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4 years ago

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It is predicted that the population of a particular state will double every 25 years. a) Determine the annual and monthly growth

rates. Express your answers as percents. b) Determine the continuous growth rate per year. Express your answer as a percent.

1 answer:

Makovka662 [10]4 years ago

4 0

B...

Hope this helps!

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Solve the triangle.

vekshin1

9514 1404 393

Answer:

b = 757.7 m
A = 17.2°
C = 14.3°

Step-by-step explanation:

From the law of cosines, you can find the length of side b to be ...

b = √(a² +c² -2ac·cos(B))

b = √(184041 +128164 -307164cos(148.5°)) ≈ √574105.36

b ≈ 757.7

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From the law of sines, you can find the measure of angle C to be ...

C = arcsin(c/b·sin(B))

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C ≈ 14.3°

A = 180° -148.5° -14.3°

A = 17.2°

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3 years ago

s) An e-mail lter is planned to separate valid e-mails from spam. The word free occurs in 50% of the spam messages and only 3% o

balu736 [363]

Answer:

A) P(F) = 0.124

B) P(S|F) = 0.8065

C) P(V|F^(c)) = 0.886

Step-by-step explanation:

Let us denote as follows;

F = Message contains word free

S = message is spam

V = message is valid

From the question, we are given that;

The probability that word free occurs in spam messages;P(F|S) = 50% = 0.5

The probability of the valid messages that contain free; P(F|V) = 3% = 0.03

Spam messages; P(S) = 20% = 0.2

Valid messages; P(V) = 1 - 0.2 = 0.8

A) From rule of total probability ;

probability that the message contains the word free is given as;

P(F) = P(F|S)•P(S) + P(F|V)•P(V)

P(F) = (0.5 x 0.2) + (0.03 x 0.8)

P(F) = 0.124

B) From Baye's theorem;

probability that the message is spam given that it contains free is given as;

P(S|F) = P(F|S)•P(S)/P(F)

P(S|F) = (0.5 x 0.2)/0.124

P(S|F) = 0.8065

C) From combination of complement rule and Baye's theorem;

probability that the message is valid given that it does not contain free is given as;

P(V|F^(c)) = P(F^(c)|V)•P(V)/P(F^(c))

Thus,

P(V|F^(c)) = [(1 - P(F|V))•P(V)]/(1 - P(F))

P(V|F^(c)) = ((1 - 0.03)•0.8)/(1 - 0.124)

P(V|F^(c)) = 0.776/0.876

P(V|F^(c)) = 0.886

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According to Damian's trail mix recipe, 2 cups of dried fruit should be used for 3 1/2 cups of salted nuts.At this rate, how man

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Yuson must complete 210 min of community service. She does 30 min each day. Which linear equation represents the number of minut

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Answer:

$y=-30x+210$

Step-by-step explanation:

Let

x -----> the number of days

y ----> the number of minutes Yuson has left

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept (initial value)

In this problem we have

The slope is equal to

$m=-30\frac{min}{day}$ ----> is negative because is a decreasing function

$b=210\ min$ ----> initial value

substitute the values

$y=-30x+210$

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4 years ago