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grandymaker [24]

3 years ago

14

Find the expected value of the following probability distribution. X 1 2 3 4 5 P(X) 0.05 0.20 0.35 0.25 0.15 Round your answer t

o two decimal place as necessary. For example, 4.56 would be a legitimate entry.Expected value = ___.

1 answer:

Phoenix [80]3 years ago

6 0

Answer:

5.63

Step-by-step explanation:

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A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

<u>Question 1:</u> $dm/dt=0.2m$ <u />

<u />

<u>Question 2:</u> $m=Ae^{(0.2t)}$ <u />

<u />

<u>Question 3:</u> $m=10e^{(0.2t)}$ <u />

<u />

<u>Question 4:</u> $m=10g$ <u />

Explanation:

<u>Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m</u>

<u></u>

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

<u>Question 2: Find the general solution of this equation. Use A as a constant of integration.</u>

a) <u>Separate variables</u>

$dm/m=0.2dt$

b)<u> Integrate</u>

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) <u>Antilogarithm</u>

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

<u>Question 3. Which particular solution matches the additional information?</u>

<u></u>

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

<u>Particular solution:</u>

$m=10e^{(0.2t)}$

<u>Question 4. What was the mass of the bacteria at time =0?</u>

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

3 years ago

7r+3r-8=8+2r. Solve?

Mazyrski [523]

Given: 7r+3r-8=8+2r

Simplify: 10r-8=8+2r

Addition: add 8 to each side: 10r=16+2r

Subtraction: Take 2r from each side: 8r=16

Division: Divide each side by 8 for answer: r=2

Answer: r=2

4 0

3 years ago

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One side of a square is 11 ft. Tom found that the area of his square is 22. Is Tom correct? Explain why he is correct or incorre

guapka [62]

Answer:

Tom is incorrect.

Step-by-step explanation:

A square by definition implies that all sides of the square are the same measurements. In the case of finding the area, A = s². Tom, however, solved it as A = 2s.

In this case:

Area of square = s² = 11² = 121 ft²

121 ft² is the correct measurement.

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3 years ago

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Can someone please awnser this for me i need to get a b in this class!!!!

Snezhnost [94]

The answer would be 30%

Explanation~

Well, you would have to add 27 and 23 first since, it says, “What percentage of the twelfth grade students have more than one college in mind” then, you’d have to figure out the percentage from there. And the percentage would be, 29.4117647059% of 170, round that to the nearest percent and it’s 30 I’m pretty sure.

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3 years ago

Kyle bought four boxes of cereal for $16.40 how much would 10 boxes of cereal cost

Scilla [17]

Answer:

Step-by-step explanation:

Price of one box = 16.40 ÷ 4 = 4.1

Price of 10 boxes = 4.1 × 10 = 41

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3 years ago

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