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Zigmanuir [339]

2 years ago

3

Storm Center 7 was tracking a cold front approaching Cedarburg. Before it rolled in, the temperature was – 7°F. Then, the temper

ature decreased by 9°F.

1 answer:

seraphim [82]2 years ago

7 0

Answer:

The tempature is now -16 F

Subtract. -7 - -9 = -16.

Hope this helps.

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Ginny Jones receives $650 gross salary biweekly. Her income tax rate is 15%. Her group health plan contribution is $24.50 per pa

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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.

<u>Amplitude</u>:

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

<u>b</u>

A time period for Pluto is T=66 years:

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

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

<u>Vertical</u> <u>Shift</u>

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

Let the premises be the statements "All foods that are healthy to eat do not taste good," "Tofu is healthy to eat," "You only ea

GenaCL600 [577]

Answer:

c. modus ponens

Explanation:

In propositional logic, we learn that <em>modus ponens</em> is a valid argument and a rule of inference. <em>Modus ponens</em> states that "P implies Q, and if P is true, then Q must be true."

Based on these propositions, we learn that all food that is healthy does not taste good, and tofu is healthy. Therefore,

<em>If all food that is healthy does not taste good,</em>

<em>and tofu is healthy to eat,</em>

<em>then tofu does not taste good.</em>

5 0

2 years ago