Answer:
12.56 mm²
Step-by-step explanation:
Plug the given values into the area equation
Therefore, the area of the circle is 12.56 mm².
I hope this helps!
Admission to a car show costs $5 for each ticket. After selling only 20 tickets, they decided to lower the price to $3 each. If
2 answers:
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Answer:
0.02275
Step-by-step explanation:
We have been given that the time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. We are asked to find the probability of completing the exam in one hour or less.
We know that 1 hour equals 60 minutes. First of all, we will find the z-score corresponding to 60 minutes.
z = z-score,
x = Sample score,
= Mean,
= Standard deviation.
Now, we will use normal distribution table to find area under z-score of as:
Therefore, the probability of completing the exam in one hour or less is 0.02275.
I know you didn't want an explanation, but I'll give you one anyway.
So, for a function, when you have f(5) = , then you'll put that 5 in for all of the x's in the function.
The first batch of problems gave you the equation f(x) =
+ 3. Now, plug in the numbers given for s and solve.
1. f(5) = <span> + 3 Plug in 5 for x
</span> =
+ 3 Make three into a fraction over 2
= + <span>
Add
= </span><span><span>
</span>2. f(-4) = </span><span> + 3 Plug in -4 for x
= </span><span>
+ 3 Divide -4 by 2
= -2 + 3 Add
= 1
For the next set, you have g(x) = x</span>² + 1.
3. Let's split this up. Solve the first equation, then the second, and then put the answers together to solve it.
g(4) = x² + 1 Plug in 4 for x
= 4² + 1 Square
= 16 + 1 Add
= 17
g(3) = x² + 1 Plug in 3 for x
= 3² + 1 Square
= 9 + 1 Add
= 10
Now, put the two together.
g(4) + g(3) = Substitute in the answers you just got.
17 + 10 = Add
= 27
4. g(-1) = x² + 1 Substitute in -1 for x
= (-1)² + 1 Square
= 1 + 1 Add
= 2
5. g(-6) = x² + 1 Plug in -6 for x
= (-6)² + 1 Square
= 36 + 1 Add
= 37
For the last set, we have h(x) = x² + 7 and k(x) = 4x - 5. We'll have to pay close attention to the starting variables here.
6. h(-6) = x² + 7 Plug in -6 for x
= (-6)² + 7 Square
= 36 + 7 Add
= 43
k(4) = 4x - 5 Plug in 4 for x
= 4(4) - 5 Multiply
= 16 - 5 Subtract
= 11
Put the two answers into the final equation.
h(-6) + k(4) = Substitute in the answers you got
43 + 11 = Add
= 54
7. k(10) = 4x - 5 Plug in 10 for x
= 4(10) - 5 Multiply
= 40 - 5 Subtract
= 35
h(2) = x² + 7 Plug in 2 for x
= 2² + 7 Square
= 4 + 7 Add
= 11
Now, put those into the equation.
k(10) - h(2) = Plug in the answers you got
35 - 11 = Subtract
= 24
8. For this one, it wants you to add h(x) and k(x). We don't need to plug anything into the equations this time because they're both already solved for x! So, you can just set this up like a standard find-x equation.
(x² + 7) + (4x - 5) =
x² + 7 + 4x - 5 = Combine like terms (7 and -5)
x² + 2 + 4x = Reorder so the variables come first
= x² + 4x + 2
So, for a function, when you have f(5) = , then you'll put that 5 in for all of the x's in the function.
The first batch of problems gave you the equation f(x) =
1. f(5) = <span>
</span> =
=
= </span><span><span>
</span>2. f(-4) = </span><span>
= </span><span>
= -2 + 3 Add
= 1
For the next set, you have g(x) = x</span>² + 1.
3. Let's split this up. Solve the first equation, then the second, and then put the answers together to solve it.
g(4) = x² + 1 Plug in 4 for x
= 4² + 1 Square
= 16 + 1 Add
= 17
g(3) = x² + 1 Plug in 3 for x
= 3² + 1 Square
= 9 + 1 Add
= 10
Now, put the two together.
g(4) + g(3) = Substitute in the answers you just got.
17 + 10 = Add
= 27
4. g(-1) = x² + 1 Substitute in -1 for x
= (-1)² + 1 Square
= 1 + 1 Add
= 2
5. g(-6) = x² + 1 Plug in -6 for x
= (-6)² + 1 Square
= 36 + 1 Add
= 37
For the last set, we have h(x) = x² + 7 and k(x) = 4x - 5. We'll have to pay close attention to the starting variables here.
6. h(-6) = x² + 7 Plug in -6 for x
= (-6)² + 7 Square
= 36 + 7 Add
= 43
k(4) = 4x - 5 Plug in 4 for x
= 4(4) - 5 Multiply
= 16 - 5 Subtract
= 11
Put the two answers into the final equation.
h(-6) + k(4) = Substitute in the answers you got
43 + 11 = Add
= 54
7. k(10) = 4x - 5 Plug in 10 for x
= 4(10) - 5 Multiply
= 40 - 5 Subtract
= 35
h(2) = x² + 7 Plug in 2 for x
= 2² + 7 Square
= 4 + 7 Add
= 11
Now, put those into the equation.
k(10) - h(2) = Plug in the answers you got
35 - 11 = Subtract
= 24
8. For this one, it wants you to add h(x) and k(x). We don't need to plug anything into the equations this time because they're both already solved for x! So, you can just set this up like a standard find-x equation.
(x² + 7) + (4x - 5) =
x² + 7 + 4x - 5 = Combine like terms (7 and -5)
x² + 2 + 4x = Reorder so the variables come first
= x² + 4x + 2