When the admission price for a baseball game was $5 per ticket, 35,000 tickets were sold. When the price was raised to $6, only 30,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively.
(a)
Find the profit P as a function of x, the number of tickets sold
Answers
The profit function is P(x) = ( - x² / 5000 ) + 11.9x - 95000.
35,000 baseball game tickets were sold at $5 per ticket.
When the price is raised to $6, then 30,000 tickets were sold.
The variable and fixed costs for the ballpark owners are $0.10 and $95,000 respectively.
Let's say x is the number of tickets sold, and P is the profit.
Then,
P = ax + b
At P = 5,
5 = (35000)a + b ---------(1)
At P = 6,
6 = (30000)a + b --------(2)
Subtracting (2) from (1),
5 - 6 = (35000)a + b - (30000)a - b
- 1 = 5000(a)
a = ( - 1/5000)
So if a = ( - 1/5000),
Then,
5 = (35000)a + b
5 = (35000)( - 1 / 5000 ) + b
5 = - 7 + b
b = 12
Therefore,
P(x) = ( - x /5000) + 12
Now, the profit function is:
Profit = Revenue - Costs
P(x) = R(x) - C(x)
Now, R(x) = xp(x)
R(x) = x[ ( - x/5000) + 12]
R(x) = ( - x² / 5000 ) + 12x
The fixed cost is F(x) = $95000
Hence, the costs will be:
C(x) = 95000 + (0.10)x
Therefore the profit function is:
P(x) = R(x) - C(x)
P(x) = ( - x² / 5000 ) + 12x - 95000 - (0.10)x
P(x) = ( - x² / 5000 ) + 11.9x - 95000
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Related Questions
A search committee is formed to find a new software engineer.
a) if 100 applicants apply for the job, how many ways are there to select a subset of 9 for a short list?
b) If 6 of the 9 are selected for an interview, how many ways are there to pick the set of people who are interviewed?
c) Based on the interveiw, the committe wil rank the top three candidates and submit the list to their boss who will make the final decision. How many ways are there to select the list from the 6 interviews?
Answers
Answer:
(a) 1,902,231,808,400
(b) 84
(c) 20
Step-by-step explanation:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
\({n\choose k}=\frac{n!}{k!\cdot(n-k)!}\)
(a)
Compute the number of ways to select 9 applicants from 100 as follows:
\({100\choose 9}=\frac{100!}{9!\cdot(100-9)!}\)
\(=\frac{100!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92}{9!}\\\\=1902231808400\)
(b)
Compute the number of ways to select 6 people from 9 as follows:
\({9\choose 6}=\frac{9!}{6!\cdot(9-6)!}\)
\(=\frac{9!}{6!\times 3!}\\\\=\frac{9\times 8\times 7\times 6!}{6!\times 3!}\\\\=\frac{9\times 8\times 7}{3!}\\\\=84\)
(c)
Compute the number of ways to select top 3 candidates from 6 as follows:
\({6\choose 3}=\frac{6!}{3!\cdot(6-3)!}\)
\(=\frac{6!}{3!\times 3!}\\\\=\frac{6\times 5\times 4\times 3!}{3!\times 3!}\\\\=\frac{6\times 5\times 4}{3!}\\\\=20\)
can someone plaese help me
Answers
i don’t see nothing
Xx
Which equation models the rational function shown in
the graph?
2(x+2)
X-2
O f(x) =
O f(x) = x-2
x+2
2(x-2)
x+2
Of(x)=.
O f(x) = x+2
X-2
Answers
At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
From given graph we can see that
At x=2, the function in the graph is approaches to infinity.
It means function is not defined at x=2
We know that a rational function is undefined when denominator is equal to zero.
For equation 1:
f(x)= 2(x+2)/(x-2)
Equating the denominator:
x-2=0
x=2
It means function is not defined at x=2
The y-intercept is: y= -2
The function is passing through the point (1,-6).
When we substitute x=1
Hence, option 1 is true.
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Which point is located in quadrant IV?
(–2, –4)
(–2, 4)
(2, –4)
(2, 4)
Answers
Answer:
the 3rd one (2,-4)
Step-by-step explanation:
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Use your calculator to work out
17.5? – 106
(7.2 + 1.092
Write down all the figures on your calculator display.
