This is a number of parts out of 100, the numerator of a fraction where the denominator is 100

Answer:

20th person

Step-by-step explanation:

Before proceeding into problem,assume that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365 day year.

The probability, p(n), of winning a prize when you are the nth person is line is:

(probability that none of the first n−1 people share a birthday)*( probability that you share a birthday with one of the first n−1 people)

So,The first person can't have the same birthday as anyone less by themselves, so lets look at the second person. At the point where we add the second person there is a 364/365 chance of them not sharing a birthday with the previous person. When we add the 3rd person there is there is a 363/365 chance of them not sharing a birthday and so on such that the (n-1)th person when added has a probability of not forming a share of (365 -n -2)/365. We can multiply these together to get the probability that none of first (n-1) people share their birthday.

Therefore the position in line that has highest chance of winning is 20th.

We want to see which position has the largest probability of winning the prize. We will find that the 18th person has the largest probability of winning.

We know that a person only will win the prize if that person has the same birthday that some in front of him/her.

So, the probability that the n-th person wins the prize is given by:

(probability that none of the persons in front share a birthday)*(probability of sharing a birthday with some of the n - 1 people in front).

Let's find the first one.

The first person can have a birthday in any of the 365 days.

The second person must not have the same birthday, so there are 364 options remaining.

The probability of this is just

p₂ = 364/365

For the third person, we have the same thing, this time, 363 remaining options:

p₃ = 363/365

For the (n - 1) person the probability is:

pₙ₋₁ =  (365 - n + 2)/365

And the n-th person must share a birthday with some of the n persons in front of him, so there are (n - 1) options to choose, so the probability is:

pₙ = (n - 1)/365

Then, the joint probability is:

P = p₂*p₃*...*pₙ

[tex]P = \frac{364*363*...*(365 - n + 2)*(n - 1)}{365^{n-1}}[/tex]

Now we have the equation, we just need to solve it for n such that we maximize the value of P in the range n ∈ [1, 50]

This is actually a really hard thing to find, but what you can notice, is that each time that n increases by 1, the denominator increases 365 times.

While the numerator increases by a factor:

(365 - n - 1)*n/(n - 1)

So we need to find the value of n such that the thing above is equal or smaller than 365.

Let's solve:

(365 - n - 1)*n/(n - 1) = 365

(365 - n - 1)*n = 365*n - 365

364*n - n^2 - 365*n + 365 = 0

-n^2 - n + 365 = 0

This is just a quadratic equation, the solutions are:

[tex]n = \frac{1 \pm \sqrt{1 + 4*365} }{-2}[/tex]

We only care for the positive solution, so we take:

[tex]n = \frac{1 - \sqrt{1 + 4*365} }{-2} = 18.6[/tex]

So, for the 19th person, the probability of winning will be smaller than for the 18th person, this happens because the numerator increased by a smaller factor than the denominator.

This means that the 18 person has the largest probability of winning.

If you want to learn more, you can read:

Answer:

i cant see all of it

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Plug in -4 wherever you see an x. So:

([tex]-4^{2}[/tex])-(3*-4)+2 --> (16) - (-12) + 2 --> 16 + 12 +2 (two negatives make a positive) --> 28 + 2 = 30

Answer:

Gary did not use the greatest common factor in the expression.

Step-by-step explanation:

Both factors of 36 and 66 are correct.

Gary also used equivalent expressions. I hope this helps.

Answer: Gary did not use the greatest common factor in the equation.

Step-by-step explanation: Gary did not use the Greatest common factor because the greatest common factor would be 33

Answer:the last one

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The area of a kite can be found, given the lengths of its diagonals

The correct option for the area of the kite ABCD is option C;

C) 162 square inches

The reason the selected value is correct is as follows:

The given parameters in the kite ABCD are;

AC = 18 inches

BE = 9 inches

The required parameter:

The area of the kite

Solution:

The area of a kite is given by the product of the lengths of the diagonals divided by 2

Therefore, we have;

[tex]\mathbf{The \ area \ of \ the \ kite \ ABCD} = \dfrac{Length (AC)\times Length (BD)}{2}[/tex]

The length of BD = BE + DE

BE = DE Given that AC is a perpendicular bisector of BD, by the properties of a kite

∴ BD = BE + BE = 2 × BE by substitution property

Therefore;

[tex]The \ area \ of \ the \ kite \ ABCD = \mathbf{\dfrac{Length (AC)\times 2 \times Length (BE)}{2} }= AC \times BE[/tex]

Which gives;

The area of the kite ABCD = 18 inches × 9 inches = 162 square inches

Learn more about the area of geometric shapes here:

https://brainly.com/question/16707557

Answer:

5/6

Step-by-step explanation:

10:12 can also be expressed as a fraction which is 10/12  then simplify, divide each number by 2 and you will get 5/6

Pls mark as brainliest, thank u and have a wonderful day.

