You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. Find the probability
that you do not get 10 points. Write your answer as a decimal rounded to the nearest thousandth.
1 answer:
The board that makes the question complete is attached with this answer.
Answer:
The probability that you do not get 10 points is 0.913 (To the nearest thousandths).
Step-by-step explanation:
Given that your dart is equally likely to hit any point inside the square board, we are required to find the probability that you do not get 10 points.
This can be obtained by first obtaining the probability of you getting 10 points, and then subtracting it from 1.
The Probability of Success plus The Probability of Failure of an event is always equal to 1.
Let p be the probability of success, and q be the probability of failure. Then
p + q = 1
=> p = 1 - q
And q = 1 - p
From the attached image, we need to find the area of the entire board, and the area of the circle that contains 10.
Area of entire board = 18² = 324
Area of the circle containing 10 = πr² = π(3²) = 9π
Where r is the radius, 3in.
Probability of hitting 10, P(10) = 9π/324
= 0.08727
≈ 0.087 (to the nearest thousandths)
Now, the probability of not hitting 10
= 1 minus probability of hitting 10.
= 1 - 0.087
= 0.913
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Answer:
The explanations for the graphs are provided down below. Please let me know if you have any questions about my answer.
12 and 13 as written on the worksheet is right.
Step-by-step explanation:
12) The answer given is correct.
The relation between x and y is given as:
with
.
I replaced the word domain with x since the domain is the set of x's for which the relation exists.
We are going to replace x with each of the x's given to see what y corresponds to each.
Let's begin with x=-4.
with
:
.
So (-4,5) is an ordered pair that should be on our graph.
To find this point you move left 4 from origin then up 5. Now you put a dot where you have landed. Your graph does show this point.
Moving on.
Let's do the next x: x=-2.
with
:
.
So (-2,-1) is an ordered pair that should be on our graph.
To find this point you move left 2 from origin and then down 1. Now you put a dot where you have landed. Your graph shows this point as well.
Now x=0.
with
:
So (0,-3) is an ordered pair that should be on our graph.
To find this point you move left and right none and down 3. Now you put a dot where you have landed. Your graph shows this point.
Now the last point will be at x=2.
with
.
So (2,-1) is an ordered pair that should be on our graph.
To find this point you move 2 units right from the origin and then down 1 unit. Now put a dot where you landed. The graph shows this point as well.
13) The answer given is correct.
is the parent function and makes like a V shaped graph where it's vertex is at (0,0).
If we want to move this graph right 3 it becomes:
.
If you move that up once it becomes:
or
which is the curve given.
If you don't know about transformations you can choose a few points to plug in to see what's going on with the graph.
Let's choose x=-5,-3,-1,0,1,3,5.
x=-5
f(-5)=|3--5|+1=|3+5|+1=|8|+1=8+1=9.
There is no room for (-5,9) on our graph but if you extended the left hand side of the absolute value function there you would see that (-5,9) is reached.
x=-3
f(-3)=|3--3|+1=|3+3|+1=|6|+1=6+1=7.
(-3,7) should be a point on the graph. Same thing for this point as (-5,9).
x=-1
f(-1)=|3--1|+1=|3+1|+1=|4|+1=4+1=5.
(-1,5) is located on the graph.
x=0
f(0)=|3-0|+1=|3|+1=3+1=4.
(0,4) is also located on the graph.
x=1
f(1)=|3-1|+1=|2|+1=2+1=3.
(1,3) is located on the graph.
x=3
f(3)=|3-3|+1=|0|+1=0+1=1.
(3,1) is located on the graph.
x=5
f(5)=|3-5|+1=|-2|+1=2+1=3.
(5,3) is located on the graph.
Now if we weren't given the graph already:
I would plot the points I found which were:
(-5,9)
(-3,7)
(-1,5)
(0,4)
(1,3)
(3,1)
(5,3)
We should get a basic idea of what the function looks like from these points.
I will graph them. You will have to connect these points because the domain isn't discrete like number 12 is. That is they didn't list out elements for the domain.
I'm going to graph one more point after x=5.
How about x=7?
So (7,5) is also a point on the graph.
You should see that the blue points are following the red path I made there.
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