Answers
Answer:
1) -88.5
2) 8.292
Step-by-step explanation:
17.5 - 106 = -88.5
7.2 + 1.092 = 8.292
You have a map of Southern California. If the distance between
Mrs. Clough's house and Badger Springs middle school on the map
is 3 inches, and the scale is 2 inches represents 12 miles, how far is
the actual distance from Mrs. Clough's house to school.
Answers
9514 1404 393
Answer:
18 miles
Step-by-step explanation:
The map distance and ground distance are proportional.
(distance to school)/(3 in) = (12 miles)/(2 in)
Multiplying by 3 in gives ...
distance to school = (12 miles)(3/2) = 18 miles
Write 5x – 4y = 10 in slope-intercept form
Answers
A population of 40 bees double every month. How many will he have in 8 months?
Answers
Answer:
640 bees
Step-by-step explanation:
8 multiplied by 2 = 16
16 multiplied by 40 = 640
What is the probability that either event will occur? 3 A 18 B 15 P(A or B) = P(A) + P(B) P(A or B) = [?] Enter as a decimal rounded to the nearest hundredth.
Answers
Answer:
the probability that either event will occur is 0.92
Step-by-step explanation:
the probability that either event will occur is 0.92
What is the probability that either event will occur?
From the question, we have the following parameters that can be used in our computation:
Event A = 18
Event B = 15
Other Events = 3
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 18 + 15 + 3
Evaluate
Total = 36
So, we have
P(A) = 18/36
P(B) = 15/36
For either events, we have
P(A or B) = 33/36 = 0.91666
Hence, the probability that either event will occur is 0.92 (rounded to nearest hundreth)
I'll mark whoever answers first!! Please help me
Answers
Answer:
Center ( -8, 1 )
Radius ( 13 )
Please help I will give anyone brainliest
Answers
Answer:
1672.50 = 37.75x + 1068.50
x = 16
There were 16 players brought to the tournament.
Step-by-step explanation:
y = mx + b
y= the total cost
m = cost of each meal
x = the number of players
b = cost of the bus
Plug in what you know and solve for x
1672.50 = 37.75x + 1068.50 Subtract 1068.50 from both sides.
604 = 37.75x Divide both sides by 37.75
16 = x
Equation: 1068.50 + 37.75x =1,672.50
Answer: X= 16
If 1,672.50 is our total it will go behind the equal sign. 37.75x and 1068.50 must be added together to help us receive our total.
Our written equation should look like this
1068.50 + 37.75x =1,672.50
X is the number of players on the team.To find out we must first subtract the amount of money spent on the bus, from the total amount spent.
1,672.50-1068.50 is 604. This means our equation now looks like this
37.75x=604. The next and final step is to divide 37.75 into 604.
604/ 37.75 is 16. Which means that there are 16 players on the team.
I hope this helps & Good luck.
help please, help me
Answers
Answer:
7.07 in^2 is what i got
Keith receives $25000 salary for working as a account. If keith spends 40% of his salary on expenses each year, then how much money does Keith have to spend on expenses? Round your answer to the nearest whole number if necessary.
Answers
Answer:
$25000 * 40% = 100.000
Step-by-step explanation:
10,000 on expenses. 25000X.40=10,000
Find the area of each figure. Round to the hundredths where necessary. 11 in 7 in 8.1 in 15 in
Answers
we are asked to determine the area of the following figure:
we have divided the figure into a rectangle and a triangle. The total area is the sum of the areas of both figures. First, we will find the area of the rectangle:
\(\begin{gathered} A_1=(7in)(11in) \\ A_1=77in^2 \end{gathered}\)Now we will find the area of the triangle using the following formula:
\(A_2=\frac{bh}{2}\)Where "b" is the base and "h" is the height. The base is found by subtracting the dimension on top to the dimension of the bottom:
\(b=15in-11in=4in\)Now we will use the formula:
\(A_2=\frac{(4in)(7in)}{2}\)Solving the operations:
\(A_2=14in^2\)Now we add both areas:
\(\begin{gathered} A=A_1+A_2 \\ A=77in^2+14in^2 \\ A=91in^2 \end{gathered}\)Therefore, the area of the figure is 91 square inches.
A city has 5 new houses for every 9 old houses. If there are 35 new houses in the city, how many old houses are there?
Answers
Answer:
20 I guess
Step-by-step explanation:
because maybe 1 is 9
A grocery store clerk has 16 oranges, 20 apples, and 24 pears. The clerk needs to put an equal number of apples, oranges, and pears into each basket. What is the greatest number of baskets that can be made so that no fruit is left?
