The cities of fayetteville, raleigh and durham form a triangle. they are building a new
baseball stadium. how should they determine where to place the stadium so it is the
same distance from all three cities to the stadium? assume a direct path.

The best chance is an illustration of probability

The 21st position in line gives you the best chance of being the first duplicate birthday

Assume you are in the nth position, the probability of getting a free ticket is:

P(n) = P'(first n - 1 people share a birthday) * P(birthday with first n -1 people)

Mathematically, the above can be represented as:

P(n) = [365/365 * 364/365 * 363/365 * ... * (365 - (n -2))/365] * [(n -1)/365]

Such that: n [tex]\le[/tex] 365

When simplified, the equation becomes

p(n)/p(n+1) = 365/(366 - n) * (n - 1)/n

Where

p(n)/p(n+1) > 1

So, we have:

365/(366 - n) * (n - 1)/n > 1

Evaluate the product

(365n -365)/(366n - n²) > 1

Cross multiply

365n -365 > 366n - n²

Collect like terms

n² + 365n - 366n - 365 > 0

Evaluate the difference

n²  - n - 365 > 0

Solve for n using a graphing calculator;

n > - 18.6 or n >19.6

n cannot be negative.

So, we have:

n > 19.6

Approximate to nearest integer

n > 20

The least integer value of n is:

n = 21

Hence, the 21st position in line gives you the best chance of being the first duplicate birthday

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[tex]\rightarrow[/tex] First side(a) of triangle = 17in.

[tex]\rightarrow[/tex] Second side(b) of triangle = 13in.

[tex]\rightarrow[/tex] Perimeter of triangle = 45in.

[tex]\rightarrow[/tex]Third side of the triangle.

[tex]\rightarrow[/tex] Perimeter of triangle = sum of all side(a+b+c).

[tex]\rightarrow[/tex] Perimeter of triangle = a + b + c.(putting the value of perimeter, side a and b from the above given)

[tex]\rightarrow[/tex] [tex]\sf{45\: = \: 17+13+c}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{45\: = \: 30+c}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{45-30\: = \:c}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{15in.\: = \: c}[/tex]

Therefore, third side = 15in.

[tex]\rightarrow[/tex]To convert this value into feet we need to divide it by 12, because there are 12 inches in a foot.

[tex]\rightarrow[/tex] [tex]\sf{\frac{15}{12}}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{1.25feet}[/tex]

________________________________

Hope it helps you:)

Answer:

Side 3 = 1.25 feet

Step-by-step explanation:

Given :

To Find :

Solving :

Step-by-step explanation:

STEP

1

:

Pulling out like terms

1.1 Pull out like factors :

-6y - 30 = -6 • (y + 5)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true:

2.1 Solve : -6 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2 Solve : y+5 = 0

Subtract 5 from both sides of the equation :

y = -5

One solution was found :

y = -5

Answer: y=-5

Explanation:

3y-1-9y=29

3y-9y=-6y

-6y-1=29

+1 on both sides

-6y=30

÷-6

y=-5

Answer:

When you divide 4/16 by 4 it equals 1/4. which is known as 0.25 or 25% of a whole.  

Step-by-step explanation:

So, the definite integral  [tex]\int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74[/tex]

Given that

[tex]\int\limits^1_0 {x^{2} } \, dx = 13[/tex]

We find

[tex]\int\limits^1_0 {(4 - 6x^{2} )} \, dx[/tex]

Definite integrals are integral values that are obtained by integrating a function between two values.

So, [tex]Integral \int\limits^1_0 {(4 - 6x^{2} )} \, dx[/tex]

So, [tex]\int\limits^1_0 {(4 - 6x^{2} )} \, dx = \int\limits^1_0 {4} \, dx - \int\limits^1_0 {6x^{2} } \, dx \\= 4[x]^{1}_{0} - \int\limits^1_0 {6x^{2} } \, dx \\= 4[x]^{1}_{0} - 6\int\limits^1_0 {x^{2} } \, dx \\= 4[1 - 0] - 6\int\limits^1_0 {x^{2} } \, dx\\= 4[1] - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6\int\limits^1_0 {x^{2} } \, dx[/tex]

Since

[tex]\int\limits^1_0 {x^{2} } \, dx = 13[/tex],

Substituting this into the equation the equation, we have

[tex]\int\limits^1_0 {(4 - 6x^{2} )} \, dx = 4 - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6 X 13 \\= 4 - 78\\= -74[/tex]

So, [tex]\int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74[/tex]

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The value of the function [tex]\rm \int\limits{(4-6x^2)} \, dx[/tex] is -74.

A definite Integral is a difference between the values of the integral at the specified upper and lower limit of the independent variable.

The given function is;

[tex]\rm \int\limits^1_0 {x^2} \, dx=13[/tex]

Calculation of the value of the function by using integration;

[tex]\rm= \int\limits{(4-6x^2)} \, dx \\\\=4 \int\limits^1_0 {} \, dx -6\int\limits^1_0 {x^2} \, dx \\\\=4 \int\limits^1_0 {} \, dx -6(13)\\\\ =4[x]^1_0-78\\\\= 4[1-0]-78\\\\=4-78\\\\=-74[/tex]

Hence, the value of the function [tex]\rm \int\limits{(4-6x^2)} \, dx[/tex] is -74.

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Answer:

i think the answer is 144

Step-by-step explanation:

ohhh so first we should try finding the slope here. since we know the points are (3.5 , 21) and (6.5, 69) we can use the formula to look for the slope

the formula is:

y2 - y1 / x2 - x1

lets substitute

69 - 21 / 6.5 - 3.5

48 / 3

16

f(x) = 16x + b

now we just substitute

btw i dont think we need to find b because this inst a linear equation? im not sure but yea i dont think we need to find the y-intercept

so anyways

f(9) = 16(9)

= 144

Answer:

ABCDEFG = 3211000

Step-by-step explanation:

A counts the number of zeroes, and there are 3 zeroes (E, F, G), so A = 3.B counts the number of ones, and there are 2 ones (C, D), so B = 2.C counts the number of twos, and there is 1 two (B), so C = 1.D counts the number of threes, and there is 1 three (A), so D = 1.There is no four, five, six in, so E, F, G are all zeroes.

Answer:

The triangles are not similar

Step-by-step explanation:

We can say whether the triangle UVW is similar to triangle LMN or not by looking at the side lengths' ratio:

If they are similar then the side's must be proportional

VU/LM = VW/NM

35/25 = 22/16 cross multiply expressions

560 = 550 this is not an equation so we cannot say the triangles are similar.

======================================================

Explanation:

SA = surface area of the sphere

SA = 4*pi*r^2

SA = 4*pi*8^2

SA = 804.247719

The surface area is roughly 804.247719 sq ft.

I used the calculator's stored version of pi to get the most accuracy possible.

Since 1 paint can covers 75 sq ft, divide that surface area over 75 to find out how many cans you need.

804.247719/75 = 10.72330292

Round up to the nearest integer to get 11

You'll have leftover paint, but it's better to go over the goal than come up short.

Answer:

4442

Step-by-step explanation:

We Cant Read A Chair So We Exclude Chairs.

Therefore, 2345+1469+628

Which is equals to 4442

Answer:

there is not enough information to solve

Step-by-step explanation:

You need two ordered pairs to calculate the average rate of change.

Let's say the value of the function at n = 1 is a, and the value of the function at n = 3 is b, then the average rate of change from n = 1 to n = 3 is

(b - a)/(3 - 1) = (b - a)/2

Answer:

  (c)  The two quantities are equal.

Step-by-step explanation:

The sine of an angle is equal to the cosine of its complement. In a right triangle, the acute angles are complementary, which means ...

  sin(A) = cos(B)

The two quantities are equal.

Answer:

Step-by-step explanation:

Sin(A) = opposite / hypotenuse

opposite = 4

hypotenuse = 5

Sin(A) = 4/5 = 0.8

Cos(B) = adjacent / hypotenuse.

adjacent = 4

hypotenuse = 5

Cos(B) = 4/5 = 0.8

Believe it or not, this will always happen if you take Sin(A) and find that Cos(90 - A) are equal

Take a simpler case. Suppose you are working with a 30 60 90 triangle.

