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,
.
For the 2 largest classrooms we distribute n = 50 chairs. Here k = 2, thus the total amount of ways to distribute them is
.
For the 3 remaining classrooms (k=3) we need to distribute the remaining 50 chairs, here we have
ways of making the distribution.
As a result, the total amount of possibilities for the chairs to be distributed is 51*1326 = 67626.
Answer:
x = 40
Step-by-step explanation:
The figure shows two similar triangles. Thus, the side lengths of similar triangles are proportional to each other. Therefore:


Cross multiply


Subtract 24x from each side


Divide both sides by -15

x = 40
The increase is D: 50% because the 1 in the parentheses stands for the 20 that was already there, with the .5 being the amount that’s actually being increased. 0.5 translates to 50%, so the answer is D.
Answer:
In 2015, the financial statements of Ultimate Medical Center reported $500,000 in total revenues and $145,000 in net income. The balance sheet showed net assets of $350,000. Calculate the operating margin ratio and the return on equity rate for Ultimate Medical Center.
Step-by-step explanation: