Let be the random variable for the number of marks a given student receives on the exam.
10% of students obtain more than 75 marks, so
where follows a standard normal distribution. The critical value for an upper-tail probability of 10% is
where denotes the CDF of , and denotes the inverse CDF. We have
Similarly, because 20% of students obtain less than 40 marks, we have
so that
Then are such that
and we find
Answer:
88 square inches
Step-by-step explanation:
if the entire square was shaded it would be 14 x 12 (as best as i can see)
the "cut out" or white part of the square is 8 x 10
Entire squre - cutout white part
14 x 12 - 8 x 10
168 - 80
88 sq in
Answer:
(-3, -3)
Step-by-step explanation:
1.) Rewrite the second equation so 3y is on one side of the equation:
3y=6+5x
2.) Substitute the given value of 3y (replacing 3y with 6+5x, since we know they equal each other) into the equation 17x=-60-3y
Should end up with this:
17x=-60-(6+5x)
3.) Solve 17x=-60-(6+5x)
Calculate Difference: 17x=-66-5x
Combine Like Terms: 22x = -66
Divided both sides by 22 to isolate and solve for x: -3
So We know x=-3, now we got to find the y value. We can use either the first or second equation to find y value, so lets use the second.
3y=6+5x
1.) We know that x=-3, so we can simply substitute x in the equation
3y=6+5x with -3
3y=6+5(-3)
2.) Solve 3y=6+5(-3)
Combine Like Term: 3y=6+-15
Combine Like Term Even More: 3y= -9
Divide by 3 on both sides to isolate and solve for y: y=-3
So now we know y=-3 and once again we know x=-3, so if we format that
(-3,-3)
^ ^
x y
If you need any steps explained lmk