The critical points of f(x) on the interval 0 < x < 10 are: (2, max), (7.5, min)
To estimate the critical points of f(x) on the interval 0 < x < 10, we need to look for points where the derivative, f'(x), equals zero or is undefined. However, we are given a table of values for f(x) instead of f'(x), so we need to first estimate f'(x) using these values.
One way to do this is to use finite differences. We can calculate the first finite difference for each pair of adjacent values in the table, which gives an estimate of the derivative at the midpoint of the interval:
f'(x) ≈ (f(x+1) - f(x)) / (1)
Using this formula, we can calculate the following table of values for f'(x): 0123456789 23-2.79-8-5
Now we can look for critical points of f(x) by finding where f'(x) equals zero or is undefined: - f'(x) = 0 when x = 2 or x = 7.5 (approximately) - f'(x) is undefined at x = 0 and x = 10 (endpoints of the interval)
To classify each critical point, we need to look at the sign of the derivative near the point. If f'(x) changes sign from positive to negative at a critical point, then it is a local maximum. If it changes from negative to positive, then it is a local minimum. If it does not change sign, then it is neither a maximum nor a minimum.
Using the values in the table for f'(x), we can see that: -
Near x = 2, f'(x) changes sign from positive to negative, so it is a local maximum. - Near x = 7.5, f'(x) changes sign from negative to positive, so it is a local minimum. - At the endpoints x = 0 and x = 10, f'(x) is undefined, so there are no critical points.
Therefore, the critical points of f(x) on the interval 0 < x < 10 are: (2, max), (7.5, min)
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How many integers between 100 and 300 have both 11 and 8 as factors?
176, 264. your welcome!
Projectile motion. the height, y metres, of a ball after it has been hit can be modelled by the equation y = -1/8x²+x+c, where x is the horizontal distance travelled by the object in metres and c is a constant. (i) given that the maximum height attained by the ball is 2.4 metres, find the value of c and the corresponding horizontal distance travelled by the ball.
The value of c is 0.4 and the corresponding horizontal distance travelled by the ball is 4 meters.
How to solve projectile equations?
We are given the projectile equation:
y = -1/8x² + x + c
To find the value of c, we can use the fact that the maximum height attained by the ball is 2.4 meters. The maximum height occurs at the vertex of the parabola, which is given by:
x = -b/2a
where a = -1/8 and b = 1.
Therefore,
x = -(1)/(2*(-1/8)) = 4
So, the corresponding horizontal distance travelled by the ball is 4 meters.
Now, we can use the maximum height attained by the ball to solve for c.
y = -1/8x² + x + c
Substituting x = 4 and y = 2.4, we get:
2.4 = -1/8(4)² + 4 + c
2.4 = -1/8(16) + 4 + c
2.4 = -2 + 4 + c
c = 0.4
Therefore, the value of c is 0.4.
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Determine the equation of the circle graphed below.
The equation of the circle graphed is given as follows:
(x + 1)² + (y + 3)² = 36.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.
The coordinates of the center of the circle are given as follows:
(-1, -3).
The radius of the circle is given as follows:
r = 6 units.
Then the equation of the circle is given as follows:
(x + 1)² + (y + 3)² = 36.
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A large box of chocolates has a width that is 2 times the height of the box and a length that is 1. 5 times the width of
the box. Each of the 48 chocolates rests in a cube with a side length of 1 inch
Let's start by using algebra to represent the relationships between the dimensions of the box:
Let h be the height of the box. Then the width of the box is 2h (since it is 2 times the height). And the length of the box is 1.5 times the width, so it is 1.5(2h) = 3h.So the dimensions of the box are: height = h, width = 2h, length = 3h.
Now let's find the volume of the box:
Volume = height x width x length Volume = h x 2h x 3h Volume = [tex]6h^3[/tex]Since we know that each chocolate rests in a cube with a side length of 1 inch, the volume of each chocolate is [tex]1^3 = 1[/tex] cubic inch. So the total volume of all 48 chocolates is 48 cubic inches.
Therefore, we can set up an equation to solve for h:
[tex]48 = (6h^3) / (1 cubic inch/chocolate)[/tex]
[tex]48 = 6h^3[/tex]
[tex]8 = h^3[/tex]
h = 2
So the height of the box is 2 inches, the width is 4 inches (since it is 2 times the height), and the length is 6 inches (since it is 1.5 times the width).
To check our work, we can calculate the volume of the box:
Volume = height x width x length
Volume = 2 x 4 x 6
Volume = 48 cubic inches
This matches the total volume of all 48 chocolates, so we can be confident in our answer.
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Find the linearization of the function z = x =√y at the point (-2, 4). L(x, y)=
The linearization of the function z = x =√y at the point (-2, 4) is L(x, y) = 2 + (1/4)(y-4).
To find the linearization of the function z = x =√y at the point (-2, 4), we need to use the formula for the linearization:
[tex]L(x, y) = f(a, b) + f_x(a, b)(x-a) + f_y(a, b)(y-b)[/tex]
where f(a, b) is the value of the function at the point (a, b), f_x(a, b) is the partial derivative of f with respect to x evaluated at (a, b), f_y(a, b) is the partial derivative of f with respect to y evaluated at (a, b), and (x-a) and (y-b) are the distances from the point (a, b) to the point (x, y).
In this case, we have:
f(x, y) = √y
a = -2
b = 4
So, we need to find the partial derivatives f_x and f_y:
[tex]f_x(x, y) = 0f_y(x, y) = 1/(2√y)[/tex]
evaluated at (a, b):
f_x(-2, 4) = 0
f_y(-2, 4) = 1/(2√4) = 1/4
Now, we can plug in all the values into the linearization formula:
[tex]L(x, y) = f(-2, 4) + f_x(-2, 4)(x-(-2)) + f_y(-2, 4)(y-4)L(x, y) = √4 + 0(x+2) + (1/4)(y-4)L(x, y) = 2 + (1/4)(y-4)[/tex]
Therefore, the linearization of the function z = x =√y at the point (-2, 4) is L(x, y) = 2 + (1/4)(y-4).
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Find the surface area of the figure below. 18 m 9sqrt(3) m 18
The surface area of the pyramid is 72 + 486√3 metres.
How to find the surface area of a pyramid?The pyramid above is an hexagonal pyramid. The surface area of the hexagonal pyramid can be found as follows:
surface area of a hexagonal pyramid = ph / 2 + B
where
B = base areap = perimeter of the baseheight of the pyramidTherefore,
Base area = 1 / 2pa
where
p = perimeter of the basea = apothemBase area = 1 / 2 × (18 × 6) × 9√3
Base area = 1 / 2 × 108 × 9√3
Base area = 54 × 9√3
Base area = 486√3 metres
surface area of a hexagonal pyramid = 108 × 18 / 2 + 486√3
Therefore,
surface area of a hexagonal pyramid = 972 + 486√3 metres
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Please help asap!! the image is attached, 35 points!!
Answer:
B
Step-by-step explanation:
Lisa's first step is to distribute, so you have to distribute all numbers.
(3+6x)-2(x+1)+5
3(1+2x)-2)x+1)+5
Hope this helps! :)
The following costs were for bikeway inc., a bicycle manufacturer that uses the high-low method:
output fixed costs variable costs total costs
950 $ 45,000 $ 95,000 $ 140,000
1,050 $ 45,000 $ 105,000 $ 150,000
1,100 $ 45,000 $ 110,000 $ 155,000
1,150 $ 45,000 $ 115,000 $ 160,000
at an output level of 1,000 bicycles, per unit total cost is calculated to be:
multiple choice
$139.13.
$145.00.
$121.50.
$126.09.
$100.00.
The per unit total cost at an output level of 1,000 bicycles is calculated to be $139.13.
To calculate the per unit total cost using the high-low method, follow these steps:
1. Identify the highest and lowest output levels (1,150 and 950 bicycles).
2. Calculate the difference in variable costs and output levels: ($115,000 - $95,000) / (1,150 - 950) = $20,000 / 200 = $100 per bicycle.
