A. Find diameter A whenx= 9..82 cm and y = 11.94 cm.B. find y when diameter A = 30.36 cm and X =23.72 cm
Answers
we can notice x is the sum of half DIA A and half BD
\(x=\frac{A}{2}+\frac{BD}{2}\)and y is the sum of half DIA A and BD
\(y=\frac{A}{2}+BD\)A. Find diameter A when x= 9..82 cm and y = 11.94 cm.
we replace x=9.8 and y=11.94 on the equations
\(\begin{gathered} 9.8=\frac{A}{2}+\frac{BD}{2} \\ \\ 11.94=\frac{A}{2}+BD \end{gathered}\)now we have two equations and two unknows, then we can solve BD from the first equation
\(\begin{gathered} 9.8=\frac{A}{2}+\frac{BD}{2} \\ \\ 9.8-\frac{A}{2}=\frac{BD}{2} \\ \\ BD=19.6-A \end{gathered}\)and replace on the second to find A
\(11.94=\frac{A}{2}+(19.6-A)\)simplify
\(\begin{gathered} 11.94=\frac{A}{2}+19.6-A \\ \\ 11.94=-\frac{A}{2}+19.6 \end{gathered}\)and solve for A
\(\begin{gathered} 11.94-19.6=-\frac{A}{2} \\ \\ -7.66=-\frac{A}{2} \\ \\ 7.66=\frac{A}{2} \\ \\ A=7.66\times2=15.32 \end{gathered}\)Value of Diameter A is 15.32 cm
B. find y when diameter A = 30.36 cm and X =23.72 cm
now on the initial equations for x and y we replace A and X
\(\begin{gathered} 23.72=\frac{30.36}{2}+\frac{BD}{2} \\ \\ y=\frac{30.36}{2}+BD \end{gathered}\)we have two equations, we realize we can simplify the first equation
\(\begin{gathered} 23.72=\frac{30.36}{2}+\frac{BD}{2} \\ \\ 23.72=15.18+\frac{BD}{2} \end{gathered}\)and we can solve BD
\(\begin{gathered} 23.72-15.18=\frac{BD}{2} \\ 8.54=\frac{BD}{2} \\ \\ BD=8.54\times2=17.08 \end{gathered}\)now we replace BD on the second equation
\(\begin{gathered} y=\frac{30.36}{2}+BD \\ \\ y=15.18+17.08 \\ \\ y=32.26 \end{gathered}\)The value of y is 32.26 centimeters
Related Questions
1. Alex weighs 5443 grams more than his
younger brother. If his brother weighs
32,658 grams, how much does Alex
weigh?
Answers
38,101 will be your answer when you add these.
Hope this helps!!
An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying. Lisa studies 4 hr for a particular test and gets a score of 72. At this rate, how many hours would she have had to study to get a score of 96?
Answers
Answer:
12 hours.
Step-by-step explanation:
Solve for c
Pythagorean theorem
Answers
By observing diagram clearly we can observe that there is a right angled triangle with :
Base, B = 3Perpendicular, P = 3Hypotenuse, H = cSo, to find hypotenuse, let's use Pythagoras' theorem :
\( \large \underline{\boxed{\bf{H^2 = B^2 + P^2}}}\)
\( \tt : \implies c^2 = 3^2 + 3^2\)
\( \tt : \implies c^2 = 9 + 9\)
\( \tt : \implies c^2 = 18\)
\( \tt : \implies c = \sqrt{18}\)
Hence, value of c is √18.
4/9 kilograms of baking soda cost $1.50. How much does 1 kilogram of baking soda cost?
Answers
Answer:
Step-by-step explanation:
divide 1.5 by 4 to get 1/9 of the cost, and then multiply that by 9 to get the cost of one kilo.
or 3.375, round it for money purposes
$3.38
Which choice describes the translations represented by the translation rule (x,y)-->(x + 2, y - 4)
1. 2 units to the right and 4 units down
2. 4 units to the right and 2 units down
3. 2 units to the left and 4 units up
4. 2 units to the left and 5 units down
Answers
Answer:
go to Brainly for the answer
Step-by-step explanation:
PQRS is a rectangle and OS = 16. Find the blanks below:
mments
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S
R
es
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О
s
bus
P
O
zes
dules
OQ =
16
BlueButton
aborations
PR =
ogle Drive
uce 365
mZQRS =
ogle Drive
Answers
Answer: 48
Step-by-step explanation:
Help, please!!!