Answer:

2

Step-by-step explanation:

since 1 inch is 100 miles, that means 200 miles would equal 2 inches

Answer:

X=5

Step-by-step explanation:

3+3 is the example and x+5 will be 5+5 since it will be the same. So 2 5

Answer:

X=5

Step-by-step explanation:

hmmmmmm ok

2x-3+3=x+5    You need to even out each side of the equation so

2x=x+5

2x5 is equivalent to 5+5 so x=5.

Answer:

$13

Step-by-step explanation:

Answer:

$13.00

Step-by-step explanation:

Answer:

(3x² + 8y)(3x² - 8y)

Step-by-step explanation:

9x^4 - 64y^2

~Rewrite

(3x²)² - (8y)²

~Apply difference of two squares

(3x² + 8y)(3x² - 8y)

Best of Luck!

Answer:

y = - (1/2) x + 1

Step-by-step explanation:

The given equation of the line is:

2 x - y - 7 = 0

solving for y gives:

2 x - 7 = y

so y = 2 x - 7

where the slope is "2", which is fundamental to know in order to construct a perpendicular line to it by using the "opposite of the reciprocal" of the given slope.

So in our case, the slope of the perpendicular line must be:  "- 1 / 2"  (negative one half).

now we can build the equation of the new line, using this slope and requesting the point (4, -1) to be in it:

y = - (1/2) x + b

-1 = - (1/2) (4) + b

-1 = - 2 + b

solve for b:

b = 2 - 1 = 1

Then the equation of the perpendicular line is:

y = - (1/2) x + 1

y= -1/2 x+1

Step-by-step explanation:

2x-y-7=0

2x-7=y

y=2x-7

Answer:

T=62

Step-by-step explanation:

Answer:

T= 62

Step-by-step explanation:

First you need to distribute

8t+16-3t+12=6t-42+8

Next you need to simplify the problem

5t+28=6t-34

-5 +34  -5.+34

62=1t

/1.  /1

t=62

Sorry if it's not specific enough

Answer:

25% of 53 is 13.25 so the new bottle should hold 66.25 ounces or 13.25 mor than the regular bottle

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

75 divided by 6 1/4 is 12.

Answer:

y=1.5x

78

Step-by-step explanation:

y=1.5x  

y=1.5(52)

y=78

Answer:

Each class will receive 2670 pencils

Step-by-step explanation:

Hope it helps :)

Have a good day/night

Brainliest pls?

Answer:

[tex]2^{100} * 6[/tex]

Step-by-step explanation:

length of finite strings = 100

number of letters : 4 { a,b,c,d }

Determine the number of strings that use ≤ two different letters

since the number of letters is 4 and we are allowed to make use of at most 2 different letters

Then the number of ways will be : [tex]^{4} C_{2}[/tex] = 6 ways

now considering the length of the Finite strings

The number of strings that use no more than two different letters

= [tex]2^{100} * 6 ways[/tex]

Answer:

B. number of bars sold in chocolate

Step-by-step explanation:

i took the test

Answer:

22:4949

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:اين الجملة؟

Step-by-step explanation:

Answer:

It is a function because the line does not pass through X two times.

Step-by-step explanation:

Answer:

it is not a function since the pattern is broken and does not stay symetrical or as a pattern

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

283lbs

Step-by-step explanation:

Answer:

Step-by-step explanation:

dang thats hard

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The only transformation that would make a shape smaller or bigger is dilation.

Since this dilation is going from bigger to smaller you will have to use a number from in between 0 and 1.

[tex](x,y)-->(\frac{1}{2}x,\frac{1}{2}y)[/tex]

Factor out 1/n⁴, and distribute the sum over each term:

[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac1{n^4}\sum_{i=1}^n(2i^3-3i)[/tex]

[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac2{n^4}\sum_{i=1}^ni^3-\frac3{n^4}\sum_{i=1}^ni[/tex]

Recall the following formulas:

[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]

[tex]\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4[/tex]

So we have

[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac{n^2(n+1)^2}{2n^4}-\frac{3n(n+1)}{2n^4}=\boxed{\dfrac{(n+1)(n^2+n-3)}{2n^3}}[/tex]