Answers
Let p(t) be the number attendees and t be the ticket price measured in units of 10s of rupees. When the price is t = 7 (i.e. Rs70), there were p(7) = 300 people in attendance.
For each unit increase in t (i.e. for each Rs10 increase in price), p(t) is expected to fall by 20, so that
p(t + 1) = p(t) - 20
Solve for p(t). Suppose t ≥ 7. By substitution,
p(t + 1) = (p(t - 1) - 20) - 20 = p(t - 1) - 2×20
p(t + 1) = (p(t - 2) - 20) - 2×20 = p(t - 2) - 3×20
p(t + 1) = (p(t - 3) - 20) - 3×20 = p(t - 3) - 4×20
and so on, down to
p(t + 1) = p(7) - (t - 6)×20 = 420 - 20t
or
p(t) = 420 - 20 (t - 1) = 440 - 20t
With t = price per ticket (Rs/ticket) and p(t) = number of attendees = number of tickets sold, it follows that the income made from ticket sales for some fixed ticket price t would be t×p(t). If one plots p(t) in the coordinate plane, the price that maximizes income and number of attendees is such that the area of a rectangle inscribed by the line p(t) and the coordinate axes is maximized.
Let A(t) be the area of this rectangle, so
A(t) = t p(t) = 440t - 20t²
Without using calculus, complete the square:
A(t) = 440t - 20t² = 2420 - 20 (t - 11)²
This is the equation of a parabola with vertex at (11, 2420), so the optiml ticket price is Rs11, and at this price the drama club can expect an income of Rs2420.
With calculus, differentiate A with respect to t and find the critical points:
A'(t) = 440 - 40t = 0 ⇒ 11 - t = 0 ⇒ t = 11
Differentiate A again and check the sign of the second derivative at this critical point:
A''(t) = -40 ⇒ A''(11) = -40 < 0
which indicates a local maximum at t = 11 of A(11) = 2420.
Related Questions
(17x + 4y) + (48x + 21y)
A.65x + 25y
B.21x + 25y
C.65x + 38y
D.21x + 38y
Answers
[tex](17x+4y)+(48x+21y)[/tex]
Simplify:
(1) Combine like terms
[tex]17x+4y+48x+21y[/tex]
[tex]65x+4y+21y[/tex]
(2) Combine like terms
[tex]65x+4y+21y[/tex]
[tex]65x+25y[/tex]
Solution:
[tex]A) 65x+25y[/tex]
Answer:
[tex]65x+25y[/tex]
Step-by-step explanation:
[tex](17x + 4y) + (48x + 21y)[/tex]
[tex]17x+4y+48x+21y[/tex]
[tex]17x+48x+4y+21y[/tex]
[tex]65x+4y+21y[/tex]
[tex]65x+25y[/tex]
I will give Brainliest!!! :D
A farmer sells eggs at a market. She offers three different sizes. For any size, the weight of each egg can vary up to 8%.
Calculate the missing values.
Is it possible for an egg to be both large and extra large?
Explain.
Answers
answers:
medium-41.4,48.6
large-55,59.4
extra large-62,57.04
yes it is possible for an egg to be large and extra large, reason: the lightest possible egg for the extra large is 57.04 and the heaviest possible egg for the large is 59.4. Therefore, an egg between the range(57.04_59.4) is both large and extra large
The missing values for Medium egg are 41.4g, 48.6g
for large eggs are 55g, 59.4g,
and extra large eggs are 62g, 57.04g.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given table for size and weight of eggs and the weight of each egg can vary up to 8%.
