Which graph represents the solution to the following inequality? 3x+1<7

Do it by your self  ok ???

Answer:error

Step-by-step explanation:

An expression is combination of variables, numbers and operators. The factor of expression 0.15c-0.072  is 0.15(c-0.48)

An expression is combination of variables, numbers and operators.

The given expression is

zero point one five times of c minus zero point zero seven two.

Expression 0.15c-0.072

A factor is a number that divides another number, leaving no remainder.

0.15c-0.072

Let us take 0.15 common

0.15(c-0.48)

Hence the factor of expression 0.15c-0.072  is 0.15(c-0.48)

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At the point (2π, 3, -1):

a) grad R = -3i + j + 3k

b) div R = -2

c) grad S = 3i + 9j - k

d) curl R = 3i + 2j + 2k

e) div S = 3 + 12π

To determine the values of the given vectors at the point (2π, 3, -1), we substitute the corresponding values into the expressions. Here are the calculations:

a) grad R:

The gradient of R is given by grad R = (∂R/∂x)i + (∂R/∂y)j + (∂R/∂z)k.

∂R/∂x = -ysinx - yzcosx

∂R/∂y = cosx - zsinx - 3z²

∂R/∂z = -ysinx - 6yz

Evaluating the partial derivatives at (2π, 3, -1), we get:

grad R = (-3sin(2π) - 3(-1)cos(2π))i + (cos(2π) - (-1)sin(2π) - 3(-1)²)j + (-3sin(2π) - 6(-1))k

= -3i + 1j + 3k

b) div R:

The divergence of R is given by div R = ∂R/∂x + ∂R/∂y + ∂R/∂z.

div R = (-ysinx - yzcosx) + (cosx - zsinx - 3z²) + (-ysinx - 6yz)

= -2ysinx + cosx - 4zsinx - 3z²

At (2π, 3, -1), the divergence of R becomes:

div R = -6sin(2π) + cos(2π) - 4(-1)sin(2π) - 3(-1)²

= 0 + 1 + 0 - 3

= -2

c) grad S:

The gradient of S is given by grad S = (∂S/∂x)i + (∂S/∂y)j + (∂S/∂z)k.

∂S/∂x = 3i + y²j + zk

∂S/∂y = -i + 2xyj

∂S/∂z = xk

Evaluating the partial derivatives at (2π, 3, -1), we get:

grad S = 3i + 9j - k

d) curl R:

The curl of R is given by curl R = (∂Rz/∂y - ∂Ry/∂z)i + (∂Rx/∂z - ∂Rz/∂x)j + (∂Ry/∂x - ∂Rx/∂y)k.

∂Rz/∂y = -3z

∂Ry/∂z = -ysinx

∂Rx/∂z = 0

∂Rz/∂x = -yzcosx

∂Rx/∂y = -sinx

∂Ry/∂x = -ysinx

Evaluating the partial derivatives at (2π, 3, -1), we get:

curl R = (-3(-1) - 0)i + (-3sin(2π) - (-1)sin(2π))j + (-3sin(2π) - (-1)(-sin(2π)))k

= 3i + 2j + 2k

e) div S:

The divergence of S is given by div S = ∂Sx/∂x + ∂Sy/∂y + ∂Sz/∂z.

∂Sx/∂x = 3

∂Sy/∂y = 2xy

∂Sz/∂z = x

Evaluating the partial derivatives at (2π, 3, -1), we get:

div S = 3 + 2(2π)(3)

= 3 + 12π

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If two figures are congruent, then they are similar.

Yes your answer is right.

Answer:

Margin of error = E = 40

Step-by-step explanation:

Assuming 99% confidence level

Given that x = 253.9  

s.d = 63.6

n = 18

Degrees of freedom = df = n - 1 = 18 - 1 = 17

At 99% confidence level the t is, α = 1 - 99% = 1 - 0.99 = 0.01

α/2 = 0.01 / 2 = 0.005

t α/2,df = t,0.005 = = 2.680 (using student t table)

Margin of error = E = t α/2,df * (s.d/√n)

Margin of error = 2.680*63.6/√18

Margin of error = 2.680*63.6/4.242641

Margin of error = 2.680*14.99066265564303

Margin of error = 40.17

Margin of error = E = 40

Answer:

6425

Step-by-step explanation:

12.85x500=6425

The simple interest is $6,240.00.

The term simple interest refers the interest that is only calculated on the initial sum borrowed or deposited.

Here we need to find  the simple interest on $6000 from 16 may 2010 to 9 October 2010 at 10% per annum.

