I need help. PLEASE, I dont know what to do

Can someone please solve this problem for me

notsponge [240]

Answer:

D. 28.54

Step-by-step explanation:

To find the area of the shaded region, find the area of the circle and divide it in 4. This will the area of the portion with the triangle.

Now, find the area of the triangle and subtract the two. The resulting value will be the area of the shaded region.

Circle:

$A = \pi r^2\\A = \pi 10^2\\A = 100 \pi\\A = 314$

Divide by 4 for the area of the section with the triangle.

314/4 = 78.5

Triangle:

$A = \frac{1}{2}bh\\A = 0.5 (10 )(10)\\A=0.5(100)\\A=50$

Subtract the two, 78.5 - 50 = 28.5.

7 0

2 years ago

In how many ways can 100 identical chairs be distributed to five different classrooms if the two largest rooms together receive

Eva8 [605]

Answer:

There are 67626 ways of distributing the chairs.

Step-by-step explanation:

This is a combinatorial problem of balls and sticks. In order to represent a way of distributing n identical chairs to k classrooms we can align n balls and k-1 sticks. The first classroom will receive as many chairs as the amount of balls before the first stick. The second one will receive as many chairs as the amount of balls between the first and the second stick, the third classroom will receive the amount between the second and third stick and so on (if 2 sticks are one next to the other, then the respective classroom receives 0 chairs).

The total amount of ways to distribute n chairs to k classrooms as a result, is the total amount of ways to put k-1 sticks and n balls in a line. This can be represented by picking k-1 places for the sticks from n+k-1 places available; thus the cardinality will be the combinatorial number of n+k-1 with k-1, ${n+k-1 \choose k-1}$ .

For the 2 largest classrooms we distribute n = 50 chairs. Here k = 2, thus the total amount of ways to distribute them is ${50+2-1 \choose 2-1} = 51$ .

For the 3 remaining classrooms (k=3) we need to distribute the remaining 50 chairs, here we have ${50+3-1 \choose 3-1} = {52 \choose 2} = 1326$ ways of making the distribution.