After dinner 3/4 of a pie remains. if tasha eats 1/6 of the remaining pie

There are two misshapen coins in a box; their probabilities for landing on heads when they are flipped are, respectively, .4 and

Leokris [45]

Answer:

E(X) = 6.0706

Step-by-step explanation:

1) Define notation

X = random variable who represents the number of heads in the 10 first tosses

Y = random variable who represents the number of heads in range within toss number 4 to toss number 10

And we can define the following events

a= The first coin has been selected

b= The second coin has been selected

c= represent that we have 2 Heads within the first two tosses

2) Formulas to apply

We need to find E(X|c) = ?

If we use the total law of probability we can find E(Y)

E(Y) = E(Y|a) P(a|c) + E(Y|b)P(b|c) ....(1)

Finding P(a|c) and using the Bayes rule we have:

P(a|c) = P(c|a) P(a) / P(c) ...(2)

Replacing P(c) using the total law of probability:

P(a|c) = [P(c|a) P(a)] /[P(c|a) P(a) + P(c|b) P(b)] ... (3)

We can find the probabilities required

P(a) = P(b) = 0.5

P(c|a) = (3C2) (0.4^2) (0.6) = 0.288

P(c|b) = (3C2)(0.7^2) (0.3) = 0.441

Replacing the values into P(a|c) we got

P(a|c) = (0.288 x 0.5) /(0.288x 0.5 + 0.441x0.5) = 0.144/ 0.3645 = 0.39506

Since P(a|c) + P(b|c) = 1. With this we can find P(b|c) = 1 - P(a|c) = 1-0.39506 = 0.60494

After this we can find the expected values

E(Y|a) = 7x 0.4 = 2.8

E(Y|b) = 7x 0.7 = 4.9

Finally replacing the values into equation (1) we got

E(Y|c) = 2.8x 0.39506 + 4.9x0.60494 = 4.0706

And finally :

E(X|c) = 2+ E(Y|c) = 2+ 4.0706 = 6.0706

6 0

2 years ago

Pluto's distance P(t)P(t)P, left parenthesis, t, right parenthesis (in billions of kilometers) from the sun as a function of tim

Xelga [282]

Answer: P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:

y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D

where:

A is amplitude A=|A|

B is related to the period by: T = $\frac{2.\pi}{B}$

C is the phase shift or horizontal shift: $\frac{C}{B}$

D is the vertical shift

In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.

Amplitude:

a = $\frac{largest - smallest}{2}$

At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:

a = $\frac{6.9-4.4}{2}$

a = 1.25

b

A time period for Pluto is T=66 years:

66 = $\frac{2.\pi}{b}$

b = $\frac{\pi}{33}$

Vertical Shift

It can be calculated as:

d = $\frac{largest+smallest}{2}$

d = $\frac{6.9+4.4}{2}$

d = 5.65

Knowing a, b and d, substitute in the equivalent positions and find P(t).

P(t) = a.sin(b.t) + d

P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

The Pluto's distance from the sun as a function of time is

P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

8 0

2 years ago

A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find

lyudmila [28]

Answer:

$f(x)=120000 \times (1.055)^{x}$

Step-by-step explanation:

We are given that the present value for the home is $120,000 and the rate of interest is 5.5% i.e. 0.055.

We will use the following formula:

$f(x)=P \times (1+r)^{x}$

where $P$ is the present value, $r$ is the rate of interest and $x$ is the number of years.

Substituting the values in the above formula to get:

$f(x)=120000 \times (1+0.055)^{x}$

$f ( x ) = 120000 \times ( 1.055 ) ^ { x }$

8 0

2 years ago

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Susan is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Com

hoa [83]

Idk if this is correct but ugh ill try my best

B = 55 + .6x

65 = 55 + .6x

subtract 55 from each side

10 = .6x

Multiply each side by .6 =

6 = x or in this case m

A charges les than B when m > 6

tell me if I'm wrong if I am

4 0

2 years ago

A rectangular Corn Hole area at the recreation center has a width of 5 feet and a length of 10 feet. If a uniform amount is adde

almond37 [142]

1. The formula for calculate the area of a rectangle, is:

A=LxW

A is the area of the rectangle
L is the length of the rectangle.
W is the widht of the rectangle

2. You have that:

-The rectangular Corn Hole area has a width of 5 feet and a length of 10 feet, so:

L1=10 feet
W1=5 feet

- When a uniform amount is added to each side (x), the area is increased to 84 feet². Then, you have a different length (L2) and a different width (W2):

3. The new length is:

L2=L1+x+x
L2=L1+2x
L2=10+2x

4. The new width is:

W2=W1+x+x
W2=W1+2x
W2=5+2x

5. The new area is:

A2=84 feet²

6. Then, you have:

A=LxW
84=(10+2x)(5+2x)

7. When you apply the distributive property, you obtain a quadratic equation:

4x²+30x-34=0

8. You can solve with by applyin the quadratic formula:

x=(-b±√(b^2-4ac))/2a

a=4
b=30
c=-34

9. Then, the answer is:

x=1 feet

5 0

2 years ago

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