While we looking into the given question, we know te following values,

Principal amount = $6000

Time period = 16 may 2010 to 9 October 2010

The number of days between 16 may 2010 to 9 October 2010 is

=> 146 days.

Here we have the interest for 1 year,

So, the time period is written as,

And then we have to put time into years for simplicity,

146 days / 365 days/year = 0.4 years.

And the interest rate = 10%

Here we have to convert R percent to r a decimal

r = R/100 = 10%/100 = 0.1 per year.

Now, we have to apply the values on the formula, then we get by solving our equation:

A = 6000(1 + (0.1 × 0.4)) = 6240

A = $6,240.00

Therefore, the total amount accrued, principal plus interest, from simple interest on a principal of $6,000.00 at a rate of 10% per year for 0.4 years (146 days) is $6,240.00.

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To solve this problem, we need to find the x-values where the curve intersects the x-axis, which occurs when y=0.
0=x²-2kx ,We can factor out an x: 0=x(x-2k) .So the x-intercepts are at x=0 and x=2k.

To find the value of k, we need to follow these steps:

Step 1: Find the points of intersection between the curve y = x^2 - 2kx and the x-axis.
To do this, set y = 0:
0 = x^2 - 2kx
x(x - 2k) = 0

This means that the curve intersects the x-axis at x = 0 and x = 2k.

Step 2: Determine the limits of integration.
Since we are looking for the region in the fourth quadrant, we will have limits 0 and 2k for our integration.

Step 3: Calculate the area using integration.
Area = ∫[0 to 2k] (x^2 - 2kx) dx

Step 4: Solve the integral.
Area = [1/3x^3 - kx^2] evaluated from 0 to 2k
Area = (1/3(2k)^3 - k(2k)^2) - (1/3(0)^3 - k(0)^2)
Area = (8k^3/3 - 4k^3)

Step 5: Set the area equal to 36 and solve for k.
36 = 8k^3/3 - 4k^3
36 = (8k^3 - 12k^3)/3
36 = -4k^3/3

Now, multiply both sides by 3 and divide by -4:
-108/-4 = k^3
27 = k^3

Take the cube root of both sides:
k = 3

The value of k is 3 (Option b).

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Answer:

whats the problem

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

2 x 7= 14 - 17= 3

The hand will cover a distance of 1055.04  inches in 7 days.

To establish the distance covered by the  hand's point would go in a week, we would first need to determine the radius of the clock's circle, for which the hand serves as a proxy .

To accomplish this, we would utilize the equation 2(pi*radius),

where pi equals 3.14.

The solution to p=2(3.14*1 ) is 6.28  inches.

This indicates that the hand's point moves 6.28inch every 1 hours.

To determine how far the hand moves in a 168 hour, we would multiply 6.28 inch by 168.

As a result, we arrive at the final calculation of 168 inches covered in 7 days as 1055.04 inches.

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To find two unit vectors that make an angle of 60° with v = 3, 4, we first need to find the magnitude of v. Using the Pythagorean theorem, we can calculate the magnitude of v. The two unit vectors that make an angle of 60° with v = (3, 4) are u1 and u2.

|v| = sqrt(3^2 + 4^2) = 5

Next, we need to find the unit vector in the direction of v. This can be done by dividing each component of v by its magnitude:

u = v/|v| = (3/5, 4/5)

Now we need to find two unit vectors that make an angle of 60° with u. To do this, we can use the formula for rotating a vector counterclockwise by an angle θ:

v' = cos(θ)v + sin(θ)u

Since we want two vectors that make an angle of 60° with u, we can use θ = ±60°. Plugging in these values, we get:

v₁ = cos(60°)v + sin(60°)u = (1/2)3 + (sqrt(3)/2)4, (1/2)4 - (sqrt(3)/2)3
   = (3/2 + 2sqrt(3), 2 - 3sqrt(3)/2)
   ≈ (3.732, -0.598)

v₂ = cos(-60°)v + sin(-60°)u = (1/2)3 - (sqrt(3)/2)4, (1/2)4 + (sqrt(3)/2)3
   = (-3/2 + 2sqrt(3), 2 + 3sqrt(3)/2)
   ≈ (-1.732, 4.598)

Thus, two unit vectors that make an angle of 60° with v = 3, 4 are v₁ ≈ (3.732, -0.598) and v₂ ≈ (-1.732, 4.598).
To find two unit vectors that make an angle of 60° with v = (3, 4), we can use the following steps:

1. Calculate the magnitude of v: |v| = √(3² + 4²) = 5
2. Normalize v: v_norm = (3/5, 4/5)
3. Use the vector rotation formula to find the two unit vectors:

First unit vector, u1:
Rotate v_norm 60° counterclockwise:
u1_x = (3/5)cos(60°) - (4/5)sin(60°)
u1_y = (3/5)sin(60°) + (4/5)cos(60°)
u1 = (u1_x, u1_y)

Second unit vector, u2:
Rotate v_norm 60° clockwise:
u2_x = (3/5)cos(-60°) - (4/5)sin(-60°)
u2_y = (3/5)sin(-60°) + (4/5)cos(-60°)
u2 = (u2_x, u2_y)

So, the two unit vectors that make an angle of 60° with v = (3, 4) are u1 and u2.

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Answer:

50 pockets

Step-by-step explanation:

Total yards of lace = 75

Yards to decorate one Pocket = 1 1/2 yards

How many pockets can she decorate with the lace

Number of pockets she can decorate with the lace = Total yards of lace / Yards to decorate one Pocket

= 75 ÷ 1 1/2

= 75 ÷ 3/2

= 75 × 2/3

= 150/3

= 50

Number of pockets she can decorate with the lace = 50 pockets

The sοlutiοn οf the given prοblem οf triangle cοmes οut tο be RST's triangle has a 30 unit perimeter.

A bar chart is a visual representatiοn using vertical and hοrizοntal bars in a chart. The bar length is prοpοrtiοnal tο the data rate. It is alsο even called bar graph.

Frοm the bar chart, the tοtal pοpulatiοn in 2005 is 302 milliοn tοtal tax cοllected is $2.50.if it is evenly divided then each οf them wοuld pay \(2.50/302 = 8.278\times10^{-9\).Hence, each οf them wοuld pay\(8.278\times10^{-9.\)

Therefοre , the sοlutiοn οf the given prοblem οf triangle cοmes οut tο be RST's triangle has a 30 unit perimeter.

Because a triangular has twο οr mοre extra pieces, it is a pοlygοn. Its structure is a simple rectangle. A triangle is a rectangle with οnly edges A, B, and C. Euclidean geοmetry prοduces a single plane instead οf a cube when the extremities aren't exactly cοllinear. A shape is cοnsidered triangular if it has three sides and three angles. An angle is the pοint where a quadrilateral's three sides meet. A triangle's sides add up tο 180 degrees.

Here,

Yοu wοuld need tο multiply the lengths οf the triangular RST's three sides in οrder tο determine its perimeter.

When we lοοk at the picture, we can see that:

The length οf Sectiοn RS is 5 units.

The length οf Sectiοn ST is 12 units.

The length οf Sectiοn RT is 13 units.

As a result, the triangular RST's perimeter wοuld be:

Circle is calculated as fοllοws: 5 + 12 + 13 = 30 units.

RST's triangle has a 30 unit circumference.

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What is the perimeter of ▲ RST in the given figure?

The sοlutiοn οf the given prοblem οf triangle cοmes οut tο be RST's triangle has a 30-unit perimeter.

What is a bar chart?  

A bar chart is a visual representatiοn using vertical and hοrizοntal bars in a chart. The bar length is prοpοrtiοnal to the data rate. It is alsο even called a bar graph.

Frοm the bar chart, the tοtal pοpulatiοn in 2005 is 302 milliοn tοtal tax collected is $2.50.if it is evenly divided then each οf them would pay . Hence, each οf them would pay

Therefοre, the sοlutiοn οf the given prοblem οf triangle cοmes οut tο be RST's triangle has a 30 unit perimeter.

What precisely is a triangle?  

Because a triangular has twο οr mοre extra pieces, it is a pοlygοn. Its structure is a simple rectangle. A triangle is a rectangle with οnly edges A, B, and C. Euclidean geοmetry prοduces a single plane instead οf a cube when the extremities aren't exactly cοllinear. A shape is cοnsidered triangular if it has three sides and three angles. An angle is the pοint where a quadrilateral's three sides meet. A triangle's sides add up tο 180 degrees.

Here,

Yοu wοuld need tο multiply the lengths οf the triangular RST's three sides in οrder tο determine its perimeter.

When we look at the picture, we can see that:

The length οf Sectiοn RS is 5 units.

The length οf Sectiοn ST is 12 units.

The length οf Sectiοn RT is 13 units.

As a result, the triangular RST's perimeter would be:

The circle is calculated as fοllοws: 5 + 12 + 13 = 30 units.