3. Calculate the variable cost for 1,000 bicycles: $100 x 1,000 = $100,000.
4. Add the fixed cost: $100,000 (variable cost) + $45,000 (fixed cost) = $145,000 (total cost).
5. Calculate the per unit total cost: $145,000 / 1,000 = $139.13 per bicycle.
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The main types of markets are called
answers)
(choose 1 of the 2 possible
1 point
O residential
customer
consumer
industrial
The main types of markets are:
Consumer markets: These are markets where individuals purchase goods or services for their personal use or consumption. Industrial markets: These are markets where businesses purchase goods or services for their own use in producing other goods or services.So, the correct answer is "consumer" and "industrial".
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Imagine some colored blocks are laid out in a row: three red, two blue, three red, two blue and so on. If there are 65 colored blocks, how many would be red?
A. 52
B. 39
C. 26
D. 13
There are 39 red blocks out of 65 total blocks.
To solve this problem, we need to find the total number of blocks in each repeating pattern. The pattern is three red blocks followed by two blue blocks. So in each pattern, there are five blocks total.
To find the number of red blocks in 65 total blocks, we need to figure out how many times the pattern repeats. We can do this by dividing the total number of blocks (65) by the number of blocks in each pattern (5):
65 ÷ 5 = 13
So the pattern repeats 13 times.
In each pattern, there are three red blocks. So to find the total number of red blocks, we need to multiply the number of red blocks in each pattern (3) by the number of times the pattern repeats (13):
3 x 13 = 39
Therefore, there are 39 red blocks out of 65 total blocks.
The correct answer is option B.
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Every line segment used to make this hospital logo is 3 meters long. What is the total area of the logo in square meters?
what is 10x10x10x10x10x10x10x10x103?
Answer:
1.03x 10^{10}
Step-by-step explanation:
No explanation, simple calculator calculation does the job.
Solve each of the following systems of equations. Find all solutions.
(a)
x+y=-1
3x=4-3y
(b)
3x-4y+2=0
10-10y=10y-15x
Answer:
Step-by-step explanation:
(a)
x + y = -1
3x = 4 - 3y
from 1st equation we can write x = -1 - y and put this x in the 2nd equation
3(-1 -y) = 4 -3y
-3 -3y = 4 -3y
now here y is getting cancel so that means this two equation has no common solution.
(b)
3x - 4y +2 = 0
10 -10y = 10y -15x
from 1st equation we can write x = (4y - 2)/3 and put this x in the 2nd equation
10 = 10y +10y -15((4y - 2)/3)
2 = 2y +2y - 3((4y -2)/3)
2 = 4y - (4y - 2)
again here 4y and 4y getting cancel so both the equation has no common solution.
What is the minimum surface area of a box whose base is a square and with no top that holds 32 cm³. a 16 b 32 c 64 d 48
The minimum surface area of the box is 68 cm², which corresponds to option (d).
How to calculate the surface area of box?Let the side length of the square base be x and the height of the box be h. Then, we have:
Volume of the box = x²h = 32
h = 32/x²
The surface area of the box is given by:
S = x² + 4(xh) = x² + 4x(32/x²) = x² + 128/x
To find the minimum surface area, we can differentiate S with respect to x, set the derivative equal to zero, and solve for x:
dS/dx = 2x - 128/x² = 0
2x = 128/x²
x⁴ = 64
x = 2 cm
Note that we need to check that this critical point gives us a minimum surface area. We can do this by checking the second derivative:
d²S/dx² = 2 + 256/x³
d²S/dx² at x = 2 is positive,
indicating that this critical point gives us a minimum surface area.
Substituting x = 2 in the equation for S, we get:
S = 2² + 128/2 = 4 + 64 = 68
Therefore, the minimum surface area of the box is 68 cm², which corresponds to option (d).
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Yvette cuts a hole from a rectangular panel to make a window. She wants to determine how
much of the panel is left after she cuts the hole. She writes:
(fraction left)
(area of panel) - (area of hole)
(area of panel)
If the panel is 3 feet by 2 feet, and the hole is 1 foot by foot, what is the fraction left?