for Medium eggs Advertised weight = 45 g
lightest weight = 45 - 8% of Advertised weight
because Advertised weight is average of lightest weight and heaviest egg weight,
lightest weight = 45 - 45(0.08)
lightest weight = 41.4 g
heaviest egg weight = 45 + 8% of Advertised weight
lightest weight = 45 + 45(0.08)
lightest weight = 48.6 g
missing values for medium egg = 41.4g and 48.6g
For Large egg
lightest weight = 50.6
Advertised weight = 50.6 + 8% of lightest weight
Advertised weight = 50.6 + 50.6(0.08)
Advertised weight = 54.9 = 55g
heaviest egg weight = 55 + 8% of Advertised weight
heaviest egg weight = 55 +55(0.08)
heaviest egg weight = 59.4g
missing values for large egg = 55g and 59.4g
For Extra large egg
heaviest egg weight = 66.96 g
Advertised weight = 66.96 - 8% of heaviest egg weight
Advertised weight = 66.96 - 66.96(0.08)
Advertised weight = 61.6 = 62 g
lightest weight = 62 - 8% of Advertised weight
lightest weight = 62 - 62(0.08)
lightest weight = 57.04 g
missing values for extra large egg is 62g and 57.04 g
Yes, an egg can be large or extra large for the following reasons: The largest egg is 59.4 pounds, while the lightest egg for an extra large is 57.04 pounds. As a result, an egg between 57.04 and 59.4 is both large and extremely large.
Hence the missing values are,
Medium egg are 41.4g, 48.6g
for large eggs are 55g, 59.4g,
and extra large eggs are 62g, 57.04g.
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What is the volume of this right prism?
96 in³
60 in³
48 in³
44 in³
Answers
Answer:
48
Step-by-step explanation:
Blood Types A medical researcher wishes to see if hospital patients in a large hospital have the same blood type distribution as
those in the general population. The distribution for the gendral population is as follows: type A, 22%; type B, 28%; type o,
38%; and type AB = 12%. He selects a random sample of 50 patients and finds the following: 11 have type A blood, 9 have type
B, 24 have type o, and 6 have type AB blood.
At a=0.10, can it be concluded that the distribution is the same as that of the general population? Use the critical value method
with tables.
Answers
We can conclude that there is not enough evidence to suggest that the distribution of blood types in hospital patients is different from that of the general population at a significance level of 0.10.
What is hypothesis testing?Hypothesis testing is a statistical method that is used to make decisions about a population based on a sample of data.
It involves testing a null hypothesis (H0) against an alternative hypothesis (Ha) using statistical techniques.
We have,
We need to perform a hypothesis test to determine if the distribution of blood types in hospital patients is the same as that of the general population.
Let's set up the null and alternative hypotheses:
Null hypothesis:
The distribution of blood types in hospital patients is the same as that of the general population.
Alternative hypothesis:
The distribution of blood types in hospital patients is different from that of the general population.
We can use a chi-squared test to test the hypothesis.
First, we need to calculate the expected frequencies for each blood type based on the general population distribution:
Expected frequency of type A = 50 x 0.22 = 11
Expected frequency of type B = 50 x 0.28 = 14
Expected frequency of type O = 50 x 0.38 = 19
Expected frequency of type AB = 50 x 0.12 = 6
Next, we can calculate the chi-squared statistic:
[tex]$\chi^2 = \frac{(11-11)^2}{11} + \frac{(9-14)^2}{14} + \frac{(24-19)^2}{19} + \frac{(6-6)^2}{6} = 2.84$[/tex]
The degrees of freedom for the test is (4 - 1) = 3.
Using a chi-squared distribution table with 3 degrees of freedom and a significance level of 0.10, the critical value is 6.251.
Since the calculated chi-squared value (2.84) is less than the critical value (6.251), we fail to reject the null hypothesis.
Thus,
We can conclude that there is not enough evidence to suggest that the distribution of blood types in hospital patients is different from that of the general population at a significance level of 0.10.
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beinggreat78, you're looking for this
Answers
Answer:
z = 6
9 followed by a lowercase number, whether it's x, y, or z usually always means add 1 or multiply by an unknown number. In this case, we are multiplying.
[tex]9 * 45 = 405(wrong)\\\\9 * 63 = 567(wrong)\\\\9 * 7 = 63(wrong)\\\\9 * 6 = 54(correct)[/tex]
That said, the answer is six.
Which expression is equivalent to 6x² - 7x-20 ?
