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Answer:
a. 40 %
b. 34.3 % ( approx )
Step-by-step explanation:
Let S is the event of the subjects studied that were sent to prison,
S' is the event of the subjects studied that won't sent to prison,
G is the event of pleading guilty,
G' is the event of not pleading guilty,
According to the question,
P(S) = 60% = 0.6 ⇒ P(S') = 1 - P(S) = 1 - 0.6 = 0.4,
P(S∩G) = 46% of 60% = 0.46 × 0.60 = 0.276,
P(S'∩G) = 36% of 40% = 0.36 × 0.40 = 0.144,
P(G) = P(S∩G) + P(S'∩G) = 0.276 + 0.144 = 0.42
a. The of getting someone who was not sent to prison, P(S') = 0.4,
b. the probability that this person was not sent to prison when it is given that the subject entered a guilty plea,
Cot θ = -24/7 and cos θ < 0
"cos θ < 0" means cosine is negative
Remember osmething like "ALL students Take Calculus"?
all is positive in quadrant 1
sine/cosecant is positive only in quadrant 2
tangent/cotangent is positive only in quadrant 3
cosine/secant is positive only in quadrant 4
since cot(angent) is the reciprocal of tangent, tangent must also be negative.
tangent is negative in quadrants II and IV
cosine is negative in quadrants II and III
therefore, θ must lie in quadrant II.
remember the tan θ = y / x. it is the y-coordinate divided by the x-coodinate. the y-coordinate would be the height of this 90 degree triangle that forms. the x-coordinate would be the bottom leg of the 90 degree triangle
then cot θ = x / y. therefore, cot θ = -24 / 7 means x = -24 and y = 7. we draw a triangle with these dimensions.
csc θ = r / y = hypotenuse over opposite (when you view the reference angle labeled as the one to base the hypotenuse/oppoiste on) because it is the reciprocal of sine
the hypotenuse can be found w/ pythagorean theorem
hypotenuse = √[(-24)² + 7²] = 25
therefore,
cot θ = 25/7
"cos θ < 0" means cosine is negative
Remember osmething like "ALL students Take Calculus"?
all is positive in quadrant 1
sine/cosecant is positive only in quadrant 2
tangent/cotangent is positive only in quadrant 3
cosine/secant is positive only in quadrant 4
since cot(angent) is the reciprocal of tangent, tangent must also be negative.
tangent is negative in quadrants II and IV
cosine is negative in quadrants II and III
therefore, θ must lie in quadrant II.
remember the tan θ = y / x. it is the y-coordinate divided by the x-coodinate. the y-coordinate would be the height of this 90 degree triangle that forms. the x-coordinate would be the bottom leg of the 90 degree triangle
then cot θ = x / y. therefore, cot θ = -24 / 7 means x = -24 and y = 7. we draw a triangle with these dimensions.
csc θ = r / y = hypotenuse over opposite (when you view the reference angle labeled as the one to base the hypotenuse/oppoiste on) because it is the reciprocal of sine
the hypotenuse can be found w/ pythagorean theorem
hypotenuse = √[(-24)² + 7²] = 25
therefore,
cot θ = 25/7