The function that gives the amount of profit at a given price and number
given are obtained from the relationship between the variables.
a) The profit in terms of the number of tickets sold, P = -0.015·n² + 250·n
(b) The profit in terms of ticket price, is P = -66.[tex]\overline 6[/tex]·p² + 3000·p + 2,333,333.[tex]\overline 3[/tex]
Reasons:
Number of tickets sold at x = $200, is y = 10,000 tickets
Number of extra tickets sold for every $15 price reduction = 1,000 tickets
Number of tickets sold at $185 = 11,000
The cost to fly a person = $100
(a) The rate of change, [tex]\frac{\Delta y}{\Delta x}[/tex], of the number of ticket sold wit price is given as
follows;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{11,000 - 10,000}{185 - 200 } = -66. \overline 6[/tex]
The equation in slope and intercept form is therefore;
n - 11,000 = -66.[tex]\overline 6[/tex]·(p - 185)
n = -66.[tex]\overline 6[/tex]·p + 12,333.[tex]\overline 3[/tex] + 11,000 = -66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex]
Number of tickets sold, n = -66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex]
[tex]Price \ per \ ticket, \ p = \dfrac{23,333.\overline {3} - n}{66. \overline{6}}[/tex]
The revenue, R = n·x
Therefore;
[tex]R = \dfrac{23,333.\overline {3} \cdot n- n^2}{66. \overline{6}}[/tex]
The profit = Revenue - Cost
The cost = 100·n
[tex]Profit, P = \dfrac{23,333.\overline {3} \cdot n- n^2}{66. \overline{6}} - 100 \cdot n = -0.015 \cdot n^2 + 250 \cdot n[/tex]
Total profit, P = -0.015·n² + 250·n(b) The total profit, P, in terms of the price p, for one ticket
Number of tickets sold, n = -66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex]
The revenue, R = n·p
∴ R = -66.[tex]\overline 6[/tex]·p² + 23,333.[tex]\overline 3[/tex]·p
Cost = 100·n
∴ Cost = 100·(-66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex])
Therefore, the profit is given as follows;
Profit = -66.[tex]\overline 6[/tex]·p² + 23,333.[tex]\overline 3[/tex]·p - (100·(-66.[tex]\overline 6[/tex]·p + 23,333.[tex]\overline 3[/tex]))
Therefore;
Total profit, P = -66.[tex]\overline 6[/tex]·p² + 3000·p + 2,333333.[tex]\overline 3[/tex]Learn more here:
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We want to express the total profit in two different ways.
The answers are:
a) P(n) = n*[n - 23,333.3]*(-15/1,000) - n*100
b) P(p) = n(p)*p - n(p)*100 = [ (-1,000/15)*p + 23,333.3]*(p - 100)
The given information is:
If the ticket price is $200, they sell 10,000 tickets.If the ticket price decreases $15, they sell 1,000 tickets more.It costs $100 to fly a person, then the cost of each ticket is $100.a) We want to get the profit in terms of the number n of tickets sold.
The number of tickets sold depends on the price, we know that it is a linear relation like:
n(p) = a*p + b
where p is the price.
we know that:
n(200) = 10,000
n(185) = 11,000
If this is a linear relation, the slope is known:
a = -1,000/15$
Then the line is something like:
n(p) = (-1,000/15)*p + b
We know that if k = 200, then n = 10,000
Replacing that we have:
n(200) = 10,000 = (-1,000/15)*200 + b
10,000 + (1,000/15)*200 = b = 23,333.3
Then the number of tickets sold as a function of the price is:
n(p) = (-1,000/15)*p + 23,333.3
Then the revenue is given by the number of tickets sold times the price, this is:
r(n) = n*p
We can write k in terms of n as:
k = [n - 23,333.3]*(-15/1,000)
Then the revenue as a function of the number of tickets sold is:
r(n) = n*[n - 23,333.3]*(-15/1,000)
The profit is the difference between the revenue and the cost, then the profit function is:
P(n) = n*[n - 23,333.3]*(-15/1,000) - n*100
Where n*100 is the cost.
b) now we want to write the same equation, but this time as a function of the price.
now the revenue is:
r(p) = n*p = [ (-1,000/15)*p + 23,333.3]*p
Then the profit is:
P(p) = n(p)*p - n(p)*100 = [ (-1,000/15)*p + 23,333.3]*(p - 100)
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someone please, i have asked this question before and nobody answered... i really need help..
Answer:
h = 5.2 cm
we can determine that the base length of the triangle is 3 cm as its a square. the hypotenuse given - 6 cmusing Pythagoras theorem:
a² + b² = c²
3² + h² = 6²
h² = 36 - 9
h² = 27
h = 3√3
h = 5.2 cm
Need help asap giving 20 points for right answer!!
Answer:
I think it's 600 I think it might be wrong
List the angles or the triangle in order from SMALLEST to LARGEST
Answer:
i think its A)
Step-by-step explanation:
Answer:
C )
CAB . . . . . .
Hope it helps any . . . . . .
Hello people ~
factorise: x^2 + 3 √3 x + 6
[tex]\\ \rm\rightarrowtail x^2+3\sqrt{3}x+6[/tex]
[tex]\\ \rm\rightarrowtail x^2+\sqrt{3}x+2\sqrt{3}x+6[/tex]
[tex]\\ \rm\rightarrowtail x(x+\sqrt{3})+2\sqrt{3}(x+\sqrt{3})[/tex]
[tex]\\ \rm\rightarrowtail (x+2)(x+2\sqrt{3})[/tex]
Using the quadratic formula,
∆=b²-4ac∆=(3√3)²-4(1)(6)∆=(9×3)-4(6)∆=27-24∆=3[tex]x1 = \frac{ - b - \sqrt{3} }{2a} = \frac{ - 3 \sqrt{3} - \sqrt{3} }{2} = \frac{ - 4 \sqrt[]{3} }{2} [/tex]
[tex]x1 = - 2 \sqrt{3} [/tex]
Similarly,[tex]x 2 = \frac{ - b + \sqrt{3} }{2a} = \frac{ - 3 \sqrt{3} + \sqrt[]{3} }{2} = \frac{ - 2 \sqrt{3} }{2} [/tex]
[tex]x2 = - \sqrt{3} [/tex]
Method 2:x²-Sx+P=0where S is the sum of the roots & P is the product of the roots.x¹+x²= -3√3 x¹x²=6Solving the system you get the same answers.Your factored equation can be written in the form of:
(x-x¹)(x-x²)
(x+2√3)(x+√3)
The polygons are similar. Find the value of x.
2-
Р
X
X
20
21
14
5
Q 12 R
L
18
K
Check the picture below.
Find the coordinate point for A that would make ABDC a rhombus
(2,3)
O (1,3)
O (3,0)
O(4,0)
1,3 is right correct right answer
The coordinate point for A is (1,3) Therefore, option B is the correct answer.
WE know that rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides.
Since a rhombus has all four sides equal just like a square.
Given that, Point C (2, 1), Point B (3,4) and Point D (4,2)
The coordinate point for A that would make ABDC a rhombus.
So, the coordinate point for A is (1,3).
Therefore, option B is the correct answer.
Learn more about the rhombus here:
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You buy a football helment signed by Peyton Manning for $110. The value increases 4% each year. What will the value be after 3 years? Round to 2 decimal places.
Answer:
12.12
Step-by-step explanation:
4% of 110 = 4.4
4.4 x 3 = 12.12
A car dealer buys a car for $500, and then sells it for $640. What
is the percentage profit?
is sold for $100.
Answer:
28%
Step-by-step explanation:
I think:
640-500= 140
140/500 = 0.28 = 28%
Congruent , connected , or in response ?
Answer:
The answer is congruent
HELP PLEASE I NEED ANDWERS❤️❤️❤️
Sorry, I couldn't figure out the last one, it just takes a lot of trial and error and luck :(
You know that S times A is the digit N. Then, A squared plus whatever the first digit of the2 digit number XN is MA.
A cannot be five because if you were to do 5 times 5 it would be 25. A squared is 25 and the last digit is already A so added on to anything else the equation would be false. So the only considerable value for S would be one, but then A times S would be 5, but N is not A. I hope you get what I mean.
A cannot be 6 for the same reason (just change the 5 to six on my last pragraph).
If A were 7 then you'd have to find something to add to 49 to make it end in 7, which means adding 6. 7 times 9 is 63, so S could be 9. 79 times 7 is 573. That is the answer. A = 7, S = 9, M = 5, N = 3.
As for NINE - FOUR = FIVE, E - R is E so R must be 0.The only one digit number a number can be subtracted by to get itself is 0.
