Tickets to a school dance cost $4 and the projected attendance is 300 people. For every $0.10 increase in ticket price, the dance committee projects that attendance will decrease by 5.Using formula R(4+.10t) (300-5t) where t is ticket price.

Determine the dance committee's greatest possible revenue. (Please show work as in #'s)

What ticket price will produce the greatest revenue? (Please show work as in #'s)

Answers

Answer 1

Answer: money made (R) = tickets sold * price of ticket
the number of $0.10 increases we make will be called t. so:
price of ticket = $4 + $0.10t
tickets sold = 300 - 5t
R = (4 + .10t)(300 - 5t)
R = 1200 + 10t - .5t^2
R = -1/2t^2 + 10t + 1200
to find the maximum, we have to find the roots of this function.
0 = -1/2t^2 + 10t + 1200
0 = -t^2 + 20t + 2400
0 = t^2 - 20t - 2400
quadratic formula
t = 20 +- sqrt((-20)^2 - 4(1)(-2400)) all over 2(1)
t = 20+-sqrt(400+9600) all over 2
t = 20+-sqrt(10000) all over 2
t = 20+-100 all over 2
t = -80/2 or t=120/2
t = -40 or 60
now find the average of these roots. this will find the "middle" of the parabola, which is where the vertex (maximum) will be.
-40 + 60 all over 2
20/2
10
the vertex is at t=10. plug this into the formula:
R = -1/2t^2 + 10t + 1200
R = -1/2(10)^2 + 10(10) + 1200
R = 50 + 100 + 1200
R = 1350
therefore, the number of 10 cent price increases should be 10, because that will lead to total profits of $1350, the maximum possible. the ticket price will be $5.

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What is 1 - 27/44 = in its simplest form?

Answers

$1 - (27 )/(44)=(44)/(44)-(27 )/(44)=(17 )/(44)$

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$970 at 4 1/4% simple interest for 2 years

Answers

For simple interest
i=prn
where i= interest p=amount invested, r=rate n=time period
i= 970*4 and 1/4 * 2
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The histogram shows the heights in meters of trees in a certain section of a park.How many trees are less than 16 meters tall?

A histogram titled Heights of Trees with Height in meters on horizontal x-axis and Frequency on vertical y-axis

5

9

16

12

Answers

Answer:

Step-by-step explanation:

Final answer:

In a histogram, the total number of trees that are less than 16 meters tall would be the sum of frequencies of all the bars representing heights less than 16 meters. To find this, locate the 16-meter mark on the x-axis and add up the frequencies of all intervals up to and including that point.

Explanation:

The total number of trees that are less than 16 meters tall would be the sum of frequencies of all the bars on the histogram representing heights less than 16 meters. Histograms provide a visual representation of data distribution. The x-axis lists the categories or numbers for the data, in this case tree heights, and the y-axis represents the frequency, or how often a particular height occurs. To find the total number of trees less than 16 meters tall, locate the 16-meter mark on the x-axis and add up the frequencies (height of the bars) of all intervals up to and including that point.