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1 year ago

What is the value of angle X and angle Y in the triangle diagram below?

Mathematics

1 answer:

andre [41]1 year ago

3 0

Sum of two interior angles=exterior angle

$\\ \rm\Rrightarrow 45+65=y$

$\\ \rm\Rrightarrow y=110$

Linear pairs have sum 180

$\\ \rm\Rrightarrow x+y=180$

$\\ \rm\Rrightarrow x+110=180$

$\\ \rm\Rrightarrow x=70$

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What would be the angles for K, J, and L?

yan [13]

Answer:

I think its 120°. I don't 100% know, but that's my guess.

3 0

2 years ago

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In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.02, 0.07, and

Leviafan [203]

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

Name the probabilities:

p₁ = 0.02, p₂ = 0.07, p₃ = 0.91

q₁ = 1-p₁ = 0.98 , q₂ = 1-p₂ = 0.93 , q₃ = 0.09

Let X and Y be the number of bits with high and moderate distortion out of three.

The function will follow multinomial distribution:

$f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})$

Substitute the values and make a table.

TABLE IN ATTACHMENT

We calculate marginal distribution by:

$P (X=x)=$ <em>∑</em> $P(X=x,Y=y)$

$fx(x)$ can be found by adding all the probabilities in each row for different value of X

For X=0 , ∑P = 0.94157441

For X=1 , ∑P = 0.057624

For X=2 , ∑P = 0.001176

For X=3 , ∑P =0.000008

The mathematic expectation E is the sum of product of each possibility with its probabiity.

$E(X)=$ <em>∑ </em> $xP(X=x)$

Find E(X):

$E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)$

$E(X)=0.06$

Condition probability states:

$P(A|B)=\frac{P(A,B)}{P(B)}$

It can also be written as:

$f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}$

Where $f_x(1)\\$ = 0.057624

Calculate the quotient:

$Y|_{x=1}$ = 0 , $f_{Y|_X=1$ = 0.862245

$Y|_{x=1}$ = 1 , $f_{Y|_X=1$ = 0.132653

$Y|_{x=1}$ = 2 , $f_{Y|_X=1$ = 0.000510

$Y|_{x=1}$ = 3 , $f_{Y|_X=1$ = 0

Find the dependency:

$f_{XY}(y)=f_X(x)f_Y(y)$

We found that

$f_{Y|_X=1$ = 0.862245

Calculate $f_Y(1)$ from summing the column from the table

$f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141$

Which are not equal.

Conclusion:

X and Y are NOT Independent

7 0

3 years ago

Help MEEEEEE Please Last Day

aalyn [17]

Jayden is correct. the pythagorean theorem states that a^2+b^2=c^2 so jayden’s work would make the most sense by plugging in what we already know into a and b and then solving for c.

i hope this helps and sorry if i’m wrong

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2 years ago

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Use the given function to find the indicated value(s) of x. (Enter your answers as a comma-separated list.)

Nady [450]

Answer:

For f(x) = √(2·x + 2) - √(x + 18), at f(x) = -1 the possible x-values includes;

-0.757, -17.5

Step-by-step explanation:

Given that the function is f(x) = √(2·x + 2) - √(x + 18)

The value of 'x' when f(x) = -1, is given as follows;

-1 = √(2·x + 2) - √(x + 18)

-1² = (√(2·x + 2) - √(x + 18))² = 3·x + 20 - 2·√(2·x + 2)×√(x + 18)

1 = 3·x + 20 - 2·√(2·x + 2)×√(x + 18)

2·√(2·x + 2)×√(x + 18) = 3·x + 20 - 1 = 3·x + 19

2·x² + 38·x + 36 = (3·x + 19)/2

2·x² + 38·x + 36 - (3·x + 19)/2 = 0

4·x² + 73·x + 53 = 0

From which we get;

x = (-73 ± √(73² - 4 × 4 × 53))/(2 × 4)

x ≈ -0.757, and x ≈ -17.5

6 0

2 years ago

See image for question.

Ostrovityanka [42]

Answer:

See below

Step-by-step explanation:

P(A) = 3/8
P(B) = 2/7

(i)

P(A and B) = P(A) * P(B) = 3/8*2/7 = 3/28

(ii)

P(A or B) = P(A) + P(B) - P(A and B) = 3/8 + 2/7 - 3/28 = 1/56(21 + 16 - 6) = 31/56

(iii)

P(not A and not B) = P(not A) * P(not B) = (1 - 3/8)*(1 - 2/7) = 5/8*5/7 = 25/56

<u>Another way:</u>

P(not A and not B) = 1 - P(A or B) = 1 - 31/56 = 25/56

Outcomes with two fair coins: TT, TH, HT, HH

Outcomes with normal dice: 1 to 6

P(odd number) = 3/6 = 1/2

P(two heads and an even number) = 1/4*3/6 = 1/8

P(head and tail) = 1/2
P(prime) = 3/6 = 1/2 (primes are 2, 3 and 5)
P(head, tail and prime) = 1/2*1/2 = 1/4

P(two tails and odd number) = 1/4*3/6 = 1/8

4 0

2 years ago