A grocery store sign indicates that bananas are 3 for $1.50, and a sign by the oranges indicates that they are 5 for $3.00. Find the total cost of buying 2 bananas and 4 oranges.
(Screen shot question number 2 "How many laps can he swim in 6 minutes?")
Answers
3.40 and 15
Step-by-step explanation:
3 for 1.50 means 1 is 50 cents each.
5 oranges for 3 dollars mean each one is 60 cents.
So this equation is 4(.60)+2(.50)
=3.40
For the swimming problem,
divide the 2 and 5 and you should get 2.5.
Multiply 2.5 by 6 to get 15.
Here are the answers for the missing blanks
(2.5, 1) (5, 2) (7.5, 3) (10, 4) (12.5, 5)
In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half. Which expression represents the total number of points the player scored in the game?
Answers
This question is incomplete
Complete Question
In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half. Which expression represents the total number of points the player scored in the game?
a) 2x + 3x + 9
b) 2x + 3 + 9
c) 2x + 3x + 9x
d) 2 + 3x + 9
Answer:
a) 2x + 3x + 9
Step-by-step explanation:
Let the number of points shots a player scores = x
In a free throw, the player scored 9 points = 9
The player also scored a number of 2-point shots = 2x
In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half = 3x
The expression represents the total number of points the player scored in the game =
2x + 3x + 9
Use the diagram to find the value of x to the nearest tenth of a foot.
a. 74.6 ft.
b. 5.3 ft.
c. 15.5 ft.
d. 73.3 ft.
Answers
Answer:
a
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan15° = \(\frac{opposite}{adjacent}\) = \(\frac{20}{x}\) ( multiply both sides by x )
x × tan15° = 20 ( divide both sides by tan15° )
x = \(\frac{20}{tan15}\) ≈ 74.6 ft ( to the nearest tenth of a foot )
Brooklyn has two summer jobs. during the week she works in the grocery store, and on the weekend she works at a nursery. she gets paid $20 per hour to work at the grocery store and $21 per hour to work at the nursery. how many total hours does she work if she does 5 hours at the grocery store and 11 hours at the nursery? how many total hours does she work if she does gg hours at the grocery store and nn hours at the nursery?
total hours, 5 hours at the grocery store and 11 hours at the nursery:
total hours, gg hours at the grocery store and nn hours at the nursery:
Answers
Total hours if Brooklyn works 5 hours at the grocery store and 11 hours at the nursery: 16 hours
If Brooklyn works 5 hours at the grocery store and 11 hours at the nursery, then she works a total of 5 + 11 = 16 hours.
Total hours if Brooklyn works gg hours at the grocery store and nn hours at the nursery: gg + nn hours
If Brooklyn works gg hours at the grocery store and nn hours at the nursery, then she works a total of gg + nn hours.
In both cases, the total number of hours that Brooklyn works is simply the sum of the number of hours she works at each job.
Here is a Python code that you can use to calculate the total number of hours that Brooklyn works:
```python
def total_hours(grocery_store_hours, nursery_hours):
return grocery_store_hours + nursery_hours
def main():
grocery_store_hours = 5
nursery_hours = 11
print("Total hours:", total_hours(grocery_store_hours, nursery_hours))
if __name__ == "__main__":
main()
This code will print the following output:
Total hours: 16
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every composite number greater than 2 can be written as a product of primes in a unique way except for their order."" is called the
Answers
The statement "every composite number greater than 2 can be written as a product of primes in a unique way except for their order" refers to the fundamental theorem of arithmetic.
The fundamental theorem of arithmetic states that every composite number greater than 2 can be expressed as a unique product of prime numbers, regardless of the order in which the primes are multiplied. This means that any composite number can be broken down into a multiplication of prime factors, and this factorization is unique.
For example, the number 12 can be expressed as 2 × 2 × 3, and this is the only way to write 12 as a product of primes (up to the order of the factors). If we were to change the order of the primes, such as writing it as 3 × 2 × 2, it would still represent the same composite number. This property is fundamental in number theory and has various applications in mathematics and cryptography.
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At a Christmas party,40 people wore a grinch or elf costume. If there were 50 people at the party and 10 were dressed as the grinch, what percent were wearing an elf costume ?
Answers
Answer:
Percent [wearing elf costume] = 60%
Step-by-step explanation:
Given:
Total number of people = 50
Grinch or elf costume = 40
Grinch costume = 10
Find:
Percent [wearing elf costume]
Computation:
Percent [wearing elf costume] = [Grinch or elf costume - Grinch costume] / Total number of people
Percent [wearing elf costume] = [40-10] / 50
Percent [wearing elf costume] = [30] / 50
Percent [wearing elf costume] = 60%
4/2 - 1/2
find a common denomator
Answers
Answer:
3/2 or 1 and 1/2 and it already has a common denominator.
Step-by-step explanation:
The Denominators are the same and 4-1=3 with the same denominator.
Answer:
The answer is 1. If it is wrong im sorry.
Step-by-step explanation:
4/2 well 2 goes in to 4 two times so that makes it 2 and 2 - 1/2 is 1
hope this help mabey even consider brainliest
a speedboat that costs $45,000 is depreciating at a rate of 20% per year. Find the value of the boat after 4 years.
Answers
Answer:
$18,432
Step-by-step explanation:
After the first year, the speedboat is now worth $36,000 because 20% of 45,000 is 9,000, and 45,000 - 9,000 = 36,000. After the second year, it is now worth $28,800. After the third year, it is worth $23,040 since 20% of 28,800 is 5,760 and 28,800 - 5,760 = 23,040. After four years, the boat that once was worth $45,000 is now worth $18,432.
After 4 years, the value of boat is $9,000.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
A speedboat costs $45,000 is depreciating at a rate of 20% per year.
So, The depreciating amount after one year = 20% of $45,000
= 20/100 × 45,000
= $9,000
Thus, The value of boat after 4 years = $45,000 - 4 × $9,000
= $45,000 - $36,000
= $9,000
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•Exercise #2. Suppose a market with two firms, 1 and 2, facing the inverse demand p()=10− p(Q)=10-Q where =1+2Q=q1+q2. The two firms incur a marginal cost of production c1=c2=2c1=c2=2, produce a homogeneous good, and are Cournot competitors.
•Q4) Draw the firms’ best-response functions with 1q1 on the vertical axis and 2q2 on the horizontal axis.
•Q5) Determine firm 2’s quantity at the Cournot equilibrium.
•Q6) Assume firm 1 adopts a raising rival’s cost strategy at the expense of firm 2. While firm 1’s marginal cost remains at c1=2c1=2, firm 2’s marginal cost increases to c2=4c2=4. On the same graph as the one used to answer Q4, show the effect of the raising rival’s cost strategy on the firms’ best-response functions.
•Q7) Determine firm 2’s quantity at the new Cournot equilibrium.
Q8) Determine the market price at the new Cournot equilibrium.
Answers
firm 2's quantity at the Cournot equilibrium is q2=5/3.the inverse demand function: p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4. firm 2's quantity at the new Cournot equilibrium is q2=4/5.
The best response of firm 1 is given by 1q1=5−0.5q21+q2, and the best response of firm 2 is given by 2q2=5−0.5q12+q1. These best response functions are illustrated in the following diagram:
At the Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect.
Therefore, solving the two best response functions simultaneously for q1 and q2 gives:
q1=q2=5/3
Therefore, firm 2's quantity at the Cournot equilibrium is q2=5/3.
The new best response function for firm 2 is given by 2q2=5−q1+2q22. This is obtained by replacing c2=2 with c2=4 in firm 2's profit function. The new best response function is illustrated below:
At the new Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect. Therefore, solving the two best response functions simultaneously for q1 and q2 gives:
q1=11/5
q2=4/5
Therefore, firm 2's quantity at the new Cournot equilibrium is q2=4/5.
To determine the market price at the new Cournot equilibrium, we substitute the new equilibrium quantities into the inverse demand function:
p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4
Therefore, the market price at the new Cournot equilibrium is p=4.
In this exercise, we consider a market with two firms, 1 and 2, facing the inverse demand p()=10− p(Q)=10-Q where =1+2Q=q1+q2.
The two firms incur a marginal cost of production c1=c2=2c1=c2=2, produce a homogeneous good, and are Cournot competitors. The best response of firm 1 is given by 1q1=5−0.5q21+q2, and the best response of firm 2 is given by 2q2=5−0.5q12+q1. These best response functions are illustrated in the diagram below:
At the Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect
. Therefore, solving the two best response functions simultaneously for q1 and q2 gives q1=q2=5/3. Therefore, firm 2's quantity at the Cournot equilibrium is q2=5/3.The new best response function for firm 2 is given by 2q2=5−q1+2q22. This is obtained by replacing c2=2 with c2=4 in firm 2's profit function.
The new best response function is illustrated in the following diagram:At the new Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect.
Therefore, solving the two best response functions simultaneously for q1 and q2 gives q1=11/5 and q2=4/5. Therefore, firm 2's quantity at the new Cournot equilibrium is q2=4/5
To determine the market price at the new Cournot equilibrium, we substitute the new equilibrium quantities into the inverse demand function: p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4. Therefore, the market price at the new Cournot equilibrium is p=4.
In conclusion, we have analyzed the effect of a raising rival's cost strategy on a Cournot duopoly. We have shown that the strategy reduces firm 2's quantity and increases the market price, but does not affect firm 1's quantity.
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Several friends (Calvin, Dean, Kelli, and Lee) went to Cal's Late Night Diner for a bite to eat. Match each person to their drink (Iced tea, Lemonade, Root Beer, and Water) and determine how much each paid ($4.99, $5.99, $6.99, and $7.99) for their meal.
Clues:
1. The Diner who paid $4.99 was either Calvin or the one who got the Root Beer.
2. Kelli paid $6.99
3. The one who got the water paid 1 dollar less than Dean.
4. Calvin paid more than Lee.
5. The one who got the Root beer paid 1 dollar less than the one who got the Iced Tea.
Answers
Based on the given clues, we can determine the person, drink, and price paid for each individual:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
How to determine how much each friends paidFrom clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.
From clue 2, Kelli paid $6.99.
From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.
From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.
Therefore, the final assignments are:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
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PLEASE HELP ME!!! WILL GIVE BRAINLIEST!!!!
Answers
is this a test I can tell you what it is
Hana has decided to purchase a new car. she decides to put 15% down and finance the remaining balance. the bank offers hana a 48 month loan at 6.76%. if the car is valued at $28,000, what will her monthly payments be? a. $567.27 c. $760.12 b. $691.32 d. $897.32
Answers
Hana's monthly payments would be $567.27. Hence, option A is the correct answer to this question.
The remaining balance after the 15% down payment is $28,000 * 85% = $23,800. To calculate the monthly payment, we can use the following formula -
payment = (loan amount * monthly interest rate) / (1 - (1 + monthly interest rate)^(-number of months))
payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
where P = $23,800, r = 6.76% / 12 = 0.0563333, n = 48 months
Substituting in the values, we get,
payment = $23,800 * 0.0563333 * ((1 + 0.0563333)^48) / ((1 + 0.0563333)^48 - 1) = $567.27
So, Hana's monthly payments would be $567.27. Answer: A. $567.27
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The total cost (in dollars) for a company to manufacture and sell x items per week is C(x)=50x+400. If the revenue brought in by selling all x items is R(x)=80x-0.05x2, find the weekly profit. How much profit will be made by producing and selling 40 items each week? Hint: P(x)=R(x)−C(x).
Answers
Answer:
$720
Step-by-step explanation:
Given the following functions
Cost function C(x)=50x+400
Revenue function R(x)=80x-0.05x^2
P(x)=R(x)−C(x).
Profit function P(x) = 80x-0.05x^2 - (50x+400)
P(x) = 80x-0.05x^2 - 50x - 400
Substitute x = 40
P(40) = 80(40)-0.05(40)^2 - 50(40) - 400
P(40) = 3200-80-2000-400
P(40) =3200-2480
P(40) = 720
Hence the amount of profit made is $720
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
Answers
Answer: 1436 units cubed (3.14) or 1437 units cubed (π)
Step-by-step explanation:
answer depends on if you substitute in 3.14 for π or not
Find the value of y. Y squared=169 I wrote 13 and I tried -13 but it’s saying it wrong PLEASE HELP
Answers
The value of y from the equation given in the task content; y squared = 169 is; ±13 and hence should be expressed as such.
What is the value of the variable according to the equation given in the task content; y squared = 169?It follows from the task content that the value of the variable y according to the equation given y squared = 169 as in the task content.
Since the equation given in the task content is;
y² = 169
To determine the value of y, take the square root of both sides so that we have;
√y² = ± √169
y = ± 13 ( This follows from the fact that 169 is a perfect square).
Therefore, the value of y which satisfies the equation given can be either of -13 and 13 and hence, the answer should be expressed as; ±13.
Ultimately, the value of y from the equation given in the task content; y squared = 169 is; ±13 and hence should be expressed as such.
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If 4 notebooks and 3 packages of pens cost $7.43 and
5 notebooks and 2 packages of pens cost $7.03, what is the
cost of 1 notebook?
Answers
Answer:
i believe its one of these!
A. $0.89 B.$0.79 C. $1.29
Step-by-step explanation:
evaluate f(g(5)) if F (x) = 5x + 2 and g (x) =X2 -4
Answers
Answer:
Step-by-step explanation:
g(5) = 5^2 - 4 = 25 - 4 = 21
f(21) = 5(21) + 2 = 105 + 2 = 107
Study the solutions of the three equations on the right. Then, complete the statements below.
There are two real solutions if the radicand is
There is one real solution if the radicand is
There are no real solutions if the radicand is
Answers
There are two real solutions if the radicand is positive.
There is one real solution if the radicand is zero.
There are no real solutions if the radicand is negative.
What is the radicand about?In mathematics, the radicand refers to the value inside a square root (√) symbol. In the given equations and solutions, we can see that there are square root symbols involved, and we can determine the nature of the solutions based on the sign of the radicand.
For the first equation, y = -16x² + 32x - 10, the solutions for x are given as x = (-32 ± √384) / -32. The radicand in this case is 384. Since 384 is positive, greater than 0, there will be two real solutions for x.
For the second equation, y = 4x² + 12x + 9, the solutions for x are given as x = (-12 ± √0) / 8. The radicand in this case is 0. Since the square root of 0 is 0, there is only one real solution for x in this case.
Therefore, For the third equation, y = 3x² - 5x + 4, the solutions for x are given as x = (5 ± √(-23)) / 6. The radicand in this case is -23. Since the square root of a negative number is not a real number, there are no real solutions for x in this case.
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See full text below
Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is 1. y = negative 16 x squared + 32 x minus 10. x = StartFraction negative 32 plus-or-minus StartRoot 384 EndRoot Over negative 32 EndFraction. 2. y = 4 x squared + 12 x + 9. x = StartFraction negative 12 plus-or-minus StartRoot 0 EndRoot Over 8 EndFraction. 3. y = 3x squared minus 5 x + 4. x = StartFraction 5 plus-or-minus StartRoot negative 23 EndRoot Over 6 EndFraction.
use integrals test, comparisons tests to determine the convergence or divergence for an alterning series
Answers
To determine the convergence or divergence of an alternating series, you can use the Alternating Series Test. This test states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges.
Additionally, if the terms do not approach zero, the series diverges.
To apply the Alternating Series Test, you need to check two conditions:
1. The terms of the series must alternate in sign.
2. The absolute value of the terms must decrease or approach zero.
If both conditions are satisfied, you can conclude that the alternating series converges. However, if either condition fails, the series diverges.
If you want to determine the convergence or divergence more precisely, you can use the Integral Test or the Comparison Test. The Integral Test allows you to compare the convergence or divergence of a series to the convergence or divergence of an improper integral. If the integral converges, the series converges, and if the integral diverges, the series diverges.
The Comparison Test is another method to determine the convergence or divergence of a series. It involves comparing the given series with a known series whose convergence or divergence is already known. If the known series converges and the terms of the given series are less than or equal to the corresponding terms of the known series, then the given series also converges. Conversely, if the known series diverges and the terms of the given series are greater than or equal to the corresponding terms of the known series, then the given series also diverges.
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Carlo’s Bakery is having a special where he packages 6 muffins together for a low price and he packages 20 cookies together for a low price. His baker realized they sold the same amount of muffins and cookies yesterday due to this great sale. What is the minimum amount of muffins that were sole yesterday? Is this a GCF or LCM problem?
Answers
Answer:
They sold 60 muffins and 60 cookies yesterday
It is a LCM problem
Step-by-step explanation:
6 muffins together
20 cookies together
To sell the same amount of muffins and cookies,
Find the lowest common multiple of 6 muffins and 20 cookies
6 muffins = 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78
20 cookies = 40, 60, 80
The lowest common multiple of 6 muffins and 20 cookies is 60
Therefore,
They sold 60 muffins and 60 cookies yesterday
It is a LCM problem
when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time. on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day. find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited
Answers
Isa took 4 hour when isa go from UK to USA and took 14 hour when she returns and time difference will be 10 hours
What is a definition distance?
the extent or amount of space between two things, points, lines, etc. the state or fact of being apart in space, as of one thing from another; remoteness
when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time.
so isa took 4 hour
on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day
isa tool 14 hour
find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited
length of flight is 18 hour
time difference will be 14-4 = 10 hour
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what is the prime number of 65
Answers
Answer:
Factors of 65: 1, 5, 13, and 65.
Prime Factorization of 65: 65 = 5 × 13.
Step-by-step explanation:
hope this helps!
Answer:
1, 5, 13, and 65.
Step-by-step explanation:
A weatherman asks 75 people from two different cities if they own rain boots. Complete the two-way frequency table to show results of the survey\
Answers
The complete two way frequency table after survey is:
13 19 32
28 15 43
41 34 75
Just count the missing numbers in the row or column:
32 - 19 = 13
This is the value that goes to the top left in the table because we can subtract here. There are no total votes.
We can now calculate the total number of positive votes to be 41.
In the value of the No column, we will again find the middle number by subtracting the top number from the total number of No votes.
34 - 19 = 15
Similarly,
From the middle row, we can simply add the values to get the total:
28 + 15 = 43.
Finally we find a total of 75.
The complete two way frequency table after survey is:
13 19 32
28 15 43
41 34 75
Complete Question:
A weatherman asks 75 people from two different cities if they own rain boots. Complete the two-way frequency table to show results of the survey.
Rain Boots
City Yes No Total
A 19 32
B 28
Total 34
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Example 3 A company sells two models of mobile phones: the basic model and the luxury model. The demand functions for the mobile phones sold are given by pb=160−0.15x−0.05y and pt=220−0.15x−0.15y, where pb and pl are the prices of the two models in dollars, x is the units of the basic mobile phones sold per week, and y is the units of the luxury mobile phones sold per week. Therefore, the total weekly revenue function R(x,y) is R(x,y)=160x+220y−0.2xy−0.15x2−0.15y2. a) Determine how many units of each model should be sold per week in order to maximize the company's total weekly revenue. b) Determine the maximum value of the total weekly revenue. Imple 1 Find any relative extrema of the function f(x,y)=x2+y2−9x−7y.
Answers
a. There should be 400/3 units of the basic model and 200/3 units of the luxury model sold per week in order to maximize the company's total weekly revenue.
b. The maximum value of the total weekly revenue is -25/2.
Part (a):
To maximize the total weekly revenue, we need to find the critical points of the revenue function R(x,y), where the partial derivatives are zero or do not exist.
∂R/∂x = 160 - 0.4x - 0.2y = 0 ...... (1)
∂R/∂y = 220 - 0.2x - 0.3y = 0 ...... (2)
Solving these two equations simultaneously, we get:
x = 400/3 and y = 200/3
Substituting these values of x and y into the revenue function R(x,y), we get:
R(400/3, 200/3) = $70,266.67
Therefore, the company should sell 400/3 units of the basic model and 200/3 units of the luxury model per week to maximize the total weekly revenue.
Part (b):
To find the maximum value of the total weekly revenue, we need to evaluate the revenue function R(x,y) at the critical point (400/3, 200/3) and at the endpoints of the feasible region (where x and y are non-negative).
At (400/3, 200/3), we have:
R(400/3, 200/3) = $70,266.67
At the endpoints of the feasible region, we have:
R(0,0) = $0
R(0,1466.67) = $32,133.33
R(2666.67,0) = $42,666.67
Therefore, the maximum value of the total weekly revenue is $70,266.67 when the company sells 400/3 units of the basic model and 200/3 units of the luxury model per week.
Example 1:
To find the relative extrema of the function f(x,y) = x^2 + y^2 - 9x - 7y, we need to find the critical points of the function, where the partial derivatives are zero or do not exist.
∂f/∂x = 2x - 9 = 0 ...... (1)
∂f/∂y = 2y - 7 = 0 ...... (2)
Solving these two equations simultaneously, we get:
x = 9/2 and y = 7/2
Substituting these values of x and y into the function f(x,y), we get:
f(9/2, 7/2) = -25/2
Therefore, the critical point (9/2, 7/2) is a relative maximum of the function f(x,y), and the maximum value is -25/2.
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