Let X be a random variable that is distributed Hypergeometrically (17, 8, 7). Determine the probability distribution of the random variable Z = (3 - X)^2

The half range  Fourier sine and Fourier cosine expansions of f is equal to 0 and constant term a₀/2 which is f(x) = (1/2π) (\(e^{\pi }\) - 1) .

Fourier cosine series of f at endpoints at x = 0 and x =π and sum of resultant infinite series is given by f(0) = (1/2π) (\(e^{\pi }\) - 1) and f(π) = (1/2π) (\(e^{\pi }\) - 1) .

Function f(x) = eˣ

over the interval 0 < x < π,

To find the half-range Fourier sine and Fourier cosine expansions,

Determine the Fourier coefficients and the corresponding series expressions.

Fourier Sine Expansion.

The Fourier sine series for f(x) can be expressed as,

f(x) = ∑[n=1 to ∞] bn sin(nx),

To find the Fourier coefficients bn, use the formula.

bn = (2/π) \(\int_{0} ^{\pi }\)f(x) sin(nx) dx

Let us calculate the Fourier coefficients bn,

bn = (2/π) \(\int_{0} ^{\pi }\) eˣ sin(nx) dx

Since f(x) = eˣ is an odd function and sin(nx) is also an odd function, the integrand eˣ sin(nx) is even.

Hence, the integral from 0 to π of an even function is zero.

Therefore, all the Fourier coefficients bn will be zero for the Fourier sine expansion.

So, the Fourier sine expansion of f(x) is simply 0.

Fourier Cosine Expansion,

The Fourier cosine series for f(x) can be expressed as,

f(x) = a₀/2 + ∑[n=1 to ∞] an cos(nx)

To find the Fourier coefficients an, we can use the formula,

an = (2/π) \(\int_{0} ^{\pi }\)f(x) cos(nx) dx

Let us calculate the Fourier coefficients an,

a₀/2 = (1/π) \(\int_{0} ^{\pi }\)f(x) dx

= (1/π) \(\int_{0} ^{\pi }\)eˣ dx

= (1/π) [eˣ] [0 to π]

= (1/π) (\(e^{\pi }\)- e⁰)

= (1/π) (\(e^{\pi }\) - 1)

an = (2/π) \(\int_{0}^{\pi }\)f(x) cos(nx) dx

= (2/π)\(\int_{0}^{\pi }\) eˣ cos(nx) dx

To evaluate this integral, integrate by parts.

u = eˣ, dv = cos(nx) dx.

du = eˣ dx, v = (1/n) sin(nx)

Using the integration by parts formula,

∫ u dv = uv - ∫ v du

an = (2/π) [(eˣ / n) sin(nx)] [0 to π] - (2/π) (1/n) \(\int_{0}^{\pi }\)eˣ sin(nx) dx

The first term in the above expression evaluates to zero because sin(nπ) = 0 for all integer values of n.

an = - (2/π) (1/n) \(\int_{0}^{\pi }\)eˣ sin(nx) dx

The integral \(\int_{0}^{\pi }\) eˣ sin(nx) dx is zero,

so the Fourier coefficients an will also be zero for the Fourier cosine expansion.

So, the Fourier cosine expansion of f(x) is simply the constant term a₀/2.

f(x) = (1/2π) (\(e^{\pi }\) - 1)

Since both the Fourier sine and Fourier cosine expansions of f(x) are zero,

evaluating the Fourier cosine series at the endpoints x = 0 and x = π will give us the sum of the resultant infinite series.

At x = 0,

f(0) = (1/2π) (\(e^{\pi }\) - 1)

At x = π,

f(π) = (1/2π) (\(e^{\pi }\) - 1)

Therefore, the half range  Fourier sine and Fourier cosine expansions of f is 0 and constant term f(x) = (1/2π) (\(e^{\pi }\) - 1) .

Fourier cosine series of f at the endpoints and the sum of resultant infinite series is equal to f(0) = (1/2π) (\(e^{\pi }\) - 1) and f(π) = (1/2π) (\(e^{\pi }\) - 1) .

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The given function is,

The graph of the g(x) will be shifted 3 units upward with respect to the parent function f(x),

Thus, the above figure is the graph of g(x).

There are 64000 distinct combinations .

The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.

The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.

