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krek1111 [17]
4 years ago
6

An angle's supplement is nine times of its complementary angle. Find the measure of the angle, the complement of the angle,and t

he supplement of the angle. Answer and Explain please.Brainliest will be given besides points .
Mathematics
1 answer:
Nezavi [6.7K]4 years ago
7 0
S = 9C
first sentence written as an expression
Where S represents the angles supplement
and C represents the angles complement
A + S = 180
definition of supplementary allows me to make this statement Where A is the original angle
A + C = 90
definition of complimentary allows this statement
now add the prior 2 statements together
A + S + A + C = 180 + 90
now simplify
2A + S + C = 270
now replace S with 9C using first statement
2A + 9C + C = 270
now simplify
2A + 10C = 270
now divide both sides by 2
A + 5C = 135
now using the second statement isolate A by adding C to both sides
A = 90 - C
now combine the two prior statements
90 - C + 5C = 135
now simplify
90 + 4C = 135
now subtract 90 from both sides
4C = 45
now divide both sides by 4
C = 11.25
so the complimentary angle is 11.25
now take the third equation and substitute in C
A + 11.25 = 90
now subtract 11.25 from both sides
A = 78.75
so the original angle is 78.75
now use the second equation and substitute in A
78.75 + S = 180
now subtract 78.75 from both sides
S = 101.25
so the suplimentary angle is 101.25
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Elodia [21]
Factors are: 0, 1, 2, 4, 8, 16
6 0
4 years ago
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In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal p
skelet666 [1.2K]

Answer:

\mathbf{P(X=5) =0.0888}    

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

\mathtt{P(X=x) =(^{n}_{x} )   \  \pi^x \  (1-\pi)^{n-x}}

\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} )   \  \pi^x \  (1-\pi)^{n-x}}

where;

n = 8 and π = 0.36

For x = 5

The probability \mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} )   \  0.36^5 \  (1-0.36)^{8-5}}

\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} )   \  0.36^5 \  (0.64)^{3}}

\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} )  \times  \ 0.0060466 \  \times 0.262144}

\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} )  \times  \ 0.0060466 \  \times 0.262144}

\mathtt{P(X=5) =({8 \times 7 } )  \times  \ 0.0060466 \  \times 0.262144}

\mathtt{P(X=5) =0.0887645}

\mathbf{P(X=5) =0.0888}     to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5)\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})

{P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times  (0.36)^0  \times  (1-0.36)^8  \ )  +  \dfrac{8!}{1!(7!)} \times  (0.36)^1  \times  (1-0.36)^7  \ +\dfrac{8!}{2!(6!)} \times  (0.36)^2  \times  (1-0.36)^6  \ +  \dfrac{8!}{3!(5!)} \times  (0.36)^3  \times  (1-0.36)^5 +  \dfrac{8!}{4!(4!)} \times  (0.36)^4  \times  (1-0.36)^4  \  +  \dfrac{8!}{5!(3!)} \times  (0.36)^5  \times  (1-0.36)^3  \ )

P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888

P(x ≤ 5 ) = 0.9707

c. x ≥ 6

The probability of P ( x ≥ 6) = 1  - P( x  ≤ 5 )

P ( x ≥ 6) = 1  - 0.9707

P ( x ≥ 6) = 0.0293

4 0
3 years ago
The campsite is square in shape and has an area of 4225 m2. What is the length of the campsite?
ziro4ka [17]
65 x 65= 4,225 m²
hope it helps! (:

7 0
3 years ago
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Which point is a solution to the system of inequalities below?
vodomira [7]

The ordered pair which is a solution to the given inequality is: C. (2, 1).

<h3>What is an inequality?</h3>

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

  • Less than (<).
  • Greater than (>).
  • Less than or equal to (≤).
  • Greater than or equal to (≥).

Next, we would test the ordered pair with the given inequality to determine a solution as follows:

For ordered pair (4, 4), we have:

3x + 2y < 15

3(4) + 2(4) < 15

12 + 8 < 15

20 < 15 (False).

For ordered pair (3, 3), we have:

3x + 2y < 15

3(3) + 2(3) < 15

9 + 6 < 15

15 < 15 (False).

7x - 4y > 9

7(3) - 4(3) > 9

21 - 12 > 9

9 > 9 (False)

For ordered pair (2, 1), we have:

3x + 2y < 15

3(2) + 2(1) < 15

6 + 2 < 15

8 < 15 (True).

7x - 4y > 9

7(2) - 4(1) > 9

14 - 4 > 9

10 > 9 (True)

For ordered pair (1, 0), we have:

3x + 2y < 15

3(1) + 2(0) < 15

3 + 0 < 15

3 < 15 (True).

7x - 4y > 9

7(1) - 4(0) > 9

7 - 4 > 9

3 > 9 (False)

Read more on inequality here: brainly.com/question/27166555

#SPJ1

7 0
1 year ago
Which is not an equation of the line going through (6, 7) and (2, –1)?
garri49 [273]
Answer - D.

you basically find the equation of the line first and eliminate the wrong answers...

Strategy:  before u do any of this, label your coordinates as (X1,Y1) and (X2,Y2) and u can choose any of ur points to be as x1 or x2 or y1 or y1...
basically, I'll choose (6,7) as (x1,y1) and (2,-1) as (x2,y2). SO,

First you have to  find the gradient (m) of the line.
  you do this by using the formula m = Y2-Y1 / X2-X1 (where '/' is division sign) ....
Put the numbers in their respective places and your gradient will be 2x. we put the x after our number to represent it as a gradient as the straight line formula is y = mx+c and you've found the m.
NOW.
use the formula Y-Y1=m(x-x1) to find the equation of the line.Again u can use any Y1 and X1 here but remember your m is 2

replace the digits and solve...Hopefully you'll get sth like this if you use the points (6,7):
Y-7 = 2(x-6) ....
y=2x-12+7...
Y=2x-5! <<<< this is your straight line equation!
Now all u gotta do is rearrange all your options into y = mx+c.
D. is incorrect as it gives us y=2x+5 and not y = 2x-5 unlike the others 
 

Hope you get it!




7 0
3 years ago
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