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dexar [7]
1 year ago
14

a polygon of 100 sides has all possible drawn from a chosen vertex to the others. how many triangles are formed

Mathematics
1 answer:
Hoochie [10]1 year ago
7 0

Answer:

98

Step-by-step explanation:

for a 4 sided polygon you can only draw one diagonal from one vertex so it forms 2 triangles.

For 5 sides  you get 3 triangles

For 6 sides  - 4

For 7 sides  - 5

For 8 sides - 6

Looks like we get 2 less triangles than the number of sides in the polygon


Answer for 100 sides is 98 triangles.

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Which expression is equivalent to (x^6y^8)^3\x^2y^2
Damm [24]

Answer:

\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}

Step-by-step explanation:

\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}

5 0
2 years ago
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Christopher wrote the number pattern below.The first term is 8. 8,6,8,7,10
Aneli [31]
8 goes to 6 that’s -2 then goes back to 8 then goes to 7 that’s -1 add -1 and -2 and you get -3 but you add it like before so it’s 7 to 10 so then it’s 10 -4 to 6 then goes back to 10 to where you add 4 to get 14
4 0
1 year ago
Charlie has the utility function u(xa, xb) =xaxb.his indifference curve passing through 32 applesand 8 bananas will also pass th
natka813 [3]
<span>On an indifference curve, all bundles give the same amount of utility. (32,8) gives a utility of U(32,8)=32x8=256 If (4,y) is on the same indifference curve, then it must give the same utility. Hence, 256 = 4y y=64 64 bananas</span>
4 0
1 year ago
A. The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.
erastovalidia [21]

Answer:

The average yearly salary of  the architect is <u>$62,000</u> and the lawyer is <u>$100,000</u>.

Step-by-step explanation:

Given:

The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

Combined, an architect and a lawyer earn $ 210 thousand.

Now, to find the average yearly salary of  an architect and a lawyer.

Let the average yearly salary of  an architect be x.

So, the average yearly salary of  the lawyer = 2x-24,000.

Combined, architect and lawyer earn = \$210,000.

Now, to get the average salary of the architect and lawyer:

x+(2x-24000)=210000

x+2x-24000=210000\\\\3x-24000=210000

<em>Adding both sides 24000 we get:</em>

3x=186,000\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\x=62000.

<u>The average salary of architect = $62,000.</u>

Now, to get the average salary of lawyer by substituting the value of x:

2x-24000\\\\=2(62000)-24000\\\\=124000-24000\\\\=\$100,000.

<u>The average salary of lawyer = $100,000.</u>

Therefore, the average yearly salary of  the architect is $62,000 and the lawyer is $100,000.

4 0
2 years ago
The time it takes a printer to print a job is an Exponential random variable with the expectation of 12 seconds. You send a job
Mnenie [13.5K]

Answer:

0.8753

Step-by-step explanation:

Calculate the probability that your job will be ready before 10.01 am

Here, the parameter of an Exponential is E(X)=12

Now, to calculate the third job probability, it follows Poisson Distribution with parameter 1/λ

Therefore, E(Y) =1/12

Here, The third job will be ready for 10:01 AM, then E(Y)=61/12

Therefore, the required probability is

P(X\geq 3)=1-P(X

=1- POISSON(3,5,true)

=1-0.1246

=0.8753

8 0
2 years ago
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