Now, N - U = V, or 1N - U = V
Let's say N is 3 and U is 6. V would be 7.
We've just took one from I. I - 1 - O = I. 1+O must be 10 or 0, but O must be positive, so O = 9. Let's say I is 5.
We just borrowed one form N. N-1 - F = F. N - 1 = 2 times F.
But we know that N is 3. 2 = 2 times F. F is 1.
Let's just make E = 8
My final answer is 3538 - 1960 = 1578
There are MANY other answers though.
N = 3, I = 5, E = 8, O = 9, U = 6, R = 0, V = 7.
a cellphone company fixed the price of a cellphone as rs4500. a dealer purchased a cell phone on which the paid 12% GST additionally. how much did the dealer paid as GST ? what is the purchase price of cell phone
Answer:
Step-by-step explanation:
Price of cellophone = ₹4500
Gst additionally = 12%
= 12% of ₹4500
= 12/100 * 4500
= ₹12*45
= ₹540
Total = ₹4500 + ₹540
= ₹5040
Answer:
Rs. 5040
Step-by-step explanation:
Price of cellphone=Rs. 4500
Gst additionally=12%
=12% of Rs. 4500
12/100 * 4500
=Rs. 12*45
=Rs.540
=Total=4,500+540
=Rs.5040
A school has 6 sports teams during the fall season, and each team has 20 members. How many fall athletes does the school have?
athletes
Answer:
120
Step-by-step explanation:
Basically you just 6x20=120
Hey there!
Answer: 120 fall athletes
Since each team has 20 members, and in total they have 6 teams
Then, we multiply
=> 20 × 6
=> 120
What is 3(x-1)+4=12 ?
Answer:
3.66666. . . = 11/3 = 3 2/3
Step-by-step explanation:
Use distributive property.
3 ⋅ x = 3x
3 ⋅ (-1) = -3
3x - 3 + 4 = 12
Add -3 to 4
1
3x + 1 = 12
Subtract 1 from both sides.
3x = 11
Divide both sides by 3
3.666666. . .
This can also be written as 11/3
11/3 can be simplified to 3 2/3
Hope I helped :)
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1. Dan painted 3/5 of a wall using 1/5 of a can of paint. How many walls can he paint using one can of paint?
One can of paint will cover 3 walls.
jayla invested $8200 in an account that grows continuously at an annual rate of 2.8%. write the function that represents the situation, where A is the value of Jaylas investment after t years. what will kayla’s investment be worth after 7 years to the nearest cent
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$8200\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ t=years\dotfill &7 \end{cases} \\\\\\ A=8200e^{0.028\cdot 7}\implies A=8200e^{0.196}\implies A\approx 9975.52[/tex]
A rocket is launched upwards from the ground. The height of the rocket above the ground is
shown in the following table:
(a) Write the quadratic regression equation that models the data. Let x = time in seconds
and let y= height in feet. Round all numbers to the nearest hundredth.
(b) Use the equation to estimate the height of rocket after 5 seconds.
The height of the rocket after 5 seconds would be 0 feet.
What is an quadratic equation?A quadratic equation is in the form:
y = ax² + bx + c
Let y represent the height after x seconds.
At point (0, 0):
0 = a(0)² + b(0) + c
c = 0
At (0.5, 20.5):
20.5 = a(0.5)² + b(0.5) +0
0.25a + 0.5b = 20.5
At point (2, 36.25):
30.41 = a(2)² + b(2) + 0
4a + 2b = 30.41
Hence:
a = -17.2, b = 49.6
Hence:
y = -17.2x² + 49.6x
At 5 seconds:
y = -17.2(5)² + 49.6(5) = -197
The height of the rocket after 5 seconds would be 0 feet.
Find out more on quadratic equation at: https://brainly.com/question/1214333
Similar or Like Terms are two monomials that are exactly alike except for their
numerical coefficients.
True
False
steve was offered $5,025 per year for a weekend lifeguarding job at a local pool he wants to know how much his monthly income will be at this salary level what is his rate of pay in dollars per month
Answer:
418.75
Step-by-step explanation:
5025/12 (12 months in one year)
418.75 or almost 420 dollars a month
to check the answer:
418.75*12
5025
point d is the interior of angleABE and point E is the interior of angleDBC....(press on the picture please) (also i scratched out where i tried to work it out)
Answer:
c)41
Step-by-step explanation:
∠DBE = (∠ABE +∠DBC) -∠ABC
= (74 + 103) -136
= 177 - 136
= 41
help i need to know what answer to this is xd
What is the average rate of change of the line whose equation is:
y−3=−12(x+4)?
PLEASE HELPPPP
Answer:
Rate of change = -12
Step-by-step explanation:
y − 3 = −12(x + 4)
Expanding, we have;
y - 3 = -12x - 48
y = -12x - 48 + 3
y = -12x - 45
Now, formula for rate of change is;
Rate of change = (y(x + h) - y)/h
y(x + h) is; y = -12(x + h) - 45
This gives;
Rate of change = (-12(x + h) - 45 + 12x + 45)/h
Rate of change = (-12x - 12h - 45 + 12x + 45)/h
Rate of change = -12h/h
Rate of change = -12
Pls help me with 8a and b
Answer:
Step-by-step explanation:
PLSSS HELPPP!!! GIVING BRANILLYYYY!!!!
Answer:
very last one
Step-by-step explanation:
hope it helps
On a map of Texas, the scale listed is 1 in = 32 miles. If the distance from San Antonio to El Paso is 17 inches on a map, how many miles is it?
Answer:
544 miles
Step-by-step explanation:
this problem is a multiplication problem, if one inch is 32 mile, and San Antonio to El Paso is 17 inches you have to multiply 17 and 32 to get 544 miles
Answer:
544 miles
Step-by-step explanation:
Since 1 inch equals 32 miles, [tex]17inches\cdot 32miles=544miles[/tex]
A prism is completely filled with 64 cubes that have edge lengths of 12 in. What is the volume of the prism? Enter your answer in the box
Answer:
answer;8
Step-by-step explanation:
I took the test and got it right
Answer:
110592 in^3
Step-by-step explanation:
12x12x12=1728
1728x64=110592
A line is an undefined term because it
A.)contains an infinite number of points
B.)can be used to create other geometric shapes
C.)describes something that does not have width or depth
D.)is a term that does not have a formal definition
Answer:
C
Step-by-step explanation:
The correct option is C because lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.
Pls rate.........
A line is an undefined term because it describes something that does not have width or depth. thus, option C is correct answer.
Which ray can be said as belonging to a line segment?If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.
(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)
A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
A lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.
A line is an undefined term because it describes something that does not have width or depth. thus, option C is correct answer.
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A scientist measured the growth rate of a bamboo plant at 6 inches in 12 hours. What is the growth rate of the Bamboo? (in inches/hr)
Growth rate
[tex]\\ \sf\longmapsto Distance/Time[/tex]
[tex]\\ \sf\longmapsto 6/12[/tex]
[tex]\\ \sf\longmapsto 0.5in/h[/tex]
math question... lol
Answer:
answer is
Step-by-step explanation:
Surface are = (3 x 4) + (3 x 5) + (4*5) x 2 is calculate as 94 squat inches
2) Mateo scored 99 out 150 on an exam. What’s his score as a percentage?
Answer:
You divide the smaller number by the bigger, or the received points out of the total, so you would divide 99 by 150 giving you 66%
Answer : 66%
Explanation : 33 ÷ 50 Or 99 ÷ 150
An investment website can tell what devices are used to access their site. The site managers wonder whether they should enhance the facilities for trading via smartphones so they want to estimate the proportion of users who access the site that way. They draw a random sample of
131
investors from their customers. Suppose that the true proportion of smartphone users is
26
%.
Complete parts a) through c) below.
a) What would the managers expect the shape of the sampling distribution for the sample proportion to be?
Skewed to the left
Unimodal and symmetric
Skewed to the right
Nonsymmetric
b) What would be the mean of this sampling distribution?
(Round to two decimal places as needed.)
c) What would be the standard deviation of the samplingdistribution?
(Round to three decimal places as need
Answer: a) Unimodal and symmetric
b) 0.26
c) 0.038
Step-by-step explanation:
Given: Sample size of investors (n)= 131
True proportion of smartphone users(p) =26%
a) Since sampling distribution for the sample proportion is approximately normal when n is larger.
Normal distribution is Unimodal and symmetric.
So correct option : Unimodal and symmetric
b) mean of this sampling distribution = p = 0.26
c) standard deviation of the samplingdistribution = [tex]\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26\times (1-0.26)}{131}}=\sqrt{0.00146870229008}[/tex]
[tex]=0.0383236518364\approx0.038[/tex]