Given a sample, {x 1
​
,x 2
​
,…,x n
​
}, from a Gaussian distributed random variable X with mean μ X
​
, variance σ X
2
​
, and is not random; please answer the following questions. (a) What is the sampling distribution of sample observation x 2
​
? (b) What is the sampling distribution of sample observation x 5
​
? (c) What is the sampling distribution of sample mean x
ˉ
n
​
=∑ i=1
n
​
x i
​
/n ? (d) What is the sampling distribution of sample variance s X
2
​
=∑ i=1
n
​
(x i
​
− x
ˉ
n
​
) 2
/(n−1) ? (e) What is the sampling distribution of (n−1)s X
2
​
/σ X
2
​
? (f) What is the sampling distribution of x
ˉ
n
​
as the sample size n is large enough?

Answer:

226.2 in³ and 452.4 in³

Step-by-step explanation:

Volume of original shape:

Volume = base area x height
Volume = πr² x 2
Volume = π(6)² x 2
Volume = 113.10 x 2
Volume = 226.2 in³

Volume with same radius but double the height:

Volume = base area x height
Volume =  πr² x 2(2) ----------> multiplied by 2 because height is being doubled
Volume = 113.10 x 4
Volume = 452.4 in³

Answer: The answer is StartFraction 1 over 10,000 EndFraction.

Step-by-step explanation: There are 10 possible digits that can be used for each of the four positions in the access code, so there are 10 x 10 x 10 x 10 = 10,000 possible access codes.

There is only one way to have the access code "1234" out of the 10,000 possible access codes.

Therefore, the probability of having an access code "1234" is 1/10,000.

So the answer is StartFraction 1 over 10,000 EndFraction.

Answer:

Step-by-step explanation:

lets take the top part as 1 and the seconds part as 2

so for the first part

1 Area= L*B

so 8*5 =40

2 Area=L*B

so 11*4=44

44+40=84cm2

Plug in the values of x and solve for y:-

y=5+4x

y=5+4(4)

y=5+16

y=21

________________________________

y=5+4x

y=5+5(5)

y=5+20

y=25

_________________________________

y=5+4x

y=5+4(8)

y=5+32

y=37

___________________________________

y=5+4x

y=5+4(10)

y=5+40

y=45

__________________________________

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

see explanation

Step-by-step explanation:

substitute the values of x from the table into the rule and evaluate for y

x = 4 → y = 5 + 4(4) = 5 + 16 = 21

x = 5 → y = 5 + 4(5) = 5 + 20 = 25

x = 8 → y = 5 + 4(8) = 5 + 32 = 37

x = 10 → y = 5 + 4(10) = 5 + 40 = 45

then

     x   y

    --------

    4   21

    5   27

    8   37

   10   45

Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

Carla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.

Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.

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In this case, the monthly payment for the car loan would be approximately $1,299.13.

To calculate the monthly payment for a bank loan using Excel, you can use the PMT function.

Here's how to do it:

1. Open Excel and create a new spreadsheet.

2. In cell A1, enter the loan amount: -40000 (negative because it's an outgoing payment).

3. In cell A2, enter the annual interest rate: 9%.

4. In cell A3, enter the loan duration in years: 3.

5. In cell A4, enter the formula to calculate the monthly payment: =PMT(A2/12, A3*12, A1).

6. The result in cell A4 will be the monthly payment.

So, in this case, the monthly payment for the car loan would be approximately $1,299.13.

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Answer:

25/6

Step-by-step explanation:

I multiplied 4/3 by 2, so the new fraction is 8/6. You add 17/6 with 8/6, and you get 25/6. I hope you understand.

Answer:

VX = 8.8 in

Step-by-step explanation:

By applying Sine rule in the right triangle WXV,

Sin(∠W) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

             = \(\frac{\text{VX}}{\text{WX}}\)

Sin(34)° = \(\frac{VX}{15}\)

VX = 15.Sin(34)°

     = 8.8379

     ≈ 8.8 in.

Therefore, measure of side VX is 8.8 in.

Answer:

x = 49

Step-by-step explanation:

the figure inside the circle is a cyclic quadrilateral.

the opposite vertices of a cyclic quadrilateral sum to 180° , then

x + 68 + 63 = 180

x + 131 = 180 ( subtract 131 from both sides )

x = 49

Answer:

  6

Step-by-step explanation:

You want to know the number of uphill integers divisible by 15, where an uphill integer is one that has its digits strictly increasing.

An integer will be divisible by 15 if and only if it is divisible by 3 and 5. An integer is divisible by 5 if it ends in 5 or 0. An uphill integer cannot end in 0, so must end in 5.

An integer is divisible by 3 if the sum of its digits is divisible by 3

An uphill integer will have differences between successive digits that are positive integers. In order for the final digit to be 5, the sum of these differences must be 5. Hence we can find uphill integers by considering the "integer partitions" of 5: the sets of positive integers whose total is 5. Those sets would be ...

  {5}, {4, 1}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}

Uphill integers will also have digit differences that are some permutation of each of these sets. For example, the digit differences may be {4, 1} or {1, 4}, corresponding to the numbers 45 or 15.

The uphill integers that end in 5 are ...

  5, 45, 15, 35, 25, 345, 145, 125, 245, 235, 135, 2345, 1345, 1245, 1235, 12345

We already know each of these is divisible by 5. The ones that have a digit total that is a multiple of 3 are ...

  15, 45, 135, 345, 1245, 12345

There are 6 uphill integers divisible by 15.

The points A(2, -1, 4), B(3, 1, 2), C(0, 5, 6), and D(-1, 3, 8) form a parallelogram. The area of the given parallelogram is 12 square units.  It is not a rectangle.

To verify if the given points form a parallelogram, we need to check if both pairs of opposite sides are parallel.

The vectors formed by the sides AB and CD are AB = (1, 2, -2) and CD = (-1, -2, 2). The vectors formed by the sides BC and AD are BC = (-3, 4, -4) and AD = (-3, 4, -4).

Comparing these vectors, we can see that AB and CD are parallel, as are BC and AD. This indicates that the given points A, B, C, and D form a parallelogram.

To find the area of the parallelogram, we can use the cross product of the vectors AB and AD (or BC and CD) to find the area of the corresponding parallelogram. The magnitude of the cross product of AB and AD is |AB × AD| = 12.

Since the area of a parallelogram is equal to the magnitude of the cross product of its adjacent sides, the area of the given parallelogram is 12 square units.

To determine if the parallelogram is a rectangle, we can check if any of its angles are right angles. However, since the given points do not have any indication of angles, we cannot determine if the parallelogram is a rectangle based on the information provided.

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Answer:

1x27

3x9

Comment me below if I need to have each possible factor.

Step-by-step explanation:

A enclose numerators and denominators in parentheses.  f(x)=x 2+4x and g(x)=1−x² is fg(x) = x² - x⁴ + 4x - 4x³ ,gf(x) = x² - x⁴ + 4x - 4x²

To find the values of (f+g)(x), (f-g)(x), fg(x), and gf(x), the respective operations on the given functions f(x) and g(x).

Given:

f(x) = x² + 4x

g(x) = 1 - x²

(f+g)(x):

To find (f+g)(x), the two functions f(x) and g(x):

(f+g)(x) = f(x) + g(x) = (x² + 4x) + (1 - x²)

= x² + 4x + 1 - x²

= (x² - x²) + 4x + 1

= 4x + 1

Therefore, (f+g)(x) = 4x + 1.

(f-g)(x):

To find (f-g)(x), subtract the function g(x) from f(x):

(f-g)(x) = f(x) - g(x) = (x² + 4x) - (1 - x²)

= x² + 4x - 1 + x²

= (x² + x²) + 4x - 1

= 2x² + 4x - 1

Therefore, (f-g)(x) = 2x² + 4x - 1.

fg(x):

fg(x), multiply the two functions f(x) and g(x):

fg(x) = f(x) × g(x) = (x² + 4x) × (1 - x²)

= x² - x⁴ + 4x - 4x³

Therefore, fg(x) = x² - x⁴ + 4x - 4x³.

gf(x):

gf(x), multiply the two functions g(x) and f(x):

gf(x) = g(x) × f(x) = (1 - x²) × (x² + 4x)

= x² - x⁴ + 4x - 4x³

Therefore, gf(x) = x² - x⁴ + 4x - 4x³.

\((f+g)(x) = 4x + 1\\\\(f-g)(x) = 2x^2 + 4x - 1\\\\fg(x) = x^2 - x^4 + 4x - 4x^3\\\\gf(x) = x^2 - x^4 + 4x - 4x^3\\\)

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The combination that best describes the process is Cp = 1 and Cpk = 1, as it indicates that the process has the potential capability to meet the specification limits and is centered within the limits.

We have,

To determine which combination of Cp and Cpk values best describes a process, we need to understand the definitions and interpretations of Cp and Cpk.

Cp is a capability index that measures the potential capability of a process to meet the specification limits.

It compares the spread of the process variation to the width of the specification range.

A Cp value of 1 indicates that the process spread is equal to the specification width, while values greater than 1 indicate that the process spread is smaller than the specification width, indicating a more capable process.

Cpk, on the other hand, is a capability index that considers both the process spread and the process centering relative to the specification limits. It measures the actual capability of the process to meet the specification limits.

A Cpk value of 1 indicates that the process is centered within the specification limits and meets the requirements, while values less than 1 indicate that the process is not centered or does not meet the requirements.

Given the options provided:

Cp = 0.75 and Cpk = 0.75:

Both Cp and Cpk are less than 1, indicating that the process is not capable of meeting the specification limits.

This combination does not best describe the process.

Cp = 1 and Cpk = 1:

Both Cp and Cpk are equal to 1, indicating that the process has the potential capability to meet the specification limits and is centered within the limits.

This combination represents an acceptable level of process capability.

Cp = 1.5 and Cpk = 2.0:

Cp is greater than 1.5, indicating a smaller process spread compared to the specification width. Cpk is greater than 1, indicating that the process is centered within the limits and meets the requirements.

This combination represents a highly capable process.

Cp = 1 and Cpk = 0.5:

Cp is equal to 1, indicating that the process has the potential capability to meet the specification limits.

However, Cpk is less than 1, indicating that the process is not centered within the limits and does not meet the requirements.

This combination does not best describe the process.

Cp = 1.5 and Cpk = 0.5:

Cp is greater than 1.5, indicating a smaller process spread compared to the specification width.

However, Cpk is less than 1, indicating that the process is not centered within the limits and does not meet the requirements.

This combination does not best describe the process.

Thus,

The combination that best describes the process is Cp = 1 and Cpk = 1, as it indicates that the process has the potential capability to meet the specification limits and is centered within the limits.

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The system of 5x + 2y ≤ 25 is given by 20x + 15y ≤ 120 and 5x + 2y ≤ 25

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the cucumber and y represent the amount of carrots, hence:

20x + 15y = 2(60)

20x + 15y ≤ 120  (1)

Also:

5x + 2y ≤ 25 (2)

The system of 5x + 2y ≤ 25 is given by 20x + 15y ≤ 120 and 5x + 2y ≤ 25

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Answer:

0.7

Step-by-step explanation:

Answer:

x^2+11x+30

Step-by-step explanation:

If the distribution of observations were perfectly symmetrical and unimodal, option B) The mean, median, and mode would be the same.

In a perfectly symmetrical and unimodal distribution, the mean, median, and mode would be equal. This is because in such a distribution, the data would be evenly spread around a central value. The mean is calculated by summing all the observations and dividing by the total number of observations. Since the distribution is symmetrical, the sum of the observations on one side of the central value would be equal to the sum on the other side, resulting in a balanced mean.

The median is the middle value when the observations are arranged in ascending or descending order. In a symmetrical distribution, the middle value would be the same as the central value, leading to the median being equal to the mean.

The mode represents the value that appears most frequently in the distribution. In a perfectly symmetrical and unimodal distribution, all values would occur with the same frequency, resulting in multiple modes. However, since the distribution is unimodal, meaning it has only one peak, all the modes would coincide, and the mode would also be equal to the mean and median. Therefore, in a perfectly symmetrical and unimodal distribution, the mean, median, and mode would all be the same value, leading to answer B) The mean, median, and mode would be the same.

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Answer:

a^2 + b^2 = c^2...a and b are the legs and c is the hypotenuse

90^2 + 120^2 = c^2

8100 + 14400 = c^2

22500 = c^2.....take the sq rt of both sides...this gets rid of the ^2

sq rt 22500 = c

150 = c

so side a = 90 ft, side b = 120 ft, and side c = 150 ft

this is called the pythagorean theorem and it only works on right triangles

Step-by-step explanation:

done sorry if im wrong

Answer:

142.5cm2 if it's correct I would appreciciate a brainliest

Step-by-step explanation:

15x19=285

285/2=142.5

Answer:

142.5

Step-by-step explanation:

19 x 15 = 285

285 / 2 = 142.5

formula for area of triangle is A = height (straight line from the base to the tip, not the length of one of the sides) x length of base / 2 ( A= hb/2)

Answer:

f(x) = 4x + 11x2 - 104x + 105  =  (x - 3)(x + 7)(4x - 5)

