To determine the number of headphones that must be sold to maximize profit and the maximum profit, we can analyze the profit function P(x) = -0.02x² + 44x - 1750. The number of headphones sold to maximize profit is 1100, and the maximum profit is $17,050.
(a) To find the number of headphones that maximize profit, we need to identify the x-value at which the profit function reaches its maximum. The maximum point occurs at the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula x = -b / (2a), wherea and b are the coefficients of the quadratic function. In this case, a = -0.02 and b = 44. Plugging these values into the formula, we find x = -44 / (2 * -0.02) = 1100. Therefore, 1100 headphones must be sold to maximize profit.
(b) To calculate the maximum profit, we substitute the value of x = 1100 into the profit function P(x). P(1100) = -0.02(1100)² + 44(1100) - 1750 = -24200 + 48400 - 1750 = 17050. Hence, the maximum profit is $17,050.
In conclusion, in order to maximize profit, 1100 headphones must be sold, resulting in a maximum profit of $17,050.
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The Zombie Apocalypse has come to Panama City Beach. It starts when 3 Spring Breakers become zombie after an encounter with a deadly fish. Waking up the next day, each Spring Breaker can infect 4 more people per day before needing a rest. Each of these zombies can, in turn, infect an additional 4 people per day. Write an Exponential Function to represent this situation. Then find out how many crazy Spring Break Zombies will be roaming the beach at the end of the week (Day 7)?
Answer:
By the end of the week there will be 49,152 zombies in Panama City Beach.
Step-by-step explanation:
Since the Zombie Apocalypse has come to Panama City Beach, starting when 3 Spring Breakers become zombie after an encounter with a deadly fish, and since waking up the next day, each Spring Breaker can infect 4 more people per day before needing a rest , and each of these zombies can, in turn, infect an additional 4 people per day, to determine how many crazy Spring Break Zombies will be roaming the beach at the end of the week the following exponential function has to be solved:
3 x 4 ^ 7 = X
3 x 16,384 = X
49.152 = X
Therefore, by the end of the week there will be 49,152 zombies in Panama City Beach.
The number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7 are 49,152 and the equation for the situation is,
[tex]x=3\times(4)^7\\[/tex]
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=ba^x+c[/tex]
Here, a, b and c are the real numbers.
The Zombie Apocalypse has come to Panama City Beach. It starts when 3 Spring Breakers become zombie after an encounter with a deadly fish.
In the next morning, each Spring Breaker can infect 4 more people per day before needing a rest. Each of these zombies can, in turn, infect an additional 4 people per day.
As total number of weeks are 7. Thus, for this situation, the exponential function for the variable x can be given as,
[tex]x=3\times(4)^7\\[/tex]
Now to find the number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7, simplify the above equation as,
[tex]x=3\times(4)^7\\\\x=3\times16384\\x=49152[/tex]
Hence, the number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7 are 49,152 and the equation for the situation is,
[tex]x=3\times(4)^7\\[/tex]
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Ben wants to buy a new car stereo and he has already saved some money. He used this inequality to represent the amount he still has to save to be able to buy the stereo, where a represents the amount still left to save.
a + 212 greater-than-or-equal-to 365
If Ben saves $15 a week for the next 10 weeks, will he be able to buy the stereo and why?
Answer:
Since Ben would have $362, he won't be able to buy the stereo as he needs to have an amount greater than or equal to 365.
Step-by-step explanation:
First, you need to determine the amount that Ben would have after saving $15 for the next 10 weeks:
$15*10=$150
Now, the inequality indicates that the amount left to save plus 212 should be greater than or equal to 365, so you have to add up 212 plus the amount Ben will save in the next 10 weeks to be able to determine if he would be able to buy the stereo:
150+$212=$362
Since Ben would have $362, he won't be able to buy the stereo as he needs to have an amount greater than or equal to 365.
Four times a first number decreased by a second number is 19. The first number increased by four times the second number is −8. Find the numbers.
Answer:
a = 4
b = -3
Step-by-step explanation:
Let a and b be the two numbers.
According to question,
4a - b = 19........(i)
And,
a + 4b = -8........(ii)
From (i),
4a - b = 19
or, b = 4a - 19
Replacing b in (ii),
a + 4(4a - 19) = -8
a + 16a - 76 = -8
17a = -8 + 76
17a = 68
a = 68/17
a = 4
And,
b = 4a - 19
= 4 x 4 - 19
= 16 - 19
= -3
A company’s stock was selling at 15 a share a month later it was selling at 27 a share what is the percent increase
Answer:
80 %
Step-by-step explanation:
I hope this helps!!
