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3 years ago

Using the law of sines, find the solutions for the missing inputs.

Mathematics

1 answer:

SashulF [63]3 years ago

5 0

$\frac{a}{ \sin(a) } = \frac{b}{ \sin(b) }$
$\frac{12}{ \sin(38) } = \frac{b}{ \sin(85) }$
$\frac{12}{ \sin(38) } = \frac{a}{ \sin(57) }$
$180 - (85 + 38) = 57$
$\frac{12}{ \sin(38) } = \frac{b}{ \sin(85) }$
$\sin(85) \times \frac{12}{ \sin(38) } = b$
$\sin(57) \times \frac{12}{ \sin(38) } = a$
sorry for the order of steps

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Yahoo creates a test to classify emails as spam or not spam based on the contained words. This test accurately identifies spam (

Amiraneli [1.4K]

Answer and Step-by-step explanation:

The computation is shown below:

Let us assume that

Spam Email be S

And, test spam positive be T

Given that

P(S) = 0.3

$P(\frac{T}{S}) = 0.95$

$P(\frac{T}{S^c}) = 0.05$

Now based on the above information, the probabilities are as follows

i. P(Spam Email) is

= P(S)

= 0.3

$P(S^c) = 1 - P(S)$

= 1 - 0.3

= 0.7

ii. $P(\frac{S}{T}) = \frac{P(S\cap\ T}{P(T)}$

$= \frac{P(\frac{T}{S}) . P(S) }{P(\frac{T}{S}) . P(S) + P(\frac{T}{S^c}) . P(S^c) }$

$= \frac{0.95 \times 0.3}{0.95 \times 0.3 + 0.05 \times 0.7}$

= 0.8906

iii. $P(\frac{S}{T^c}) = \frac{P(S\cap\ T^c}{P(T^c)}$

$= \frac{P(\frac{T^c}{S}) . P(S) }{P(\frac{T^c}{S}) . P(S) + P(\frac{T^c}{S^c}) . P(S^c) }$

$= \frac{(1 - 0.95)\times 0.3}{ (1 -0.95)0.95 \times 0.3 + (1 - 0.05) \times 0.7}$

= 0.0221

We simply applied the above formulas so that the each part could come

8 0

3 years ago

Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rat

butalik [34]

Answer:

8,000-24x

Step-by-step explanation:

there's 24 months in 2 years. If it's value decreased from 8,000 at a constant rate over a 2 year period, the equation would be 8,000-24x

5 0

3 years ago

Read 2 more answers

What is the quotient of 1,387÷19?

Rus_ich [418]

73

73 * 19 = 1,387

Hope I helped you!

3 0

3 years ago

If the same BLANK number is multiplied to each side of a true inequality, the inequality sign is reversed to make the resulting

Maurinko [17]

Answer: Negative
If the same negative number is multiplied to each side of a true inequality, then the inequality sign flips to make the new inequality true as well

Example:
Take 1 < 5 and multiply both sides by -2 and we get -2 > -10. The "less than" sign flips to "greater than" since -2 < -10 is false. The value of -10 is further to the left of -2 so -10 is smaller in value. The negative basically takes the complete opposite which is why the flip must happen.

This sign flip rule does not happen if you multiply both sides by a positive number.

5 0

3 years ago

Solve for x & y solve x = 3 + yy = -2x + 9

sergey [27]

x = 3 + y Eqn(1)

y = -2x + 9 Eqn(2)

Let us solve the system of equations with the substitution method

x - 3 = y (Subtracting 3 from both sides of the Eqn(1))

Replacing y = x - 3 in Eqn (2), we have:

x - 3 = -2x + 9

x = -2x + 9 + 3 (Adding 3 to both sides of the equation)

x + 2x = 9 + 3 (Adding 2x to both sides of the equation)

3x = 12 ( Adding like terms)

x = 12/3 (Dividing by 3 on both sides of the equation)

x = 4

Replacing x=4 in Eqn(1), we have:

4 = 3 + y

4 - 3 = y (Subtracting 3 from both sides of the equation)

y=1

The answers are:

x= 4 and y=1

6 0

1 year ago