Answer:
108 student tickets, and 176 adult tickets were sold
Step-by-step explanation:
Adult ticket $8 Call the number of adult tickets sold "a"
Student ticket $5 Call the number of student tickets sold "s"
Since we are talking about TWO consecutive days of sold out seats, the total number of seats sold were 2* 142 = 284
Then we create two different equations with the information given:
a + s = 284
8 * a + 5 * s = 1948
we can solve for s in the first equation as follows: s = 284 - a
and use it in the second equation
8 a + 5 (284 - a) = 1948
8 a + 1420 - 5 a = 1948
combining
3 a = 528
a = 528/3
a = 176
we find the number of student tickets using this answer in the substitution equation we used:
s - 284 - 176 = 108
Therefore 108 student tickets, and 176 adult tickets were sold.
The Lagrangian is
It has critical points where the first order derivatives vanish:
From the first two equations we get
Then
At these critical points, we have
(maximum)
(minimum)
6>x take 12 from both sides
Answer:
The chance of an average six-sided number cube landing one one number is 1/6, or approximately 16.67%. When rolling a number cube 100 times, the average number of times it lands on any specific number should be fairly close to 16.67.
A 6 being rolled 42 times and 33 times means that it is <em>very likely</em> not to be a standard number cube. Although we cannot know for certain, the chance of this happening is very low.
It took about 0.66 hour, which is basically 40 minutes.
