Evaluate 2^3 [(15-7)] (4 divided by 2)].
1 answer:
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Answer:
y = 13*( -x/9 + 1/5)
Step-by-step explanation:
Given:
- The curve has an equation as follows:
Find:
a. Verify that the given point (2,2) lies on the curve.
b. Determine an equation of the line tangent to the curve at the given point.
Solution:
- To verify whether the point lies on the given curve we will substitute the coordinates of the point into the equation as follows:
44 = 5*(2)^2 + 3*(2)(2) + 3*(2)^2
44 = 20 + 12 + 12
44 = 44 ......Hence proven.
- The equation of the line tangent to the curve is expressed as a linear function as follows:
y = m*x + C
Where, m is the gradient of the line.
C is the y-intercept.
m = Δy / Δx = dy/dx
- We will take the derivative of the given curve with respect to x as follows:
- Evaluate y' at the point (2,2) we get:
y' = - ( 10(2) + 3(2) ) / ( 3(2) + 6(2) )
y' = - ( 26 ) / (18)
y'= m = - 13/9
- To evaluate C, we will use the point (2,2) for linear expression above with m as follows:
y = -13*x/9 + C
2 =-13*(2)/9 + C
C = 13 / 5
- The equation of the tangent is as follows:
y = 13*( -x/9 + 1/5)
Answer:
Option D -0.67
Step-by-step explanation:
Given : Preference of Brand A =30% ⇒
Preference of Brand B =70% ⇒
Prefer Brand A and are Female = 20% ⇒
Prefer Brand B and are Female = 40% ⇒
To find : Selected consumer is female, given that the person prefers Brand A
Solution : Using Bayes' theorem, which state that
where, P(A) and P(B) are probabilities of observing A and B.
P(B/A)= is a conditional probability where event B occur and A is true
P(A/B)= also a conditional probability where event A occur and B is true.
Now, applying Bayes' theorem,
Therefore, Option D is correct probability that a randomly selected consumer is female, given that the person prefers Brand A -0.67