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3 years ago

If f(x) = 5x2+2, then what is the slope of f(x) at x = 4?

Mathematics

1 answer:

REY [17]3 years ago

6 0

The slope of a function at a point is the value of its derivative there.

... f'(x) = 5·(2x) + 0 = 10x . . . . . . using the power rule: (d/dx)(xⁿ) = n·xⁿ⁻¹

Then

... f'(4) = 10·4 = 40 . . . . . the slope at x=4

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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

4 years ago

64 Divied by 3274? sorry erally bad at this

Evgen [1.6K]

64/3274=0.019547954
Hope this helps.

6 0

3 years ago

Can 6 fit into 36 and if so how many times

ratelena [41]

Yes.
This is the same thing as:
$\frac{36}{6} =6$

How many times can 6 go into 36?
6 times
Try:
6*6=36

So true.

Hope this helps! :D

6 0

4 years ago

Read 2 more answers

Explain why triangle abc is similar to triangle ade.

mihalych1998 [28]

Answer:

They are both right triangles

Step-by-step explanation:

The triangles are both the same shape but one is bigger than the other.

5 0

4 years ago

A, B and C form the vertices of a triangle. BC = 6.9cm and ∠ CBA = 137°. Given that the area of the triangle is 12.6cm^2, calcul

Anon25 [30]

Answer:

9304t5492860534795782437904209872423897897458790532870925879048790248309787904879525492898977042247980424372

Step-by-step explanation:

assho;le

8 0

4 years ago