Answers
Answer:
(3x+4)(2x−5)
Step-by-step explanation:
The first term is, 6x2 its coefficient is 6 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 6 • -20 = -120
Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is -7 .
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14
-15 + 8 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 8
6x2 - 15x + 8x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x-5)
Add up the last 2 terms, pulling out common factors :
4 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (2x-5)
Which is the desired factorization
What is the value of the expression 2.5 (j.k) j when je 6 and K = 4? OA) 6 OB) 8 OC) 10 OD) 12
help ASAP
Answers
Answer:
C
Step-by-step explanation:
substitute the given values for j and k into the expression
[tex]\frac{2.5(6)(4)}{6}[/tex]
= [tex]\frac{2.5(24)}{6}[/tex]
= [tex]\frac{60}{6}[/tex]
= 10
The area of a rectangle is 45 square inches. The length of the rectangle is 6 inches.
What is the width of the rectangle?
Enter your answer as a mixed number in simplest form in the box.
inches
Answers
Step-by-step explanation:
the area of a rectangle is
length × width.
so, we have here
45 = 6 × width
width = 45/6 = 15/2 = 7.5 in = 7 1/2 in
The parts of a solid are faces, vertices and __________.
Answers
Answer:
edges
Step-by-step explanation:
Tyler and Gabe went to the arcade and played the same two games. Tyler played 5 rounds of one game and two rounds of the other for $24. Gabe played 4 rounds of each game for $30. Write two equations for the amounts the two boys spent. Then find the cost for one round of each game.
Answers
Answer:
Tyler: 5x + 2y = 24
Gabe = 4x + 4y = 30
x = 3
y = 4.5
Step-by-step explanation:
4y = 30 - 4x
y = 7.5 - x
5x + 2(7.5 - x) = 24
3x + 15 = 24
x = 3
y = 7.5 - 3
y = 4.5
Please help meeeee!!
Answers
1/9
[tex]\bold{EXPLANATIONS:}[/tex]
solvr 5 3/4 = z- 6 3/8
Answers
Answer:
x=12 1/8
hope this helps
can i get brainliest
Mrs. Vanwhy made a two-way table to show which students made honor roll and which students study a foreign language. Which is the best two-way table for Mrs. Vanwhy to organize her data?
A 4-column table with 3 rows. Column 1 has entries honor roll, no foreign language, total. Column 2 is labeled foreign language. Column 3 is labeled not on honor roll. Column 4 is labeled total.
A 4-column table with 3 rows. Column 1 has entries honor roll, not on honor roll, total. Column 2 is labeled foreign language. Column 3 is labeled no foreign language. Column 4 is labeled total.
A 4-column table with 3 rows. Column 1 has entries honor roll, no foreign language, total. Column 2 is labeled not on honor roll. Column 3 is labeled no foreign language. Column 4 is labeled total.
A 4-column table with 3 rows. Column 1 has entries foreign language, honor roll, total. Column 2 is labeled no foreign language. Column 3 is labeled not on honor roll. Column 4 is labeled total.
Answers
The most appropriate chart for Mrs. Vanwhy is the one where the columns are foreign language and honor roll, no foreign language, honor roll, and total (option D).
How to identify the relevant table for Mrs. Vanwhy?To identify the most appropriate table for Mrs. Vanwhy we must identify what data she wants to include in the table.
Taking the above information into account, it can be inferred that the most appropriate table for Mrs. Vanwhy is option D because it includes all the data that she wants to tabulate.
Honor roll.Foreign language.Learn more about tables in: https://brainly.com/question/10670417
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Answer:
D.) The last table is the answer
Step-by-step explanation:
I finished the test.
A local gym charges a flat monthly fee plus a fee for each day the gym is used. The total cost in dollars, y, to use the gym for x days can be found by the equation; y=6x+81. What is the daily cost of using the gym and why?
Answers
Answer:
The daily cost is $6 because that is being multiplied by the x which represents days. The 81 represents the flat fee.
Step-by-step explanation:
What would the quadratic equation be in standard form?
Answers
Answer:
ax^2 + bx + c = 0
Step-by-step explanation:
This is the standard form of the quadrartic equation. "a" is the leading coefficient and a non-zero real number.