How many possible three-number combinations are there?

You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.

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Adjacent angles in parallelograms are supplementary angles thus :

\(x + 130 = 180\)

\(x = 180 - 130\)

\(x = 50\)

The process of adding the matrix is explained blow.

Matrices are powerful tools used to analyze data and solve complex equations.

A 3x3 matrix, or E₁₃, is a matrix composed of 3 rows and 3 columns. It can be used to perform various operations, including adding two rows together.

(a) To answer the first question, a 3x3 matrix E₁₃ can add row 3 to row 1 by performing a row operation. This involves taking the second row and adding it to the first, thus adding the values on each row together.

(b) To answer the second question, a 3x3 matrix E₁₃ can add row 1 to row 3 and at the same time add row 3 to row 1 by performing a row exchange operation. This results in a 3x3 matrix where each value in the first row is equal to the corresponding value in the third row.

(c) To answer the third question, a 3x3 matrix E₁₃ can add row 1 to row 3 and then add row 3 to row 1 by performing two separate row operation and then taking the third row and adding it to the first, thus adding the values of each row together again.

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Answer:

55042

Step-by-step explanation:

Answer:

55042

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

It's the first one, a statement. :)

Answer:

the answer is 1. A statement that is author presents as true in order to support his or her position

The floor area of the engineer's model of the sugar factory is 10.825 square feet.

To determine the floor area of the engineer's model of a sugar factory in square feet, we need to convert the given measurements from inches to feet. Since there are 12 inches in a foot, we can divide both dimensions by 12 to convert them.

The length of the model in feet is 30 inches / 12 = 2.5 feet, and the width is 52 inches / 12 = 4.33 feet.

To find the floor area, we multiply the length by the width:

Area = Length × Width

= 2.5 feet × 4.33 feet

= 10.825 square feet

It's important to note that the given measurements are not a standard aspect ratio or scale for a sugar factory. The given dimensions may be scaled down for the model's convenience, so the calculated floor area is only applicable to the scale of the model.

In actuality, a sugar factory would have much larger dimensions.

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Answer:

combine like terms 6x &-9x =-3x and 2. & -6 = -4 3÷4= 0.75 x= 0.75

Answer:

the answer has to be ac+ad+bc+bd

Step-by-step explanation:

First, let's define what we mean by a collision-resistant hash function. A hash function is collision-resistant if it's hard to find two different inputs that produce the same output. In other words, if we have a hash function h(x) and two inputs a and b such that a ≠ b, it should be difficult to find a value c such that h(a) = h(b) = c.

Now let's look at the hash function h(x) = 5x + 11 mod 19. To show that this hash function is not strongly collision-resistant, we need to find two different inputs that produce the same output.

Here's one way to do that:

Start by picking two different values for x, let's say x = 2 and x = 7.

Plug each value of x into the hash function h(x) = 5x + 11 mod 19 to get the hash values:

h(2) = 5(2) + 11 mod 19 = 10 + 11 mod 19 = 1

h(7) = 5(7) + 11 mod 19 = 35 + 11 mod 19 = 8

As you can see, h(2) = 1 and h(7) = 8, which are not the same. However, if we add a multiple of 19 to each hash value, we can find two inputs that produce the same output:

h(2) + 19 = 1 + 19 = 20 = 8 mod 19

h(7) + 19 = 8 + 19 = 27 = 8 mod 19

So we have found a collision: h(2) + 19 = h(7) + 19 = 8 mod 19.

This shows that the hash function h(x) = 5x + 11 mod 19 is not strongly collision-resistant, since we were able to find two different inputs that produced the same output relatively easily. A strong hash function should make it very difficult to find such collisions.

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The present value of Mark's prize, considering the $10,000 annual payments for 10 years and the subsequent $20,000 annual payments for 30 years, with an 8% discount rate, amounts to $171,391.44.

To calculate the present value of Mark's prize, we need to determine the current worth of the future cash flows he will receive. The $10,000 annual payments for 10 years can be considered an annuity, while the subsequent $20,000 annual payments for 30 years can be viewed as a perpetuity starting from the 11th year.

First, we calculate the present value of the annuity using the formula for the present value of an ordinary annuity:

PV_annuity = \(C * [1 - (1 + r)^(-n)] / r\),

where PV_annuity is the present value of the annuity, C is the annual cash flow, r is the discount rate, and n is the number of years. Plugging in the values, we have:

PV_annuity = $10,000\(* [1 - (1 + 0.08)^(-10)] / 0.08\) = $85,394.45.

Next, we calculate the present value of the perpetuity using the formula for the present value of a perpetuity:

PV_perpetuity = C / r,

where PV_perpetuity is the present value of the perpetuity. Plugging in the values, we have:

PV_perpetuity = $20,000 / 0.08 = $250,000.

Finally, we sum up the present values of the annuity and the perpetuity to obtain the total present value:

Total present value = PV_annuity + PV_perpetuity = $85,394.45 + $250,000 = $335,394.45.

Therefore, with an 8% discount rate, the present value of Mark's prize is $171,391.44.

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Answer:

Step-by-step explanation:

B. 4.35miles

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Answer:

put 4 okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

Step-by-step explanation:

Step-by-step explanation:

∫x1/4 dx   =   1/8 x^2   + c        where c is a constant of some value

To calculate a three-month moving average for monthly forecasting, you need to follow these steps: Gather the historical data, Determine the time period, Calculate the moving average, Repeat the process.

Gather the historical data: Collect the monthly data for the specific variable you want to forecast. For example, if you want to forecast sales, gather the sales data for the past several months.

Determine the time period: Decide on the time period for your moving average. In this case, it is three months.

Calculate the moving average: Add up the values for the variable you are analyzing over the past three months and divide the sum by three to get the average. This will be your moving average value for the third month.

Repeat the process: Shift the time period by one month and calculate the moving average for the new three-month period. Continue this process for each subsequent month, updating the time period and calculating the moving average accordingly.

For example, let's say you have the following sales data for the past six months:

Month 1: 100 units

Month 2: 120 units

Month 3: 110 units

Month 4: 130 units

Month 5: 140 units

Month 6: 150 units

To calculate the three-month moving average for Month 4, you would add up the sales values for Month 2, Month 3, and Month 4 (120 + 110 + 130 = 360) and divide it by three to get an average of 120 units. Repeat this process for each subsequent month to obtain the moving average values for your forecast.

Note that the number of data points you include in the moving average calculation and the frequency of the data (monthly in this case) can be adjusted based on your specific needs and the nature of the data.

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Answer:

2

to find the slope you get the rise which is the difference between the y coordinates over the run which is the difference between the x coordinates. so 6/3=2

Answer:

The first one has a slope of 4

The second one has a slope of 0.3 repeating

Step-by-step explanation:

You pick two points on the graph.

You find the x and y coordinates of each point.

You find the difference between the two x coordinates.

You find the difference between the two y coordinates.

Divide the difference in the y coordinates by the x coordinates.

If im wrong sorry owo im only in elementary school... <3

Answer:

4/6

Step-by-step explanation:

Answer:

slope = - 9 , y- intercept = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2 - 9x , or

y = - 9x + 2 ← in slope- intercept form

with slope m = - 9 and y- intercept c = 2

Answer:

g^8

Step-by-step explanation:

The "." means multiplication. Therefore take g as common.

But, for the powers its different.  

When constants are being multiplied, the powers will be added together:

g^5 x g^3

=g^ 5+3

=g^8

If the constants were being added then the powers would hv been multiplied: g^5 + g^3

= g^5 x 3

=g^15

Similarly, if the constants were being divided then the powers would hv been substracted: g^5/g^3

=g^5-3

=g^2

And if the constants were being substracted the the powers would hv been divided: g^5 - g^3

=g^5/3

So, therefore ur answer is g^8.

Hope u understood :D

Answer:

40%

Step-by-step explanation:

add both numbers together to get the total amount of guests

170 + 255 = 425

divide the number of guests who called for room service by the total guests

170 ÷ 425 = 0.4

convert the decimal to a percentage

0.4 = 40%

Answer:

We can write 360 distinct passwords using the numbers 1, 2, 3, 4, 5, and 6.

Step-by-step explanation:

We have to find how many passwords with 4 different digits can we write with the numbers 1, 2, 3, 4, 5, and 6.

Firstly, it must be known here that to calculate the above situation we have to use Permutation and not combination because here the order of the numbers in a password matter.

Since we are given six numbers (1, 2, 3, 4, 5, and 6) and have to make 4 different digits passwords.

So, the number of passwords with 4 different digits we can write = \(6 \times 5 \times 4 \times 3\)  = 360 possibilities.

Hence, we can write 360 distinct passwords using the numbers 1, 2, 3, 4, 5, and 6.

Answer:

T(3, 8)

Step-by-step explanation:

Yes, it can.

Use the midpoint formula with points S and Z, and solve for point T.

M( (x_1 + x_2)/2 , (y_1 + y_2)/2 )

Z(3, 5) = ( (3 + x)/2 , (2 + y)/2 )

(3 + x)/2 = 3

3 + x = 6

x = 3

(2 + y)/2 = 5

2 + y = 10

y = 8

T(3, 8)

Answer:

f(x)= -10cos(3x)+10

Step-by-step explanation:

I hope this is right !

Answer:

B

Step-by-step explanation:

If you make a straight line it would go through the origin and have a constant rate

Using the definition of divisibility, 2p is the greatest common factor.

In the given question we have to factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.

The given polynomial is 2p^3+6p.

Now taking 2p common from both terms

=2(p^2+3)

By the definition of divisibility, we get

2p | 2p^3 and 2p|6p, 2| 2p^3 and 2|6p also p|2p^3 and p|6p.

So, 2,p and 2p are common factors of 2p^3 and 6p.

Hence, 2p is the greatest common factor.

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The right answer is:

Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.

2p^3+6p

The researcher should obtain a sample size of at least 670 adults to estimate the percentage of adults who support abolishing the penny with a 3 percentage point margin of error and 99% confidence.

To determine the sample size needed for estimating the percentage of adults who support abolishing the penny with a margin of error within 3 percentage points and 99% confidence, we can use the formula:

\[ n = \frac{{Z^2 \cdot p \cdot (1-p)}}{{E^2}} \]

Where:

- \( n \) represents the sample size

- \( Z \) is the Z-score corresponding to the desired confidence level (99% confidence corresponds to a Z-score of approximately 2.576)

- \( p \) is the estimated proportion (we don't have an estimate yet, so we will assume 50% for a conservative estimate)

- \( E \) is the margin of error (3 percentage points)

Plugging in the values, we get:

\[ n = \frac{{2.576^2 \cdot 0.5 \cdot (1-0.5)}}{{0.03^2}} \]

Simplifying this equation gives us:

\[ n = 669.33 \]

Since we can't have a fraction of a person, we round up to the nearest whole number.Therefore, the researcher should obtain a sample size of at least 670 adults to estimate the percentage of adults who support abolishing the penny with a 3 percentage point margin of error and 99% confidence.

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The a sample size of approximately 1067 adults should be obtained to estimate the percentage of adults who support abolishing the penny with a 99% confidence level and a margin of error within 3 percentage points.

To estimate the percentage of adults who support abolishing the penny with a 99% confidence level and a margin of error within 3 percentage points, we need to determine the required sample size.

To calculate the sample size, we use the formula:

n = (Z^2 * p * (1-p)) / E^2

Where:
- n is the required sample size
- Z is the Z-value corresponding to the desired confidence level (in this case, 99% confidence level)
- p is the estimated proportion (percentage) of adults who support abolishing the penny
- E is the desired margin of error (in this case, 3 percentage points)

Since we don't have an estimated proportion (p) from previous studies or surveys, we can use 0.5 (50%) as an approximate value, which maximizes the sample size.

Using a Z-value of 2.58 (for a 99% confidence level), a desired margin of error of 3 percentage points, and an estimated proportion of 0.5, we can calculate the required sample size:

n = (2.58^2 * 0.5 * (1-0.5)) / 0.03^2
n ≈ 1066.67

Therefore, a sample size of approximately 1067 adults should be obtained to estimate the percentage of adults who support abolishing the penny with a 99% confidence level and a margin of error within 3 percentage points.

Note: It is important to consider that the sample size may vary depending on the specific context and the assumptions made. Additionally, the calculation assumes a simple random sample and other statistical assumptions that need to be met for accurate estimation.

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Answer:

x = -7

Step-by-step explanation:

We are looking for the x value when f(x) = -3. From the table, we see that when f(x) = -3, x = -7. Therefore, our answer is the 1st option.