Abdul rolls a fair six-sided die and a fair four-sided die simultaneously. The sample space of all possible outcomes is shown be
low.
Let A be the event that the six-sided die is three and B be the event that Abdul rolls doubles (rolls the same number on each die).
What is P(A or B) , left parenthesis, the probability that the six-sided die is three or Abdul rolls doubles?
Let A be the event that the six-sided die is three and B be the event that Abdul rolls doubles (rolls the same number on each die).
What is P(A or B) , left parenthesis, the probability that the six-sided die is three or Abdul rolls doubles?
1 answer:
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Hello!
If this long ribbon measures 144 feet, you can see, it was only multiplied by one number, which has the be the diameter of a column to get our circumference. If we divide this by our diameter 6 (diameter is double the radius, 3), we get our answer below.
144/6=24
Therefore, our answer is C) 24.
I hope this helps!
Answer:
Horizontal shift to the RIGHT of <u>one unit</u>
Step-by-step explanation:
When looking at a square root equation, the transformation form is:
'h' represents a horizontal shift of the graph. Therefore, in this instance:
This means that there is a horizontal shift to the RIGHT of <u>one unit.</u>
Answer:
Part A)
Part B)
Step-by-step explanation:
Please refer to the table of values.
Part A)
A. 1)
We want to find f(1).
According to the table, when x=1, f(x)=2.
Hence, f(1)=2.
A. 2)
We want to find f⁻¹(1).
Notice that when x=0, f(x)=1.
So, f(0)=1.
Then by definition of inverses, f⁻¹(1)=0.
A. 3)
We want to find f’(1).
According to the table, when x=1, f’(x)=1.4.
Hence, f’(1)=1.4.
A. 4)
We will need to do some calculus.
Let g(x) equal to f⁻¹(x). Then by the definition of inverses:
Take the derivative of both sides with respect to x. On the left, this will require the chain rule. Therefore:
Solve for g’(x):
Substituting back f⁻¹(x) for g(x) yields:
Therefore:
We already determined previously that f⁻¹(1) is 0. Therefore:
According to the table, f’(0) is 0.7. So:
Hence, (f⁻¹)’(1)=10/7.
Part B)
We want to find the equation of the tangent line of y=f⁻¹(x) at x=4.
First, let’s determine the points. Since f(2)=4, this means that f⁻¹(4)=2.
Hence, our point is (4, 2).
We will now need to find our slope. This will be the derivative at x=4. Therefore:
We know that f⁻¹(4)=2. So:
Evaluate:
Now, we can use the point slope form. Our point is (4, 2) and our slope at that point is 5/14.
So:
Solve for y:
Adding 2 to both sides yields:
Hence, our equation is: