There are 143 men. There are 65 education majors. There are 26 men who have an education major. So, the total number of students who meet the criteria (man or education major) = Total number of Men + Total number of Education Majors - Total number of men with education majors = 143 + 65 - 26 = 182.
There are a total of 291 students. So, the probability that the student was a man or education major = 182 / 291 = 0.625.
Answer:
1/3n=12
Step-by-step explanation:
The reason why it is 1/3n=12, is because you know that the number in front of n is 1/3. By figuring that out, you have already ruled out 3n=12 and 3n=-12. Finally, you know that 12 is a positive number leaving you with 1/3n=12.
(a) The integral is equal to the area of the triangle; it has height 20 and base 10, so the area is 20*10/2 = 100.
(b) The integral is equal to the area of the semicircle with radius 10. It's also under the horizontal axis, so the area is negative. The semicircle has area
, so the integral is -50π.
(c) First compute

which is the area of the triangle on the right. It has height and base 5, so its area is 25/2.
Then split up the desired integral as

and plug in the integral values you know:

we have

Find the roots
Equate the function to zero

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.


Rewrite as perfect squares

Square root both sides




therefore
<u>the answer is</u>