Step-by-step explanation:

f(x) = 4x^3 + 11x2 - 104x + 105

has the coefficients {4, 11 -104, 105}.  We perform synthetic division using the given -7 as divisor:

-7   /   4      11     -104     105

                -28     119     -105

     -----------------------------------

          4      -17      15         0

Since the remainder is zero (0), we have shown that -7 is a zero of f(x).  The coefficients of the quotient (above) are {4, -17, 15}.  Let's try factoring the corresponding polynomial again using synthetic division.  Start out by using 5 as divisor and determining whether or not the remaindeer is zero:

5    /     4     -17      15

                    20     15

     -------------------------

             4        3     30           No, the remainder is 30 and so 5 is not a

                                               root of this quadratic.  Try the divisor 3 instead:

3     /     4      -17      15

                      12      -15

      ---------------------------

             4       -5        0        Yes, the remainder is 0 and so 3 is a root.

Thus, the given f(x) = 4x + 11x2 - 104x + 105 factors as follows:

f(x) = 4x + 11x2 - 104x + 105  =  (x - 3)(x + 7)(4x - 5).  Notice that the coefficients of the last factor come from those we found above when using 3 as a divisor in synthetic division.  

Answer:

The independent variable in Pedro's experiment is the winds ( its presence and absence)

Step-by-step explanation:

The independent variable is the variable whose values do not depend on the values of another variable. It is also known as the input variable.

In the case study, the independent variable in Pedro's experiment is the winds ( its presence and absence)

Answer:

5 more adults than students have phones.

Step-by-step explanation:

55% of 80 students have phones. This is:

.55 × 80, which is 44 students.

For adults, 98% of 50 is .98 × 50, which is 49.

49 adults have phones. 44 students have phones.

49 - 44 is 5

5 more adults have phones than students.

Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

Answer:

the answer is

X + 40 + 155 =180

Answer:

Please find attached sketch of the path of the ball, having plot area and plot points, created with MS Excel

Step-by-step explanation:

Question;

The equation representing the path of the ball obtained from a similar question posted online are;

h₁ = -4·(t + 1)·(t - 5), h₂ = -4·(t - 2)² + 36, h₃ = -4··t² + 16·t + 20

The above equations represent the same path

The equation, h₁ = -4·(t + 1)·(t - 5), gives the roots of the height function, h(t), used in determining the height of the ball after time t

At (t + 1) = 0 (t = -1) or at (t - 5) = 0 (t = 5), the ball is at ground level

The ball reaches the ground, is at ground level at t = 1, and at t = 5 seconds after being tossed, where h(t) = 0

The equation of the path of the ball in vertex form, y = a·(x - 2)² + k, is h₂ = -4·(t - 2)² + 36, where, by comparison, we have;

The vertex of the ball = The maximum height reached by the ball  = (h, k) = (2, 36)

The coefficient of the quadratic term, t², is negative, therefore, the shape of the parabola is upside down, ∩, shape

The sketch of the path of the ball created with MS Excel, used in plotting the vertex, the initial value and the root points of the parabola, through which the ball passes and joining of the points with a 'smooth' curve is attached

Answer:

48 pizzas

60 pizzas

72 pizzas

Step-by-step explanation:

So pretty straight forward

So first you divide the amount of cheese by 3

so for the first one you have 18 pounds of cheese

Now 18/3=6

Now using that quotient (6) you multiply that by 8

6*8=48

So 18 pounds of cheese is 48 pizzas

Same thing with the others, even with the decimal one

Answer:

8/13 cups of sugar

Step-by-step explanation:

Jamal is baking 4 batches of chocolate chip cookies. He needs 2 13 cups of sugar for each batch. Which expression could be used to determine the total amount of sugar that Jamal needs?

For the above question

1 batch of chocolate chips cookies = 2/13 cups of sugar

4 batches = x

Cross Multiply

x = 4 × 2/13 cups of sugar

x = 8/13 cups of sugar

There are 5 ways that the sum of the dice be equal to 6 if a pair of distinct dice are rolled one time

It is the ordered arrangement of members belonging to a set with no repeats.

Analyzing the possibilities for the sum of the dice be equal to 6, assuming that each die has six sides:

Red die = 6 sides

Blue die = 6 sides

The possibilists are:

(Bleu, red)

(1,5)

(2,4)

(3,3)

(4,2)

(5,1)

There are 5 ways to get at sum of 6 if a pair of distinct dice are rolled one time

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