Find the Laplace Transform of number 1 using the definition via integration. F(t) = 5 sin 3t Solve for the Laplace transform using the formula for numbers 2 and 3. G(t) = t^5 — 1/4 e^-9t + 5(t − 1)² F(t) = e^-2t-5
The Laplace Transform of the function F(t) = 5sin(3t) can be found by using the definition of the Laplace Transform, which involves integrating the function with respect to time. The Laplace Transform of F(t) is not a number, but rather a function in the complex domain.
To find the Laplace Transform of F(t) = 5sin(3t) using the definition, we need to integrate the function with respect to time from 0 to infinity. The Laplace Transform is defined as L{F(t)} = ∫[0,∞] F(t)e^(-st) dt, where s is a complex number.
Integrating [tex]5sin(3t)e^(-st)[/tex]with respect to t results in a complex function that depends on s. The integration involves applying the integration rules and evaluating the integral limits. The resulting Laplace Transform is a function of s, denoted as L{F(t)}.
However, for the functions G(t) = [tex]t^5 - (1/4)e^(-9t) + 5(t - 1)^2 and F(t) = e^(-2t - 5)[/tex], the Laplace Transform can be computed using the Laplace Transform formulas. These formulas provide specific transformations for various types of functions, making the calculation more straightforward. By applying the Laplace Transform formulas to G(t) and F(t), we can obtain their respective Laplace Transform expressions, denoted as L{G(t)} and L{F(t)}. These expressions will involve algebraic manipulations and the use of the Laplace Transform tables to identify the corresponding transformations.
Overall, the Laplace Transform is a powerful tool in the field of mathematics and engineering that allows us to transform functions from the time domain to the complex frequency domain, facilitating the analysis and solution of differential equations and systems of equations.
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Use the following probability distribution to answer questions
x -15 -10 -5 0 5 10 15
P(X=x) 0.05 0.34 0.13 0.24 0.08 0.11 0.05
1. Find P(X=0) a. 0
b. 0.24 c. 0.48 d. 0.52 e. 0.08
The probability P(X=0) is equal to 0.24.
In the given probability distribution, we are provided with the probabilities associated with each value of the random variable X. To find P(X=0), we need to identify the probability assigned to the value 0.
Looking at the table, we see that the probability P(X=0) is given as 0.24. Therefore, the correct answer is option b. 0.24.
The probability distribution assigns probabilities to specific values of the random variable X. In this case, the value 0 has a probability of 0.24. This indicates that there is a 0.24 chance of observing the value 0 when the random variable X is sampled from this distribution.
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what is the rate of change for y=38x+20
A. 38
B. 20
C.1
D. it has no term
Answer:
A
Step-by-step explanation:
Find the greatest common factor of 24x^2 and 42xy^3 .
Answer:
12y2
Step-by-step explanation:
What is the equation of the line shown in the graph?
Answer:
-6
Step-by-step explanation:
it is going through the y axis
The following sentence contains three kinds of numbers: cardinal, ordinal and nominal. The student with identification number 87 earned a 93 on test 4. a. 93 is__ b. 87 is__ c. 4 is__
The values 93, 87 and 4 are cardinal , ordinal and nominal numbers respectively
The value 93 is a cardinal number as it represents a specific number, in this case the student's test score.
The value 87 is an ordinal number as It represents the student's identification number, which indicates their place in a sequence.
The value 4 is a nominal number as It represents the test number, which is a label or name for something.
In general, cardinal numbers are used to count things, ordinal numbers are used to rank things, and nominal numbers are used to identify things.
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Find the Range of the following set of data. (Round to the
nearest whole number.)
1, 1, 3,0, 7, 2, 0, 3, 1, 6, 8, 1
PLEASE HELP IM DESPERATE
Step-by-step explanation:
put them in least to greatest, so that would be: 0,0,1,1,1,1,2,3,3,6,8,7,8, then do the greatest minus the lowest: 8-0=8
For K4,5, represent an represent an adjacency matrix, and a graph representstion for the graph.
The adjacency matrix for the graph K4,5 will consist of two distinct sets of vertices with edges connecting every vertex from one set to every vertex in the other set.
The graph K4,5 is a complete bipartite graph with two sets of vertices, let's call them A and B. Set A contains four vertices (A1, A2, A3, A4), and set B contains five vertices (B1, B2, B3, B4, B5). In the adjacency matrix representation, the rows correspond to the vertices of set A, and the columns correspond to the vertices of set B. Therefore, the adjacency matrix will have dimensions 4x5.
To construct the adjacency matrix, we assign a value of 1 to the element at row i and column j if there is an edge between vertex Ai and vertex Bj. Since K4,5 is a complete bipartite graph, every vertex in set A is connected to every vertex in set B. Thus, all elements in the matrix will be 1.
The graph representation of K4,5 will consist of two distinct sets of vertices, A and B, with edges connecting every vertex from set A to every vertex in set B. This means that there will be a total of 20 edges in the graph. The graph can be visualized as two distinct groups of vertices, with no edges connecting vertices within the same set but with edges connecting every vertex from one set to every vertex in the other set.
In summary, the adjacency matrix for K4,5 will be a 4x5 matrix with all elements equal to 1. The graph representation will consist of two sets of vertices, A and B, with 20 edges connecting every vertex from one set to every vertex in the other set.
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HELP THIS IS DUE IN LIKE 20 MINS
Answer:
I cant see the full question enough to help you. Its showing like part of the question.
Answer:
4x+y=-7
Step-by-step explanation:
Which quadrilateral's diagonals are congruent and perpendicular bisectors of each other?
Diagonals congruent: rectangle, square, isosceles trapezoid
Perpendicular bisectors: Rhombus, Square
You just obtained a credit card. You immediately purchase a stereo system for $200. your credit limit is $1000. Let's assume that you make no payments and purchase nothing more and there are no other fees. The monthly interest rate is 1.42%.
What is the growth rate of your credit card balance?
A. 0.42
B. 0.0142
C. 14.2
D. 142
Answer:
its b
Step-by-step explanation:
have a great day <3
The growth rate of your credit card balance is approximately 0.0142.
Therefore, the correct option is B.
Given that you got a credit card, you purchased a stereo system for $200. your credit limit is $1000.
The monthly interest rate is 1.42%.
We need to determine the growth rate of your credit card balance,
To calculate the growth rate of your credit card balance, we need to consider the monthly interest rate and the initial purchase amount.
The monthly interest rate is 1.42%, which can be expressed as a decimal by dividing it by 100: 0.0142.
The initial purchase amount is $200.
Assuming no payments are made and no additional purchases are made, the credit card balance will increase each month due to the accrued interest.
To calculate the growth rate, we can divide the accrued interest by the initial purchase amount.
Accrued interest = Monthly interest rate x Initial purchase amount
= 0.0142 x $200
= $2.84
Growth rate = Accrued interest / Initial purchase amount
= $2.84 / $200
≈ 0.0142
Therefore, the growth rate of your credit card balance is approximately 0.0142, which corresponds to option B.
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Need this answer ASAP the last missing square says “take the square root of both sides”
Answer:
add 5 to both sides, divide by 2, take square root, subtract 3/4
Step-by-step explanation:
I think you maybe do the reverse order of operations, which is SADMEP (subtract/add, then divide/multiply, then take care of exponents and square roots, then do that same order for whatever's in parenthesis.)
Use series to approximate the definite integral to within the indicated accuracy:
the integral from from 0 to 0.4 of e^?x^3 dx with an error <10?4
Note: The answer you derive here should be the partial sum of an appropriate series (the number of terms determined by an error estimate). This number is not necessarily the correct value of the integral truncated to the correct number of decimal places.
We evaluate S_n by substituting x = 0.4 into the nth partial sum and obtain our approximation for the integral.
To approximate the definite integral ∫(0 to 0.4)
[tex] {e}^{-x^3} [/tex]
dx with an error less than
[tex] {10}^{ - 4} [/tex]
we can use a Taylor series expansion for
[tex]{e}^{-x^3} [/tex]
The Taylor series expansion of
[tex]{e}^{-x^3} [/tex]
centered at x = 0 is:
[tex] {e}^{-x^3} = 1 - x^3 + (x^3)^2/2! - (x^3)^3/3! + ...[/tex]
By integrating this series term by term, we can approximate the integral. Let's denote the nth partial sum of the series as S_n.
To estimate the number of terms needed for the desired accuracy, we can use the error estimate formula for alternating series:
|Error| ≤ |a_(n+1)|, where a_(n+1) is the absolute value of the first omitted term.
In this case, |a_(n+1)| =
[tex]|(x^3)^{n+1} /(n+1)!| ≤ {0.4}^{(3(n+1)} /(n+1)!
[/tex]
By setting
[tex]{0.4}^{(3(n+1))} /(n+1)! < 10^(-4)[/tex]
and solving for n, we can determine the number of terms required.
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Which function is equivalent to (x)=-7(x+4)2-1?
a : f(x)=-7x2 + 8x+15
b : F(x)=-7x2-56x-113
C : f(x)=-7x2-56x-105
d : f(x)=-7x2 + 111
Answer:
answer : b
Step-by-step explanation:
hello :
calculate : f (x)=-7(x+4)²-1
f(x) = -7(x²+16+8x) -1 use identity : (a+b)² = a²+b²+2ab
f(x) = -7x²-112 -56x -1
f(x) = -7x²-56x -113
The Beachside Boutique has an average starting salary of $25,100 but the actual salary could differ from that average by as much as $1,040. Which absolute value inequality could be used to determine if a salary falls within this range?
a) |x − 25,100| ≥ 1040
b) |x − 1040| ≤ 25,100
c) |x − 25,100| ≤ 1040
d) |x − 1040| ≥ 25,100
Answer:
is it 160167
Step-by-step explanation:
hope i helped out
HELPP ME
About what percent of Australia's total medals were gold?
A. 5%
B. 2%
C. 50%
D. 20%
Answer:
20%
Of Australia's total percent were gold!
How many solutions does this system of equations have? x+y=10 2x+2y=20
Answer:
Infinitely many solutions
Step-by-step explanation:
ive learned thiss
Answer: Infinite amount of solutions since the two equations are equal
Basically x = x and y = y all numbers would work
Step-by-step explanation:
Cheryl moves houses. Her old house is 3 kilometers from her new house. How many meters is it from the old house to the new house?
Answer:
3000 here hope this helps you out
PLEASE HELP FIRST ONE TO GET IT RIGHT GETS brainiest :oooo
A. x and y are both within the same solar system.
7.2 light years= 455336 AU
Worth five points! it doesnt tell me if what answer is right but if i get 75% or up i will mark the first person who answered with an actual answer brainliest and i don't lie about brainliest!!
What is m∠U?
A. 17
B. 29
C. 46
D. 134
Answer:
A
Step-by-step explanation:
Remarks
The given angle is an exterior angle.It's value is 46 degrees. An exterior angle is the sum of the two remote angles. (A remote angle is one that is not supplementary to the given exterior angle.Solution
46 = <u + <t<t = 2946 = <u + 29 Subtract 29 from both sides.46 - 29 = <u<u = 17 degrees
Can you say a coefficient is
significantly different from zero at 5% level if the coefficient of
a variable is twice as large as its estimated standard error?
Explain.
A coefficient is significantly different from zero at 5% level if the coefficient of a variable is twice as large as its estimated standard error. This is because, at the 5% level of significance, the critical value for the t-distribution, when a two-tailed test is used, is equal to 1.96. To be significantly different from zero, the calculated t-value has to be greater than 1.96 or less than -1.96.
Suppose the estimated standard error is SE and the coefficient of the variable is β. The standard error of β, denoted by SE(β), is equal to SE/√n, where n is the sample size. Thus, if the coefficient of the variable is twice as large as its estimated standard error, then β > 2SE.
And, the calculated t-value would be greater than (β/SE) > 2, which is greater than 1.96. Therefore, we can say that the coefficient is significantly different from zero at the 5% level.
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Raymond has two bags of candy. • Bag A has 15 total pieces of candy, 9 are chocolate candies. Bag B has 10 total pieces of candy, 5 are chocolate candies. Which statement is true?
Answer:
The probability of selection of chocolate candy from bag A is ( 10%) bigger than from the bag B
Step-by-step explanation:
From bag A the probability (p₁ ) of selection ( in a random sample) of one chocolate candy is
p₁ = 9/15 p₁ = 0,6
From bag B the probability ( p₂ ) of selection ( in a random sample) of one chocolate candy is:
p₂ = 5/10 p₂ = 0,5
Then the probability of selection of chocolate candy from bag A is bigger than from the bag B
p₁ > p₂ p₁ - p₂ = 0,6 - 0,5 p₁ - p₂ = 0,1 p₁ - p₂ = 10%
p
Multiply and combine like terms. Use^ for exponents. (2x-10)(3x-3)
Answer:
69
Step-by-step explanation:
Simplify:
5a+6a^2+2a^0-3a^2-9a
3a^2-4a+2
-a^3+2
-a^2+2
3a^2-4a+1
Answer:
I believe that the answer is '3a^2-4a+2
Factor the expression below. A. (x + 5)(x + 5) B. (x - 5)(x + 5) C. 5(x2 - x + 5) D. (x - 5)(x - 5)
Answer:
A. x² +10x +25
B. x² - 25
C. 5x² -5x + 25
D. x²- 10x + 25
Step-by-step explanation:
A. (x+5)(x+5)
x² + 5x + 5x + 25
x² +10x + 25
B. (x-5)(x+5)
x² + 5x - 5x - 25
x² -25
C. 5(x² -x +5)
5x² -5x + 25
D. (x-5)(x-5)
x² - 5x -5x + 25
x²- 10x + 25
5 in=? feet fraction form