Cos(60) = Sin(90 - 60) = 1/2

Answer:

15/56

Step-by-step explanation:

multiply the top fractions by making the equation the following

3x5

-------

8x7

_________________________

3x5 =15

8x7= 56

hope this helps :)

The solution to the product of fractions is 13/56

From the question, we have the following parameters that can be used in our computation:

3/8 * 5/7

Evaluate the product of 3 and 5

So, we have

3/8 * 5/7 = 13/8 * 1/7

Evaluate the product of 8 and 7

So, we have

3/8 * 5/7 = 13/56

Hence, the solution is 13/56

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Answer:

NO, but I know who can

Step-by-step explanation:

Answer:

Answer:

z3 = 216      take the cube root of both sides

z = 6 cm  = the side length

Given,

Distance (d)= 2955 km

Time (t)= 13 hr

To Find,

Speed (s)=?

[tex]s = \frac{d}{t} \\ \\ s = \frac{2995}{13} \\ \\ s = 227.308 \: \: \text{km/hr}[/tex]

Rounding To Nearest Whole Number= 227 Km/hr

[tex] \therefore \text{speed} = 227 \text{km/hr}[/tex]

Answer:

As Per Provided Information

Distance travelled by the car is 2955 Km

and it takes 13 hours to cover that distance .

We have been asked to determine the speed of the car .

[tex] \boxed{\bf \: speed \: = \dfrac{Distance Travelled by Car}{Total Time Taken }}[/tex]

substituting the value we get

[tex] \longrightarrow\sf \: Speed = \dfrac{2955}{13} \\ \\ \\ \longrightarrow\sf \: Speed = \cancel\dfrac{2955}{13} \\ \\ \\ \longrightarrow\sf \: Speed =227.30 \\ \\ \\ \longrightarrow\sf \: Speed \approx227 \: km {hr}^{ - 1} [/tex]

Therefore,

Answer:

c

Step-by-step explanation:

a line of credit with a fixed total amount.

The closed line of the credit is the line of credit with the fixed total amount. Option c is the correct option.

On the bases of the requirement, a person or firm takes the open or closed line of credit.

Thus, the closed line of the credit is the line of credit with the fixed total amount. Option c is the correct option.

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Answer:

4x8-12=m

Step-by-step explanation:

4 trays x each containing 8 muffins - 12 muffins(giving away)

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$25000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]25000=P\left(1+\frac{0.08}{12}\right)^{12\cdot 5}\implies 25000=P\left( \frac{151}{150} \right)^{60} \\\\\\ \cfrac{25000}{\left( \frac{151}{150} \right)^{60}}=P\implies 16780.26 \approx P[/tex]

Answer:

No, it isn't.

Step-by-step explanation:

In (-9, 8), -9 is the x coordinate. The y is 8. In order for -9 to have been a solution, the y would have had to been -9.

Here's what I mean:

(The graph I drew is in the image. I hope it makes sense! Sorry for my bad handwriting, I'm not used to writing on computers.)

I hope this helps!

-No one

Answer:

10 kg

Step-by-step explanation:

Let x be the mass of her cat.

1)

2x + 6 = 16

2x = 16 - 6

2x = 10

x = 10/2

x = 5

2)

2(5)

= 10

Answer:10kg

Step-by-step explanation:

Answer:

Step-by-step explanation:

When the stick hits the ground it has the height of zero.

Substitute h with 0 and solve the given equation for t:

[tex]- 16t^2 + 95 = 0\\16t^2 = 95\\t^2 = 95/16\\t = \sqrt{5.93} \\t=2.44[/tex]

Answer: 20

Step-by-step explanation: a to d, just count how many squares. and you get 5, and there are 4 sides and it's a perfect square so 5 x 4 = 20, so it is 20, you didn't show what the unit will be so don't forget to write that down!

Answer:

78.1428571429

Step-by-step explanation: