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3 years ago

What is the slope of the line below?

Mathematics

1 answer:

horsena [70]3 years ago

5 0

Answer:

The answer is the green answer choice which is 5/7.

Step-by-step explanation:

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Evaluate sin 300° without using a calculator.

Anni [7]

Answer:

$-\sqrt{3} /2$

Step-by-step explanation:

300 degrees is in the fourth quadrant (it's between 270 and 360); sine is negative in the fourth quadrant.

Given we're in the fourth quadrant, the reference angle is 360 - 300 = 60 degrees

sin(60°) = $\sqrt{3} /2$

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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

5 0

4 years ago

What is the equation of the blue line?

sergejj [24]

Answer:

• From the general equation of a line:

${ \rm{y = mx + b}} \\$

m is slope
b is y-intercept.

→ Consider points (4, 4) and (2, 3)

${ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \rm{m = \frac{3 - 4}{2 - 4} = \frac{ - 1}{ - 2} }} \\ \\ { \underline{ \rm{ \: \: m = \frac{1}{2} \: \: }}}$

→ find the y-intercept:

${ \rm{y = mx + b}} \\ { \rm{3 = ( \frac{1}{2} \times 2) + b}} \\ \\ { \rm{3 = 1 + b}} \\ \\ { \underline{ \rm{ \: \: b = 2 \: \: }}}$

• Therefore, equation of a blue line is

${ \boxed{ \rm{y = \frac{1}{2}x + 2 }}} \\$

6 0

3 years ago