While the Pareto distributions are continuous, they tend to be used to model discrete data in humanities and actuarial sciences. Moreover, with its roots in power functions, Pareto distributions may be used in the growing popularity of the studies of networks. The probability density function (PDF) for a Pareto distribution is

Answer:

[tex]\frac{2}{12}[/tex] simplified to [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

4 = [tex]\frac{1}{12}[/tex]

2 = [tex]\frac{1}{12}[/tex]

[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{2}{12}[/tex] ÷ 2 = [tex]\frac{1}{6}[/tex]

Answer:

a) The domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex]  [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex], b) The range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex], c) The ball is 73 meters off of the ground at x = 3 seconds.

Step-by-step explanation:

The complete statement is: A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function [tex]f(x) = -5\cdot x^{2} + 6\cdot x + 100[/tex] represents this situation where x is time and y is the distance off of the ground.

a) What domain does the function make sense?

b) What range does the function make sense ?

c) How far off the ground is the ball at time x = 3 seconds?

a) Let [tex]x[/tex] and [tex]f(x)[/tex] be the time, measured in seconds, and the distance of the ground, measured in meters, respectively. Time is a positive variable, so domain corresponds to the interval when [tex]f(x) \geq 0[/tex] and [tex]t \geq 0[/tex]. That is:

[tex]-5\cdot x^{2} + 6\cdot x + 100 \geq 0[/tex]

[tex]-(x-5.112\,s)\cdot (x+3.912\,s) \geq 0[/tex]

Therefore, the domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex]  [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex]

b) The distance off of the ground is also a positive variable, where ball is thrown upward at a height of 100 meters and hits the ground at a height of 0 meters. Hence, the range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex]

c) The distance of the ball off of the ground at x = 3 seconds is found by evaluating the function:

[tex]f(3\,s) = -5\cdot (3\,s)^{2} + 6\cdot (3\,s) + 100[/tex]

[tex]f(3\,s) = 73\,m[/tex]

The ball is 73 meters off of the ground at x = 3 seconds.

Answer:

A

Step-by-step explanation:

Answer:

{1,5}

Step-by-step explanation:

The intersection of the sets are all of the numbers that appear in both sets. In this case, the only numbers that appear in both are 1 and 5.

Answer:

{ 1,5}

Step-by-step explanation:

The intersection is what the two sets have in common

{1, 5, 10, 15}∩ {1, 3, 5, 7}

= { 1,5}

Answer:  16y² - x²

Step-by-step explanation:  The - sign means a difference, so the choices with + signs are eliminated (though 64x² and 9 are squares)

10 is not a square so that one is eliminated (though the y² and the 4x² are squares)

16 is the square of 4, y² is the square of y, and x² is the square. That expression shows a difference of squares.

Answer:

11 - 9 = 2 trick-or-treaters out of 11 were not dressed as pirates so the proportion is 2/11.

Answer: Ratio is 2:11

Step-by-step explanation:

So your ratio of pirates to non-pirates would be 9:11

So you subtract number of pirates from total trick-or-treaters and get 2.

So the proportion of non-pirates would be 2:11.

Answer:

3lbs

Step-by-step explanation:

Answer:

x = 12

y = 12

Step-by-step explanation:

Each triangle is a right angle triangle

5² + x² = 13²

x² = 169 - 25

x = √144

x = 12

The shape is a parallelogram

Therefore

x = y

y = 12

Answer:

8 years old.

(3x+9)

(3(8)+9)=33

Answer:

133

Step-by-step explanation:

1000 = 2 * 2 * 2 * 5 * 5 * 5

To not have a multiple of 10, you cannot have 2 and 5 as factors of the same number.

One number is 2^3 = 8.

The other number is 5^3 = 125.

8 * 125 = 1000, so the two do multiply to 1000.

Neither 8 nor 125 is a multiple of 10.

8 + 125 = 133

Answer:

133

Step-by-step explanation:

We are given that the product of two numbers is 1000. Let's first list out the factors of 1000 (factors are numbers that evenly divide into 1000):

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

We see that the pairs are:

(1, 1000)

(2, 500)

(4, 250)

(5, 200)

(8, 125)

(10, 100)

(20, 50)

(25, 40)

An easy way to see if a number is divisible by 1000 is to check is it has a zero at the end. Notice that all of the pairs have at least one number that ends with at least 1 zero except (8, 125), so this is the pair of numbers we're looking for.