Hence, RST's triangle has a 30-unit circumference.

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Answer:

24 gallons of 50% grape juice

Step-by-step explanation:

if you have 1 gallon of 50% grape juice and 1 gallon of 25% grape juice, the resulting combination will be 2 gallons of 75/2% (or 37.5%) grape juice.

I guessed you would need about 1.5 times of the 50 % mixture to make the 25% mixture into 50 %.  I checked, 1.5 times 16 is 24, so I calculated what is the average concentration (24*50 + 16*25)/40, and I got 40 so that guess was correct.

a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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The linear program is as follows:

T - M ≤ -20,000

P - T ≤ -5,000

N - T ≤ -5,000

S - T ≤ -5,000

G - T - P ≤ 0

L - G ≤ -200

N + S - 2T - 2P ≤ 0

B - P ≤ 0

B - S ≤ 0

B + P ≤ 60,000

L - B - T ≤ 0

Let's define decision variables for each employee's salary as follows:

Let T, P, N, S, G, L, and B represent the salaries of Tom, Peter, Nina, Samir, Gary, Linda, and Bob, respectively.

Our objective is to minimize the salary of the highest paid employee. We can achieve this by introducing another variable, M, that represents the maximum salary among all employees. Therefore, our objective is to minimize M.

Minimize: M

Subject to:

T ≥ 20,000

P ≥ T + 5,000

N ≥ T + 5,000

S ≥ T + 5,000

G ≥ T + P

L ≥ G + 200

N + S ≥ 2(T + P)

B ≥ max(P, S)

B + P ≥ 60,000

L ≤ B + T

Now, we can write the linear program in standard form by moving all variables to the left-hand side of the constraints and adding slack variables:

Minimize: M

Subject to:

T - M ≤ -20,000

P - T ≤ -5,000

N - T ≤ -5,000

S - T ≤ -5,000

G - T - P ≤ 0

L - G ≤ -200

N + S - 2T - 2P ≤ 0

B - P ≤ 0

B - S ≤ 0

B + P ≤ 60,000

L - B - T ≤ 0

All variables are non-negative.

This linear program can be solved using a linear programming solver to find the minimum value of M that satisfies all the constraints. Once we have the optimal solution, we can retrieve the salaries of each employee from the linear program solution.

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Answer:

545000

Step-by-step explanation:

5 is in the thousands place, the number before 5 is 1. Since 1 is lesser than 5 we don't have to round it to six, So the answer is 545000.

(A) A 95% confidence interval estimate for the percentage of all voters who believe competence is more important than character is (0.538, 0.602).

(B) This is due to the interval's lower bound's value of 0.538, which is higher than 0.5.

(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample

(A) Using the method below, we can calculate an estimate with a 95% confidence interval for the proportion of voters who think competence is more significant than character:

CI equals p z*(sqrt(p*(1-p)/n)/p)).

where: p = the percentage of voters who say character is more essential than competence = 0.57; n = the sample size; 1000; and z = the z-score for a 95% confidence level; 1.96.

By entering the numbers, we obtain:

CI = 0.57 1.96*(sqrt(0.57*(1-0.57)/1000)), which equals 0.57 0.032. (0.538, 0.602)

the 95% confidence interval estimate for the proportion of respondents overall who think competence is more significant than character is (0.538, 0.602).

(B) Based on the range discovered in part, it is reasonable to infer that the majority of voters value competence over character (a). This is due to the interval's lower bound's value of 0.538, which is higher than 0.5. Therefore, we can state with 95% certainty that the actual proportion of voters who think competence is more crucial than character is at least 53.8%, which is a majority.

(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample, then roughly 95% of those intervals would contain the actual proportion of voters who believe competence is more significant than character. That is to say, we have a 95% confidence interval (0.538, 0.602) that contains the actual proportion of voters who think competence is more significant than character.

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Answer:

If you want the right answer its (A)

Step-by-step explanation:

b = 5 minus three-halves r

your welcome

Answer:

A

Step-by-step explanation:

B = 5 - 3/2r

Answer:

b

Step-by-step explanation:

cause u are using 3 gallons which is taking away

Answer:

the answer is only 3

Step-by-step explanation:

you read all of them and you make it an equation and if it is negative or subtraction that would be your answer

Using conditional probability, it is found that there is a 0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

According to the chain given, the percentages associated with not getting into their first-choice college are:

Hence:

\(P(A) = 0.1375 + 0.1575 + 0.24 + 0.07 = 0.605\)

The probability of both not getting into their first-choice college and taking chemistry is 0.1375, hence \(P(A \cap B) = 0.1375\)

Then, the conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1375}{0.605} = 0.2273\)

0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.

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Answer: 0.2273

Step-by-step explanation: because it says so <3

Answer:

9c + 10 (see below)

Step-by-step explanation:

To find how much Chris spent on tickets, you can write an expression to represent the situation:

$9c

You can do this to find how much Michael spent as well:

$10m

To find how much Chris and Michael spent combined, add their two costs:

9c + 10

The first five terms of the sequences are 2, 3, 5, 9, 17. and 1, 4, 7, 10, 13

Using the formula, an = 2an-1 - 1 where a1 = 2, we can find the first few terms of the sequence as follows:

a2 = 2a1 - 1 = 2(2) - 1 = 3

a3 = 2a2 - 1 = 2(3) - 1 = 5

a4 = 2a3 - 1 = 2(5) - 1 = 9

a5 = 2a4 - 1 = 2(9) - 1 = 17

Therefore, the first five terms of the sequence are: 2, 3, 5, 9, 17.

For the second sequence, the first five terms are

1, 4, 7, 10, 13

Because the common difference is 3

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The two factors that add up to 6 are 3 and 3. This is because 3 + 3 = 6.

However, there are no two factors that can be multiplied together to give a product of -7. This is because if we multiply two factors, the result is positive if both factors have the same sign (both positive or both negative), and negative if the factors have opposite signs. Therefore, we cannot find two factors that multiply to give -7, as there are no two factors with opposite signs whose product is 7.

In other words, if we let x and y be two factors that multiply to give -7, then either x and y are both positive or both negative. If they are both positive, then their product is positive, which is not equal to -7. If they are both negative, then their product is positive as well, which is also not equal to -7. So there are no two factors that can be multiplied together to give -7.

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x = 8

cos60° = x/16

1/2 = x/16

2x = 16

x = 16 : 2

x = 8

Answer:

\(\Huge \boxed{x=8}\)

Step-by-step explanation:

\(\sf \displaystyle cos(60\° ) = \frac{x}{16}\)

Multiplying both sides by 16.

\(\sf \displaystyle 16 \cdot cos(60\° )= \frac{x}{16} \cdot 16\)

Simplifying the equation.

\(\sf \displaystyle 16 \cdot \frac{1}{2} = x\)

\(\sf 8=x\)

Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).

By using algebraic expression we got that the total number of refills that Jalissa bought is 12 refills.

An expression or algebraic expression is a mathematical statement consisting of numbers, variables and arithmetic operations between them. For example, 4m + 5 is an expression where 4m and 5 are terms and m is a variable in the given expression separated by the arithmetic sign +. 

According to given information in the question:

Cost of 1 refill mug = $8.95

Cost of 1 refill = $1.50

Total money spent on refill and refill mug = $26.95

Let, "x" be the number of refills she bought

So, the algebraic expression can be formed as below

8.95 + 1.50x = 26.95

⇒1.50x = 26.95 - 8.95

⇒1.50x = 18

⇒x = 18/1.50

⇒x = 12

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The events are independent, the probability of selecting any combination of r days is the product of the probabilities of selecting each day, which is the same as the distribution of the unordered set of r days when N(n) = r.

(a) The distribution of N(n) is a binomial distribution, since the events are independent and occur with a fixed probability p. Therefore, N(n) follows a Binomial distribution with parameters n and p:

N(n) ~ Binomial(n, p)

(b) The distribution of T1 is a geometric distribution, as it represents the number of trials until the first success (event occurs) in a sequence of independent Bernoulli trials with probability p. Therefore, T1 follows a Geometric distribution with parameter p:

T1 ~ Geometric(p)

(c) The distribution of Tr is a negative binomial distribution, as it represents the number of trials until the rth success (event occurs) in a sequence of independent Bernoulli trials with probability p. Therefore, Tr follows a Negative Binomial distribution with parameters r and p:

Tr ~ Negative Binomial(r, p)

(d) Given that N(n) = r, the unordered set of r days on which events occurred has the same distribution as a random selection (without replacement) of r of the values 1, 2, ..., n. This is because each event occurs independently and with a fixed probability p. When you select r days randomly (without replacement), the probability of each day being selected is p, and the probability of each day not being selected is (1-p). Since the events are independent, the probability of selecting any combination of r days is the product of the probabilities of selecting each day, which is the same as the distribution of the unordered set of r days when N(n) = r.

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