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Kruka [31]
3 years ago
10

State whether each pair of expressions are equivalent. Show your work.

Mathematics
1 answer:
wolverine [178]3 years ago
6 0

Answer:

Both of them are NOT equivalent.

Step-by-step explanation:

Use the distributive property to see if 5(x - 1) and 5x - 1 were equivalent.

5(x - 1)

= 5x - 5

This tells us 5(x - 1) is not equivalent to 5x - 1.

You might be interested in
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:

<h3 /><h3>STEP 1:</h3>

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.

<h3>STEP 2:</h3>

A.

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

<h3>STEP 3:</h3>

B.

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

<h3>STEP 4:</h3><h3>C.</h3>

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

<h3>STEP 5:</h3>

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
Find the midpoint of endpoints -6 and -10
Fed [463]
The midpoint would be -8 because it is 2 away from both ends.
3 0
2 years ago
the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9. write down the co
vodomira [7]

Answer:

k = 3

Step-by-step explanation:

If the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9, then their slopes are equal

For coordinate AB;

slope m1 = 3 - 3k/k-(-1)

m1 = 3-3k/k+1

For the line 2y+3x = 9

2y = -3x + 9

y = -3/2 x + 9/2

Slope m2 = -3/2

Since m1 = m2

3-3k/k+1 = -3/2

Cross multiply

2(3-3k) = -3(k+1)

Expand

6 - 6k = -3k - 3

-6k+3k = -3 - 6

-3k = -9

k = -9/-3

k = 3

Hence the value of k is 3

4 0
2 years ago
What's 3.82e+7 in standard form
kenny6666 [7]
If you simplify, it equals 10.82e.
8 0
3 years ago
Read 2 more answers
1.1<br>Solve the following equations:<br>1.1.1 (x+5)(x-3)=33​
schepotkina [342]

Step-by-step explanation:

x²-3x +5x -15=33

x²-3x+5x=33+15

x²-3x+5x=48

x²+2x=48

divide both sides by 2

x²+x =24

x²= 24

x= ✓24

dunno from here

8 0
3 years ago
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