The sum is thus 8 + 125 = 133.

~ an aesthetics lover

Answer:

a. AEB

b. BEC

c. CED

d. AED

Step-by-step explanation:

Each angle is made up of three points. All three points in order is the name of the angle.

Answer:

a. ∠1 = ∠AEB or ∠BEA

b. ∠2 = ∠BEC or ∠CEB

c. ∠3 = ∠CED or ∠DEC

d. ∠4 = ∠DEA or ∠AED

Step-by-step explanation: Penn <3

Answer:

  x ≈ 48.3177

Step-by-step explanation:

This is what logarithms are for (among other things).

  log(1.1^x) = log(100)

  x·log(1.1) = 2

  x = 2/log(1.1) ≈ 48.3177

Answer:

C

Step-by-step explanation:

C is the solution

Answer:

Option C

Step-by-step explanation:

The graph is a horizontal translation 4 units left and a vertical translation 2 units down ⇒ y= |x+4|-2

Step-by-step explanation:

solution.

if variable d increases then w reduces

w=k.u ×1/d

=ku/d

therefore w=k.u/d

Answer:

[tex]\frac{7\sqrt{x} }{x}[/tex]

Step-by-step explanation:

To simplify 7/√x, we need to rationalize:

[tex]\frac{7}{\sqrt{x} } (\frac{\sqrt{x} }{\sqrt{x} } )[/tex]

When we multiply the 2, we should get our answer:

[tex]\frac{7\sqrt{x} }{x}[/tex]

Answer:

[tex]\frac{7\sqrt{x} }{x}[/tex]

Step-by-step explanation:

[tex]\frac{7}{\sqrt{x} } \\\\\frac{7}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } \\\\\frac{7\sqrt{x} }{\sqrt{x\sqrt{x} } } \\[/tex]

[tex]\frac{7\sqrt{x} }{x}[/tex]

Hope this helps! :)

Answer:

25.02% probability that exactly 19 men and 18 women are chosen

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the men and the women are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

19 men, from a set of 25

18 women, from a set of 22

[tex]D = C_{25,19}*C_{22,18} = \frac{25!}{19!6!}*\frac{22!}{18!4!} = 1295486500[/tex]

Total outcomes:

37 people from a set of 25 + 22 = 47. So

[tex]T = C_{47,37} = \frac{47!}{37!10!} = 5178066751[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{1295486500}{5178066751} = 0.2502[/tex]

25.02% probability that exactly 19 men and 18 women are chosen

Answer:

-3 , 9

Step-by-step explanation:

Sum = - 6

Product = -27

Factors = 3, -9

x² - 6x-27 = 0

x² + 3x - 9x - 9*3 = 0

x(x + 3) - 9(x + 3)  = 0

(x + 3) (x - 9) = 0

x +3 = 0   ; x - 9 = 0

x = - 3     ; x = 9

Solution: x = -3 , 9

Answer:

Jet= 420 mph     Wind = 10mph

Step-by-step explanation:

The speed of the plane in a tailwind can be modeled by x+y where x is the speed of the plane and y is the speed of the wind. Dividing 1290 by 3 gets you the average speed of the jet in a tailwind, which is 430.

The speed of the plane in a headwind can be modeled by x-y where x is the speed of the plane and y is the speed of the wind. Dividing 1230 by 3 gets you the average speed of the jet in a tailwind, which is 410.

This can be modeled by a system of equations, where x+y=430 and x-y=410. Solving the equation you get x=420 and y=10.

So, the speed of the jet is 420 mph and the speed of the wind is 10 mph.

Answer:

C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.

Step-by-step explanation:

Duran uses cost accounting technique to identify cost per unit for its products. The costing techniques allows us to identify the cost of unit that are not completely finished. It is not necessary that all unit must be completed in order to find out the cost per unit of the product. The process costing is the best method to identify cost per unit for products that are in process.

1) The marginal profit is [tex]4.3 - 0.7 ln(x)[/tex].

