<span>Given the two end of the diameter of the circle, we are able to compute the center of the circle as 0.5*[(-1,3)+(7,-7)]=(3,-2). The radius of the circle is 0.5*sqrt[(-1-7)^2+(3+7)^2]=sqrt(41). Therefore the equation of the circle is (x-3)^2+(y+2)^2=41.</span>
Answer:
Part (a) The value of Z is 0.10396. Part (b) The value of Z is 0.410008.
Step-by-step explanation:
Consider the provided information.
Part (a)
In order to find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.5414, simply find 0.5414 in the table and search for the appropriate Z-value.
Now, observing the table it can be concluded that the value of Z is 0.10396.
Part (b)
Consider the number 65.91%
The above number can be written as 0.6591.
Now, find 0.6591 in the table and search for the appropriate Z-value.
By, observing the table it can be concluded that the value of Z is 0.410008.
This is solved by setting up two equations and then using one to answer the other.
The first step (use what is given to set up the two separate equations)
We are looking for two numbers, let us call them X and Y.
We are told that X + Y = 59
We are also told that (9 more than) 9+ (4times the smaller number) 4Y is the bigger number X
Then we combine that into 9+4Y=X
so we now have two separate equations and we can use one to solve the other. Everywhere we have X in the first equation, we will fill in with the second equation
(9+4Y) +Y = 59 [then combine like terms]
9+5Y=59 [subtract 9 from both sides]
5Y=50 [divide both sides by 5 to isolate the Y]
Y=10 [now plug this into either equation to solve for X]
9+4(10)=X
9+40=X
<u><em>49=X and 10=Y</em></u>
Answer: 150-170 free throws
Step-by-step explanation:
200 times 80% or .8 will give you 160
5% of 200 is 10 so add and subtract that to/from 160 and you'll get your range