2. Which of the following is equivalent to (g+h)(p+q-r)?
Ogp+gq+gr + hp + hq + hr
Ogp+hq-hr
Ogp+hq-r
Ogp+gq-gr + hp +hq - hr
Answers
Answer:
[tex]\boxed{D)\;gp+gq-gr+hp+hq-hr}[/tex]
Step-by-step explanation:
[tex]\left(g+h\right)\left(p+q-r\right)[/tex]
[tex]gp+gq+g\left(-r\right)+hp+hq+h\left(-r\right)[/tex]
[tex]gp+gq-gr+hp+hq-hr[/tex]
Hope it helps!
Answer:
D. gp + gq - gr + hp + hq - hr
Step-by-step explanation:
I got it right on my test.
A company surveyed all of the employees in their Columbus, Ohio office,
one of their six national offices. Based on the survey they determined that
72% of all employees were satisfied with their job. Which of the following
explains why this is NOT a random sample?
A. They only surveyed people who had been at their job for five years or
more.
B. They did not survey employees in other offices around the country.
C. The survey was conducted electronically.
D. The survey had a time limit.
Answers
Answer:
B. They did not survey employees in other offices around the country
Step-by-step explanation:
1. A random sample is when you randomly choose options from the whole list. In this case, they make it clear that there are other offices. They didn't give a chance to the rest of the offices to take a survey.
2. Surveying "all" the employees is not what a random sample is. A random sample is supposed to help make it more distributed among the people you survey. Making all of them take it in a cluster is not random.
3. The other choices don't make sense because they don't mention anything about them: nothing about the employees working 5 years, nothing about it being conducted electronically, and nothing about a time limit.
A town has a population of 14000 and grows at 5% every year. What will be the population after 14 years, to the nearest whole number?
Answers
Answer:
I got 27,719.
Step-by-step explanation:
I Did the long route and multiplied 14,000 by .05 and adding that and doing that to my answer 14 times. so 14,000-14,700-15,435-16,206.75,17,017 so on and on. Tbh I would know tho
NESESITO LA RESPUETA URGENTEEEEEE
[tex]\frac{(6)}{(3)}[/tex]
Answers
How you do this pls help
Answers
Answer:
why do ask the question which answer is given below
The amount of money that college students spend on food each week during the academic year is normally distributed with
a mean of $31.28 and a standard devitation of $11.42.
What is the probability that one randomly selected student will spend less than $25 per week on food?
If you randomly select 10 students, what is the probability that their mean will be less than 525?
Answers
Answer:
~ 70 %
Step-by-step explanation:
(31.28 - 25)/ 11.42 means 25 is .5499 S.D. below the mean
z -score = .7088
70.88 % chance of less than = 25 dollars
The required probability for one randomly selected student will spend less than $25 per week on food is 0.2911 and for randomly selected 10 students, what is the probability that their mean will be less than $25 is 0.040.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
a) X = 25 , μ = 31.28 and σ = 11.42
[tex]Z = \frac{X - \mu}{\sigma}\\z = \frac{25 - 31.28}{11.42}\\z = -0.5499[/tex]
Using z score
Now a probability that one randomly selected student will spend less than $25 per week on food is given.
P(x<25) = p(z = -0.5499)
= 0.2911
b) number of sample = 10
standard deviation = 11.42/√10
= 3.611
Herr,
[tex]Z = \frac{X - \mu}{\sigma}\\z = \frac{25 - 31.28}{3.611}\\z = -1.7444[/tex]
Probability (x<25) = p(z = -1.7444)
Using the Z score table,
Probability (x <25) = 0.040
Thus, the required probability for one randomly selected student will spend less than $25 per week on food is 0.2911 and for randomly selected 10 students, what is the probability that their mean will be less than $25 is 0.040.
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Jaylon has 20 math problems for homework. He has completed 60% of the
problems so far. How many problems has he completed?
Answers
Answer:
Jaylon has completed 12 problems.
