Answer:
The value is 
Step-by-step explanation:
From the question we are told that
The probability that the student knows the answer to the question is 
The probability that that the student will guess is 
The probability that that the student get the correct answer given that the student guessed is 
Here W denotes that the student gets the correct answer
Generally it a certain fact that if the student knows the answer he would get it correctly
So the probability the the student got answer given that he knows it is

Generally from Bayes theorem we can mathematically evaluate the probability that the student knows the answer given that he got it correctly as follows

=> 
=> 
Answer:
Each of the remote angles shares one side with the angle adjacent to the exterior angle. The equation means that the sum of measures of the remote interior angles is equal to the measure of the exterior angle of the triangle.
If it is perpendicular to the line 14x-7y=4, then we know our line has the opposite and inverse slope of that line. Solving for y of the first line, we get y=2x-(4/7). All we care about is the coefficient of the x term, because that will give us our slope. The slope of the first line is 2, so the slope of out line is the opposite and inverse of that slope, which -(1/2).
Plugging into our slope- point formula, where y1=(-9), x1=2, and m=(-1/2), then:
y-(-9)=(-1/2)(x-2)
y+9=(-1/2)x+1
y=(-1/2)x-8
Answer:
Part 1) The unit rate is 
Part 2) The unit rate is 
Part 3) The unit rate is 
Part 4) The unit rate is 
see the attached figure
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to

where
d ----> number of dollars (dependent variable or output value)
n ---> number of ounces (independent variable or input value)
Remember that the slope of the linear equation is the same that the unit rate
<u><em>Verify each case</em></u>
1) we have

This is a proportional relationship between the variables d and n
The slope is

therefore
The unit rate is 
2) we have
<em>First table</em>
take two points from the table
(4,1) and (16,4)
substitute in the formula of slope



simplify

therefore
The unit rate is 
3) we have

This is a proportional relationship between the variables d and n
isolate the variable d

The slope is

therefore
The unit rate is 
4) we have
<em>Second table</em>
take two points from the table
(1,4) and (2,8)
substitute in the formula of slope



therefore
The unit rate is 