Answers
Answer:
4 oranges, 5 apples, 6 pears in each bag
Step-by-step explanation:
theyre all divisible by 4
A population of insects can double in 30 days. After
80 days, how many times greater will the population be than
after 30 days?
Answers
Answer:
about 2.666 times
Step-by-step explanation:
you know that 80 days have past and it only takes 30 days for the population to double. if you do 80/30 you get 2.666 meaning that the population would of been 2.666 times greater.
The population be than after 30 days about 2.666 times greater.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given; A population of insects can double in 30 days.
After 80 days, We need to find that how many times greater will the population be than after 30 days
We know that 80 days have past and it only takes 30 days for the population to double.
if we do 80/30 = 2.666 meaning that the population would of been 2.666 times greater.
Therefore, The population be than after 30 days about 2.666 times greater.
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Find the distance between the points P and Q shown.
Answers
The distance between points P and Q is √73
How to find the distance between the two points?First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:
distance = √( (a - c)² + (b - d)²)
Here we can see that the coordinates of the two shown points are:
P = (-3, 2)
Q = (5, -1)
Replacing that in the distance formula we will get:
distance = √( (-3 - 5)² + (2 + 1)²)
distance = √( (-8)² + (3)²)
distance = √73
So the correct option is the third one.
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Find the equation of the line which passes through (−2, 3) and the point of intersection of the lines x + 2y=0 and 2x − y − 12=0.
Answers
Answer:
First, let's find where the lines:
x + 2y = 0
2x - y - 12 = 0
intersect.
First, let's isolate the variable y in one side of the equalities.
y = (-x/2)
y = 2x - 12
Now we have:
-(x/2) = 2x - 12
We can solve this for x.
12 = 2*x + x/2 = 2.5*x
12/2.5 = x = 4.8
Then, replacing that value in any of the lines, we can find the value of y.
y = 2*8 - 12 = 2*4.8 - 12 = -2.4
Then those lines intersect in the point (4.8, -2.4)
Now we want to find the line that passes through the points (-2, 3) and (4.8, -2.4)
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then, the slope for our line is:
a = (3 - (-2.4))/(-2 - 4.8) = -0.79
And the
y-intercept will be:
y = -0.79*x + b
when x = -2, y = 3.
3 = -2*-0.79 + b
3 - 2*0.79 = b = 1.42
The line is:
y = -0.79*x + 1.42
actions with Unlike Denominators Find the sum. Give your answer in simplest form. 3 16 + 5 8
Answers
9514 1404 393
Answer:
13/16
Step-by-step explanation:
The sum can be found by rewriting the second fraction to have the same denominator as the first.
\(\dfrac{3}{16}+\dfrac{5}{8}=\dfrac{3}{16}+\dfrac{2\cdot5}{2\cdot8}=\dfrac{3}{16}+\dfrac{10}{16}=\dfrac{3+10}{16}=\boxed{\dfrac{13}{16}}\)
Pls help me with this question
Answers
The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.
When two lines intersect, then their opposite angles are equal. Then the equation is given as,
m° + 66° + m° = 120°
Simplify the equation for m, then the value of 'm' is calculated as,
m° + 66° + m° = 120°
2m° = 120° - 66°
2m° = 54°
m° = 27°
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The average age for the 62 observed milk cows as they first produced
Answers
Answer:
32
Step-by-step explanation:
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Rebecca and Blake decide to roll a pair of fair 6-sided dice to determine who has to clean their dishes.
If the sum is 5 or 6, then Rebecca will clean the dishes.
If the sum is 8 or 9, then Blake will clean the dishes.
If the sum is anything else, they'll roll again.
Is this a fair way to decide who cleans the dishes? Why or why not?
Answers
Answer:
it's not fair
Step-by-step explanation:
... if Rebecca rolled the dice it's most likely going to give a 6 or a higher number if Blake rolled the same too would have happened thus it would be fair if the dice was 3 sided
Rebecca and Blake decide to roll a pair of fair 6-sided dice to determine who has to clean their dishes. If the sum is 5 or 6, then Rebecca will clean the dishes. If the sum is 8 or 9, then Blake will clean the dishes. If the sum is anything else, they'll roll again. This is a fair method of decision making by law of probability because both Rebecca and Blake are equally likely to wash the dishes.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
Total number of observations in sample space when a pair of dice is rolled = 6² = 36
Number of observations where sum is 5 or 6 = 9
((1,4)(4,1)(2,3)(3,2)(1,5)(5,1)(4,2)(2,4)(3,3))
Probability that Rebecca will clean the dishes = 9/36 = 0.25
Number of observations where sum is 8 or 9 = 9
((2,6)(6,2)(3,5)(5,3)(4,4)(3,6)(6,3)(4,5)(5,4))
Probability that Blake will clean the dishes = 9/36 = 0.25
Since, the probabilities of Rebecca and Blake cleaning the dishes are equal, the method of decision making is fair.
