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2 years ago

Which of the following describes point H? (-3, 3) (3, 3) (-3, -3) (3, -3)

Mathematics

2 answers:

Anastaziya [24]2 years ago

8 0

Answer:

So coordinates of H will be ( 3, -3 )

Step-by-step explanation:

In the given graph we have to choose the point H defined by ordered pair.

In this graph one vertical line ( y-axis ) and one horizontal line ( x-axis ) are intersecting each other at a point (origin).

Point H is 3 block away from origin horizontally on x-axis and 3 block away vertically on y-axis.

Now we should always remember there are 4 quadrants in a graph

Point F is in 1st, J in second, E in 3rd and H in 4th quadrant.

2nd quadrant ⇒ ( - , + )

3rd quadrant ⇒ ( -, - )

4th quadrant ⇒ ( +, - )

So coordinates of H will be ( 3, -3 )

Dominik [7]2 years ago

3 0

H (3,-3)

hope it helps

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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

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2 years ago

The point (–1, 0.5) lies on the graph of f –1(x) = 2x. Based on this information, which point lies on the graph of f(x) = log2x?

Taya2010 [7]

<span>(0.5, -1)
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2 years ago

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