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2 years ago

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Mathematics

2 answers:

Zepler [3.9K]2 years ago

4 0

It took 12 days for all the 60 gallons of water to leak out of the barrel. If you divide 60 by 5 you will get 12.

babunello [35]2 years ago

3 0

Answer:

36 days

Step-by-step explanation:

1.)60 / 5=12

2.)12*3=36

It will take 36 days for the barrel to empty out all 60 gallons of water

Hope this answers your question

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If f(x) = 4x - 3 and g(x) = x + 4, find (f - g)(x).

aleksandrvk [35]

Answer:

(f - g)(x) = 3x - 7

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

= 4x - 3 - ( x + 4 )

= 4x - 3 - x - 4

= 3x -7

8 0

3 years ago

Find the slope between: (1, -4) (-6, -1)

alexdok [17]

Use gradient formula

4 0

2 years ago

Read 2 more answers

I need help on number 11! Can anyone help?

Zanzabum

I might be wrong but I think you divide each number by each other to get the answers

8 0

2 years ago

An e-mail filter is planned to separate valid e-mails from spam. The word free occurs in 60% of the spam messages and only 4% of

ANEK [815]

Answer:

(a) 0.152

(b) 0.789

Step-by-step explanation:

Let's denote the events as follows:

F = The word free occurs in an email

S = The email is spam

V = The email is valid.

The information provided to us are:

The probability of the word free occurring in a spam message is, $P(F|S)=0.60$
The probability of the word free occurring in a valid message is, $P(F|V)=0.04$
The probability of spam messages is,

$P(S)=0.20$

First let's compute the probability of valid messages:

$P (V) = 1 - P(S)\\=1-0.20\\=0.80$

(a)

To compute the probability of messages that contains the word free use the rule of total probability.

The rule of total probability is:

$P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

The probability that a message contains the word free is:

$P(F)=P(F|S)P(S)+P(F|V)P(V)\\=(0.60*0.20)+(0.04*0.80)\\=0.152\\$

The probability of a message containing the word free is 0.152

(b)

To compute the probability of messages that are spam given that they contain the word free use the Bayes' Theorem.

The Bayes' theorem is used to determine the probability of an event based on the fact that another event has already occurred. That is,

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

The probability that a message is spam provided that it contains free is:

$P(S|F)=\frac{P(F|S)P(S)}{P(F)}\\=\frac{0.60*0.20}{0.152} \\=0.78947\\$

The probability that a message is spam provided that it contains free is approximately 0.789.

(c)

To compute the probability of messages that are valid given that they do not contain the word free use the Bayes' Theorem. That is,

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

The probability that a message is valid provided that it does not contain free is:

$P(V|F^{c})=\frac{P(F^{c}|V)P(V)}{P(F^{c})} \\=\frac{(1-P(F|V))P(V)}{1-P(F)}\\=\frac{(1-0.04)*0.80}{1-0.152} \\=0.90566$

The probability that a message is valid provided that it does not contain free is approximately 0.906.

4 0

3 years ago

Geometry PLS HELP due soon

egoroff_w [7]

Answer:

(3) $x = 7.5$ and $y = 51$

(4) $x = 6$

Step-by-step explanation:

Question 3

Required

Solve for x and y

We have:

$16x - 18 + 10x +3 = 180$ --- angle on a straight line

Collect like terms

$16x + 10x = 180 + 18 - 3$

$26x = 195$

Solve for x

$x = 195/26$

$x = 7.5$

Also:

$16x - 18 = 2y$ ---- opposite angles

So, we have:

$16 * 7.5 - 18 = 2y$

$120 - 18 = 2y$

$102 = 2y$

Divide by 2

$51 = y$

$y = 51$

Question 4:

Required

Solve for x

We have:

$11x - 2 + 5x - 4 = 90$ ---- angle at right-angled

Collect like terms

$11x + 5x = 90 +2 + 4$

$16x = 96$

Divide by 16

$x = 6$

7 0

2 years ago