2) The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.

Thus, option (A) is correct.

C) To maximize profit 462,481 thousands of candles should be sold.

Given: [tex]P(x) = 5 x - 0.7 x[/tex] [tex]{\text}ln x.[/tex]

1) Take the derivative of the profit function P(x) with respect to x.

P(x) = 5x - 0.7x ln(x)

To find P'(x), differentiate each term separately using the power rule and the derivative of ln(x):

[tex]P'(x) = 5 - 0.7(1 + ln(x))[/tex]

       = [tex]5 - 0.7 - 0.7 ln(x)[/tex]

       = [tex]4.3 - 0.7 ln(x)[/tex]

2) Substitute x = 10 into the derivative:

P'(10) = 4.3 - 0.7 ln(10)

         = 4.3 - 0.7(2.30259)

         = 4.3 - 1.61181

         = 2.68819

Therefore, the additional profit for selling a thousand candles once 10,000 candles have already been sold.

Thus, option (A) is correct.

C) Set P'(x) = 0 and solve for x:

[tex]4.3 - 0.7 ln(x) = 0[/tex]

[tex]0.7 ln(x) = 4.3[/tex]

[tex]{\text} ln(x) = 4.3 / 0.7[/tex]

[tex]{\text} ln(x) = 6.14286[/tex]

[tex]x = e^{6.14286[/tex]

[tex]x = 462.481[/tex]

Therefore, 462,481 thousands of candles should be sold.

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1) The marginal profit, P'(x), is -0.7ln(x) + 4.3.

2) The number of thousands of candles that should be sold to maximize profit is approximately 466.9.

1) To find the marginal profit, P'(x), we need to take the derivative of the profit function, P(x), with respect to x. Using the power rule and the chain rule, we can differentiate the function:

P(x) = 5x - 0.7x ln(x)

Taking the derivative with respect to x:

P'(x) = 5 - 0.7(ln(x) + 1)

Simplifying:

P'(x) = 5 - 0.7ln(x) - 0.7

P'(x) = -0.7ln(x) + 4.3

2) To find P'(10), we substitute x = 10 into the marginal profit function:

P'(10) = -0.7ln(10) + 4.3

Using a calculator, we can evaluate this expression:

P'(10) ≈ -0.7(2.3026) + 4.3 ≈ -1.6118 + 4.3 ≈ 2.6882

The value of P'(10) is approximately 2.6882.

Now, let's interpret what P'(10) represents:

The correct interpretation is A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.

P'(10) represents the rate at which the profit is changing with respect to the number of candles sold when 10,000 candles have already been sold. In other words, it measures the additional profit (in thousands of dollars) for each additional thousand candles sold once 10,000 candles have already been sold.

Lastly, to determine the number of thousands of candles that should be sold to maximize profit, we need to find the critical points of the profit function P(x). This can be done by setting the derivative P'(x) equal to zero and solving for x.

-0.7ln(x) + 4.3 = 0

-0.7ln(x) = -4.3

ln(x) = 4.3 / 0.7

Using properties of logarithms:

x = e^(4.3 / 0.7)

Using a calculator, we can evaluate this expression:

x ≈ e^(6.1429) ≈ 466.9

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Answer:

10/91

Step-by-step explanation:

Number of Red balls = 4

Number of Yellow balls = 3

Number of green balls=7

Total=4+3+7=14

If we pick three balls of the same color, there are three possibilities: (All Red, All Green Or all Yellow).

Therefore:

The probability that all three balls are the same color (note that the selections are without replacement)

=P(RRR)+P(GGG)+P(YYY)

[tex]=(\frac{4}{14} \times \frac{3}{13} \times \frac{2}{12})+(\frac{3}{14} \times \frac{2}{13} \times \frac{1}{12})+(\frac{7}{14} \times \frac{6}{13} \times \frac{5}{12})\\\\=\frac{1}{91} + \frac{1}{364}+ \frac{5}{52}\\\\=\frac{10}{91}[/tex]

The probability that all three balls are the same color is 10/91.

Answer:

170

one-hundred seventy

Step-by-step explanation:

[tex]2(5(7+4(17 - 9)-22))=\\2(5(7+4(8)-22))=\\2(5(7+32-22))=\\2(5(39-22))=\\2(5(17))=\\2(85)=\\170[/tex]

Answer:

170.

Step-by-step explanation:

2{ 5[7 + 4(17 - 9) - 22]}

2{5[7+32 -22]}

2{5[17]}

2[85] = 170

Answer:

4d + 6

Step-by-step explanation:

Helen ate d donuts.

Andrea ate 6 more than 4 times d.

4d + 6

Complete Question

Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. Could they take 9 children and 4 adults to both shows? Show your work. A yes or no answer is not sufficient for credit.

Answer:

Yes it is  possible to take the  9 children and 4 adults to both shows

Step-by-step explanation:

From the question we are told that

    The  cost of the Matinee tickets for a child is  z =  $4

    The  cost of the Matinee tickets for an adult is  a  = $ 4

     The cost of the Evening tickets for  a child is  k =  $6

      The cost of the Evening tickets for an adult is  b =  $8    

      The  maximum amount to be spent on Matinee tickets is  m = $80

       The maximum amount to be spent on Evening tickets is  e =  $100

       The  number of child to be taken to the movies is  n  = 9

        The number of adults to be taken to the movies is  j  =  4

Now the total amount of money that would be spent on Matinee tickets is  mathematically evaluated as      

           [tex]t = 4 n + 4 j[/tex]

substituting values

           [tex]t = 4 * 9 + 4* 4[/tex]

           [tex]t = 52[/tex]

Now the total amount of money that would be spent on  Evening ticket is mathematically evaluated as      

      [tex]T = 6n + 8j[/tex]

substituting values

     [tex]T = 6(9) + 8(4)[/tex]

    [tex]T = 86[/tex]

This implies that it is possible to take 9 children and 4 adults to both shows

given that

      [tex]t \le m[/tex]

i.e  $56  [tex]\le[/tex]$ 80

and  

      [tex]T \le e[/tex]

i.e   $ 86 [tex]\le[/tex] $ 100

Answer:

4. 8 5/12

Step-by-step explanation:

4 2/3 + 3 3/4 =

= 4 + 2/3 + 3 + 3/4

= 4 + 3 + 8/12 + 9/12

= 7 + 17/12

= 7 + 12/12 + 5/12

= 7 + 1 + 5/12

= 8 5/12

Hey there!

To find the answer, we just need to see which point falls in this blue, which represents the inequality.

We see that the point (5,-5) is not on the blue.

We see that the point (1,5) is on the blue.

(-3,-3) is on the dotted line but not a solution of the inequality. The dotted line is excluded from the inequality. If it were a bold line, then it would be a solution of the inequality.

(3,-1) is also on the dotted line so it is not a solution.

Therefore, the answer is B. (1,5)

I hope that this helps!

We want to see which point is a solution for the graphed inequality.

We will find that the correct option is B, (1, 5)

Notice that the line that defines the inequality contains the points (-3, -3) and (3, -1)

Then the slope of that line is:

[tex]a = \frac{-1 -(-3)}{3 - (1)} = 1/2[/tex]

Then the line is something like:

y = (1/2)*x + b

To find the value of b, we use the fact that this line passes through the point (3, -1), then we have:

-1 = (1/2)*3 + b

-1 - 3/2 + b

-5/2 = b

So the line is:

y = (1/2)*x - 5/2

And we can see that the line is slashed, and the shaded area is above the line, then we have:

y > (1/2)*x - 5/2

Now that we have the inequality, we can just input the values of the points in the inequality and see if this is true.

First, options C and D can be discarded because these points are on the line, and the points on the line are not solutions.

So we only try with A and B.

A) x = 5

   y = -5

then we have:

-5 > (1/2)*5 - 5/2

-5 > 0

Which clearly is false.

B) x = 1

   y = 5

Then we have:

5 > (1/2)*1 - 5/2 = -4/2

5 > -4/2

This is true, then the point (1, 5) is a solution.

Thus the correct option is B.

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The pizza is cut into 6 slices so each slice would be 1/6 of the pizza.

He at 1/2 of a slice:

1/6 x 1/2 = 1/12 of the pizza

Answer:

The answer is: 325 517 424 395 494

Step-by-step explanation: