Answer:
a) 0.82
b) 0.18
Step-by-step explanation:
We are given that
P(F)=0.69
P(R)=0.42
P(F and R)=0.29.
a)
P(course has a final exam or a research paper)=P(F or R)=?
P(F or R)=P(F)+P(R)- P(F and R)
P(F or R)=0.69+0.42-0.29
P(F or R)=1.11-0.29
P(F or R)=0.82.
Thus, the the probability that a course has a final exam or a research paper is 0.82.
b)
P( NEITHER of two requirements)=P(F' and R')=?
According to De Morgan's law
P(A' and B')=[P(A or B)]'
P(A' and B')=1-P(A or B)
P(A' and B')=1-0.82
P(A' and B')=0.18
Thus, the probability that a course has NEITHER of these two requirements is 0.18.
Answer:
(2, -3) and r = 3.
Step-by-step explanation:
you can also plug this equation in desmos but I guess it's good to know how to do it also:
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2
Now in order to make a perfect square on both sides, we need to do this:
First add 9 to both sides:
x^2 + 6x + 9 + y^2 -4y +4 = 9.
I purposely shifted it to show the perfect square created when you add 9 to both sides. Factor:
(x+3)^2 + y^2 - 4y + 4 = 9.
now the second bolded part is allso a perfect square. Factor:
(x+3)^2 + (y-2)^2 = 9
Based on the equation of a circle, the center must be at (2, -3) and the radius is the square root of 9 which is 3.
:)
Always do brackets first
a) -40/10 = -4
b) 36/4 -2 = 7
c) -2 x 7 = -14
38.4? Since if she runs 24 feet in five seconds add that two times she would run 48 feet in ten second so.. divide 24 with 5 and get 4.8. So 48 minus 9.6 makes 38.4.
See in the explanation
<h2>Explanation:</h2>
<h3>1. Are exponential function one to one. How can you tell?</h3>
- A function
is one-to-one if each value of 
corresponds to exactly one value of 
.
To demonstrate this, we take the Horizontal Line Test that states:
<em>A function has an inverse function if and only if there is no any horizontal line that intersects the graph of at more than one point.</em>
As you can see in the first figure, the horizontal line 
(the green one) intersects the graph of the exponential function 
(the red one) in just one point. If you take every horizontal line 
with 
any real number, you will find that every line intersects the exponential function in just one point. Therefore, this function is one-to-one
<h3>2. What does this tell you about their inverses?</h3>
Another important thing is that:
- A function has an inverse function if and only if is one-to-one.
As we have demonstrated that exponential functions are one-to-one by Horizontal Line Test, then we conclude exponential functions have inverse functions. The domain of the inverse function is the range of the original one and the range of the inverse function is the domain of the original one. The inverse of is 
whose graph is the second figure below.
<h2>Learn more:
</h2>
How to find the inverse of a function? brainly.com/question/9980183
#LearnWithBrainly