Step-by-step explanation:
(This is how I learned it- I'm not sure if you have been taught this way..)
Step 1. Set up a proportion
[tex]\frac{60}{100} = \frac{x}{20}[/tex]
Step 2. Do 200x 60 to get 1200
Step 3. Get this equation
[tex]\frac{1200}{100} = x[/tex]
Step 4. Get the answer of 12
I hope this helps! :)
Answer:
Jaylon has completed 12 problems so far
Step-by-step explanation:
Step 1: Determine the amount of problems that were completed
(Total number of problems) * (Percent of completed problems)
(20) * (60% / 100%)
(20) * (0.6)
12
Answer: Jaylon has completed 12 problems so far
In AFGH, f = 60 cm, g = 10 cm and h=62 cm. Find the measure of LF to the
nearest degree.
Answers
Answer:
∠F ≈ 74°
Step-by-step explanation:
The law of cosines is used to find the measures of angles in a triangle when the side lengths are known.
__
f² = g² +h² -2gh·cos(F) . . . . . law of cosines relating to angle F
cos(F) = ((g² +h² -f²)/(2gh)) . . . . . solve for cos(F)
F = arccos((g² +h² -f²)/(2gh)) . . . . . . solve for angle F
F = arccos((10² +62² -60²)/(2·10·62)) = arccos(344/1240)
∠F ≈ 74°
13-28 Sketch the region enclosed by the given curves and find its area.
19. [tex]y=\cos \pi x, \quad y=4 x^{2}-1[/tex]
Answers
Answer:
Area (A) 0.0682
Step-by-step explanation:
The sketch for the region enclosed by the given curves can be found in the image attached below.
From the image below;
The two curves intersect in the area of tan 9x = 2 sin 9x
Recall that:
making x the subject; then:
The subdivision of the domain is in two intervals
where;
Area (A) =
Area (A) = 0.06818
Area (A) 0.0682
Ricky is 11 years old. Mel and Kim are both five years older than Ricky. Jaz is 29 . What is the mean of their ages?
Answers
Answer:
18 years
Step-by-step explanation:
The average of 4 ages:
(11 + 16+16 + 29 )/4
Answer:
The mean of their ages is 18.
Step-by-step explanation:
11 + 16 + 16 + 29 = 72
72 ÷ 4 = 18
a small pizza has a diameter of 8 inches what is the circumference
Answers
C=2 π(4)
*The radius is 4 because radius is half of the diameter, and the diameter is 8 so 8/2=4
C=25.13
Answer:
Given :-
Diameter of Pizza is 8 inches , radius = 4 inchesTo find :-
Circumference of Circular pizzaSolution :-
Formula for circumference of Circular pizza = 2πrPutting the known values
Circumference = 2 × 3.14 × 4
Circumference = 25.12 cm
Margot needs to gallons of paint for his living room he has 10 quarts of paint is that enough
Answers
Answer:
"Quart" is shorthand for "quarter of a gallon." So that means there are 4 quarts in each gallon. Which means 8 quarts in 2 gallons.
So if he's got 10 quarts, that means 2 and a half gallons.
Step-by-step explanation:
Michelle bought 3000 shares of a stock at $24 per share. The company paid annual
dividends of $0.42 per share. What is the total annual dividend?
Answers
Answer:
$ 12.60
Step-by-step explanation:
30 shares × $ 0.42 = $ 12.60
Answer:
$1,260
Step-by-step explanation:
3000 x .42 = 1260
Find the missing side or angle.
Round to the nearest tenth.
C=95°
b=6
a=5
c=[?]
Answers
No diagram is visible!
You might have to repost the question again.
Answer: For the acellus people its 8.1
Step-by-step explanation:
Figure ABCD is similar to figure WXYZ. Which proportion must be true for these figures?
Answers
Answer:
Polygon WXYZ is the same shape and size as polygon ABCD. Each side of WXYZ is double the length of ABCD. The ratio of the length of each side of WXYZ to its corresponding side of ABCD is 2. A characteristic of figures that have the same shape is that ratios of corresponding sides are equal.
Step-by-step explanation: