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antoniya [11.8K]

1 year ago

15

Circle O has a circumference of approximately 250π ft. Circle O with diameter d is shown. What is the approximate length of the

diameter, d? 40 ft 80 ft 125 ft 250 ft

2 answers:

lidiya [134]1 year ago

7 0

Answer:

The answer is D (250) on Edge 2020

Step-by-step explanation:

I did the Quiz

Vinil7 [7]1 year ago

4 0

Answer:

250 ft

Step-by-step explanation:

circumference of circle 'C' is defined as

C = 2πr

250π = 2πr

r = 250π/2π

r= 125

d = 2r = 2×125 = 250 .

diameter of the given circle is 250 ft

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A town has a population of 5000 and grows 3.5% every year. To the nearest tenth of a year, how long will it be until the populat

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is

$y=a(b)^x$ where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then

a = 5000

If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So

b = 1.035

Our function is

$y=5000(1.035)^x$ where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.

$7300=5000(1.035)^x$ and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.

Begin by dividing both sides by 5000 to get

$1.46=1.035^x$ and take the natural log of both sides:

$ln(1.46)=ln(1.035)^x$

The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:

$ln(1.46)=xln(1.035)$ To solve for x, we now divide both sides by ln(1.035):

$\frac{ln(1.46)}{ln(1.035)}=x$

Do that division on your calculator and get that

x = 11.0 years.

That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)

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2 years ago

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2 years ago

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

2 years ago