15)

= 5x + 25 -2x - 15

collect like terms

5x -2x +25-15

3x +10

therefore Tom's pencil is longer than Ellen's pencil with ( 3x+10) cm

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Answer:

A = $ 7,299.92

A = P + I where

P (principal) = $ 6,000.00

I (interest) = $ 1,299.92

Step-by-step explanation:

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Answer: In summary, all integers can be classified as either positive, negative, or zero.

Step-by-step explanation:

There are three types of integers: positive integers, negative integers, and zero.

Positive integers: Positive integers are numbers greater than zero, such as 1, 2, 3, 4, and so on.

Negative integers: Negative integers are numbers less than zero, such as -1, -2, -3, -4, and so on.

Zero: Zero is an integer that is neither positive nor negative. It is the only integer that is neither positive nor negative, and it is often referred to as the "origin" on a number line.

In summary, all integers can be classified as either positive, negative, or zero.

Answer: The three types of integers are Zero (Neutral Integers), Negative Integers, and Positive Integers.

Step-by-step explanation:

Negative Integers are the ones that has a value less than zero, examples of these are -7, -8, -9.

Positive integers, on the other hand. Are the ones that has a value more than zero, examples of these are 10, 11, 12, 13.

Note: The key difference between Negative Integers and Positive Integers is that a negative integer has a "-" sign, while a positive integer does not.

Zero are the neutral integers which means that it's the integer that's in the middle of the positive and negative integers, it has neither a positive sign or a negative sign.

Another note: Integers do not include fractions or decimals, only whole numbers.

Answer:

C

Step-by-step explanation:

\(\angle A + \angle D = 180\)

\(\angle A + y = 180\)

\(180 = 75 + y\)

\(y = 180 - 75 = 105\)

i) The probability that an observation is considered as having a galaxy cluster is 0.34.ii) The probability that an observation with log-intensity measurement greater than 3 units is from a galaxy cluster is 0.10.

i) Calculation of the probability that an observation is considered as having a galaxy cluster:Let Z denote the measured log-intensity. Then the probability that a patch contains a galaxy cluster can be calculated by using Bayes’ rule:P(Z < c|cluster) = 0.02 and P(Z < c|no cluster) = 0.01where c is a number that satisfies the two conditions.Using the given data, we can find the value of c as:c = μcluster + 2σcluster = 10 + 2×3 = 16

So, the probability that a patch contains a galaxy cluster is:P(cluster|Z < 16) = P(Z < 16|cluster) P(cluster) / [P(Z < 16|cluster) P(cluster) + P(Z < 16|no cluster) P(no cluster)]P(cluster|Z < 16) = 0.02 × 0.01 / (0.02 × 0.01 + 0.01 × 0.99)P(cluster|Z < 16) = 0.3358 ≈ 0.34ii) Calculation of the probability that an observation with log-intensity measurement greater than 3 units is from a galaxy cluster:

Let A denote the event that an observation is from a galaxy cluster and B denote the event that the log-intensity measurement is greater than 3 units. Then, the probability that an observation with log-intensity measurement greater than 3 units is from a galaxy cluster is:P(A|B) = P(B|A) P(A) / [P(B|A) P(A) + P(B|A') P(A')]

We need to calculate P(B|A) and P(B|A').The given distributions imply that if the observation is from a galaxy cluster, then the log-intensity follows a normal distribution with mean 10 and standard deviation 3. So, we have:P(B|A) = P(Z > 3|cluster)where Z ∼ N(10, 3)P(B|A) = P(Z < 3|cluster) using the symmetry of the normal distribution

P(B|A) = P(Z < -3|cluster) because of the symmetry of the normal distributionP(B|A) = Φ(-3 - 10/3) where Φ denotes the standard normal cumulative distribution functionP(B|A) = Φ(-13/3)P(B|A) = 0.0026Similarly, if the observation is not from a galaxy cluster, then the log-intensity follows a normal distribution with mean 1 and standard deviation 1. So, we have:

P(B|A') = P(Z > 3|no cluster)where Z ∼ N(1, 1)P(B|A') = P(Z > 2) using standardizing and Z ∼ N(0, 1)P(B|A') = Φ(-2)P(B|A') = 0.0228Hence, we can use the above formula to get:P(A|B) = 0.0026 × 0.01 / (0.0026 × 0.01 + 0.0228 × 0.99)P(A|B) = 0.1008 ≈ 0.10Therefore, the probability that an observation with log-intensity measurement greater than 3 units is from a galaxy cluster is 0.10.

Therefore, the solution to the problem is summarized below:i) The probability that an observation is considered as having a galaxy cluster is 0.34.ii) The probability that an observation with log-intensity measurement greater than 3 units is from a galaxy cluster is 0.10.

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Answer:

12/100*133= 15.96

approx 16oz

Answer:

D

Step-by-step explanation:

5 (x + 6) = 45

Multiply 5 by what's in parenthesis.

5 times x = 5x ** use the + sign ** 5 times 6 = 30

5x + 30 = 45

The equation that is equivalent to  5x + 30 = 45 is 5(x + 6) = 45.

The option that would be equivalent to the value of x in the equation. The first step is to determine the value of x.

5x + 30 = 45

Combine similar terms

5x = 45 - 30

5x = 15

Divide both sides by 5

x = 3

Option A

35x = 45

In order to determine the value of x, divide both sides by 35

x = 45 / 35  = 1.3

Option B

5x = 75

In order to determine the value of x, divide both sides by 5

x = 75/5 = 15

Option C

5(x + 30) = 45

Divide both sides of the equation by 5

x + 30 = 9

Combine similar terms

x = - 30 + 9

x = -21

Option D

5(x + 6) = 45

Divide both sides of the equation by 5

x + 6 = 45 / 5

x + 6 = 9

Combine similar terms

x = 9 - 6

x = 3

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Answer:

m = 1/2

Step-by-step explanation:

\(m = \frac{ - 2 - ( - 3)}{0 - ( -2)} = \frac{1}{2} \)

The value of E(x- μ) for the population for any given data is always equal to option b. 0.

Sum of squared deviations,

ss = 100

variance, σ² = 4

The value of E(x - μ) for the population can be determined .

Using the relationship between the sum of squared deviations (ss) and the variance (σ²).

ss = n × σ²

where ss is the sum of squared deviations,

σ² is the variance,

and n is the population size.

Substituting these values into the equation, solve for n,

⇒ 100 = n × 4

⇒ n = 100 / 4

⇒ n = 25

The expected value (E) of (x - μ) for the population is zero.

This means that on average, the difference between each data point (x) and the population mean (μ) is zero.

Therefore, the value of the expected operator E(x- μ) for the population is equal to option b. 0

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The above question is incomplete, the complete question is:

A population has sum of squared deviations, ss = 100 and variance, σ² = 4. What is the value of E(x- μ) for the population?

a. 400

b. 0

c. 10

d. 25

Answer:

0

Step-by-step explanation:

All the numbers equal each other out.

for example:

-6+6=0

so if you have -6+-5+-4+-3+-2+-1+0+1+2+3+4+5+6, all of the numbers equal each other out.

Hope this helps!