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The perimeter of a rectangular garden is 40 it. The length is 2 ft more than the width. Find the length and the width of the garden.
Answers
Answer: Length = 11
Width = 9
Step-by-step explanation:
Let x represent the unknown length.
Let x - 2 represent the unknown width.
The perimeter is equal to 2 times x + (x -2)
Equation:
2 (x + (x - 2)) = 40
x + (x - 2) = 40/2
x + x - 2 = 20
2x - 2 = 20
2x -2 + 2 = 20 + 2
The length is: 2x = 22 -> x = 22/2 -> x = 11
The width is: x - 2 = 9
40
100%
Complete the table to show different percentages of the steaming time.
Time (min)
Percentage
100% of 40 min
50% of 40 min
250% of 40 min
Answers
The percentages to complete the table for the steaming time are 40 min, 20 min and 100 min respectively
How to complete the table to show different percentages of the steaming time?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given: Percentage: 100% of 40 min, 50% of 40 min and 250% of 40 min
100% of 40 min:
100% of 40 min = (100/100) × 40 min = 1 × 40 min = 40 min
50% of 40 min:
50% of 40 min = (50/100) × 40 min = 0.5 × 40 min = 20 min
250% of 40 min:
250% of 40 min = (250/100) × 40 min = 2.5 × 40 min = 100 min
Therefore, the value of the percentages to complete the table for the steaming time are 40 min, 20 min and 100 min for 100% of 40 min, 50% of 40 min and 250% of 40 min respectively.
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Sarah has two pizzas each pizza is cut into 10 equal slices she and her friends 14
slices what part of the pizza did they eat and how much is left right your answer as a decimal
Answers
The quotient of fifteen and five subtracted from seven
Answers
Answer:
4
Step-by-step explanation:
7 - (15 / 5)
7 - (3)
= 4
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A 2-gallon container of disinfectant costs $20.48. What is the price per cup?
Answers
Answer:
$0.64 per cup
Step-by-step explanation:
There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:
1 gallon: 16 cups
2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups
So we need to find the price of each cup:
1 cup = ($20.48 / 32 cups) = $0.64 per cup.
Four scenarios of statistical studies are given below. Decide which study uses a sample statistic.
Answers
A sample statistic is the specific group that you will collect data from.
What is a sample statistic?A sample statistic is any number derived from your sample data. The sample average, median, sample standard deviation, and percentiles are some examples. Because it is based on data obtained through random sampling, which is a random experiment, a statistic is a random variable. As a result, a statistic is both known and random.
A population is an entire group about which you want to draw conclusions. A sample is the specific group from which you will collect data. The sample size is always less than the total population size.
A sample is an analytic subset of a larger population in statistics. The use of samples enables researchers to conduct studies with more manageable data and more quickly. Randomly drawn samples have little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
Note that an overview of sample was given as the information is incomplete.
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A wiring job requires 4 electricians to work for 6 hours to finish the job.
On the day of the job, one electrician does not report. How long would it
take to complete the same job by the remaining electricians?
Answers
if we are talking about 24hrs. 24/4=6 so 24/3=8 (3 bc there is one less)!
The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.
How are number of people to time needed to complete a task related?More people to do a task means less time it will take.
Less people to do a task means more time it will take.
Thus, they are inversely related.
If x men take y time for a work,
We can define a constant as "Manpower" needed for doing that specific work.
Let we define:
Manpower needed for a work = y + y + y + .. + y = Time per man × count of men
Manpower needed for a work = xy
We are given that;
Number of electricians= 4
Number of hours= 6
Now,
We can use the formula:
workers × time = work
where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.
In this case, we know that 4 electricians can complete the job in 6 hours. So:
4 × 6 = work
work = 24
This means that the total amount of work required to complete the job is 24 "units".
Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".
So we have:
3 × t = 24
Dividing both sides by 3, we get:
t = 8
Therefore, by work and time answer will be 3 electricians and 8 hours.
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