The area of the panel left after she cuts the hole is 5.215 ft²
Given that a circular hole of 1 foot by foot has been cut out of a rectangular panel of 3 feet by 2 feet,
We need to find the area of the remaining part after the cutting of the hole,
So, we will find the same by subtracting the area of the hole from the area of the panel.
So, area of the hole = π×radius² = 3.14×0.5² = 0.785 ft²
Area of the panel = length × width = 3 × 2 = 6 ft²
Area remaining part = 6-0.785 = 5.215 ft²
Hence the area of the panel left after she cuts the hole is 5.215 ft²
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Find the area of the shaded region:
Answer:
approximately 42.85 of whatever unit
sin^2(x) + sin(x) = 0
A little more difficult question.
8) John went to a vending machine and bought 2 bags of chips and 2 Powerades for
$3. 50. He then went back to the same vending machine and bought another bag of
chips and 3 Powerades for $3. 75. How much does a bag of chips cost, how much
does a Powerade cost?
The cost of a Powerade is $0.75 if 2 bags of chips and 2 Powerades cost $3.50 and one bag of chips and 3 Powerades cost $3.75.
Let the cost of one Powerade be x
The cost of one bag of chips be y
Cost of 2 bags of chips and 2 Powerades = $3.50
Cost of 2 bags of chips = 2y
Cost of 2 Powerades = 2x
2x + 2y = 3.50 ----(i)
Cost of one bag of chips and 3 Powerades= $3.75
Cost of 1 bag of chips = y
Cost of 3 Powerades = 3x
x + 3y = 3.75
Multiply the above equation by 2
2x + 6y = 7.50 -----(ii)
Subtract (ii) and (i)
4y = 4
y = $1
The cost of one bag of chips is $1
x + 3 = 3.75
x = $0.75
The cost of one Powerade is $0.75
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Bob and Anna are planning to meet for lunch at Sally's Restaurant, but they forgot to schedule a time. Bob and Anna are each going to randomly choose from either 1\text{ p. M. }1 p. M. 1, start text, space, p, point, m, point, end text, 2\text{ p. M. }2 p. M. 2, start text, space, p, point, m, point, end text, 3\text{ p. M. }3 p. M. 3, start text, space, p, point, m, point, end text, or 4\text{ p. M. }4 p. M. 4, start text, space, p, point, m, point, end text to show up at Sally's Restaurant. They must both choose exactly the same time in order to meet. Bob has a "buy one entree, get one entree free" coupon that he can only use if he meets up with Anna. If he successfully meets with Anna, Bob's lunch will cost him \$5$5dollar sign, 5. If they do not meet, Bob's lunch will cost him \$10$10dollar sign, 10. What is the expected cost of Bob's lunch?
The expected cost of Bob's lunch is $9.69, rounded to the nearest cent.
To figure out the probability of Bob and Anna successfully meeting up, we need to use a unitary method. The probability of Bob choosing a specific time is 1/4, and the probability of Anna choosing the same time is also 1/4. Since they both need to choose the same time, we can multiply their individual probabilities to find the probability of them meeting up:
1/4 x 1/4 = 1/16
This means that the probability of Bob and Anna successfully meeting up is 1/16 or 0.0625.
Now we can use this probability to find the expected cost of Bob's lunch. If Bob and Anna meet up, Bob will get a discount on his lunch and pay $5. If they don't meet up, he'll have to pay the full price of $10. So the expected cost of Bob's lunch is:
(Probability of meeting up x Cost if they meet) + (Probability of not meeting up x Cost if they don't meet)
(1/16 x $5) + (15/16 x $10) = $0.3125 + $9.375 = $9.69
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Stacy and clinton are setting up the community center for a freshman orientation. they set up 8 rectangular tables with 6 chairs each and 5 round tables with 4 chairs each. the chairs are randomly numbered starting with 1 and the freshman will be randomly assigned a seat number.
what is the probability that the first freshman to arrive will be seated at a round table?
a 1/20
b 12/17
c 5/17
d 5/13
"The probability that the first freshman to arrive will be seated at a round table is (5/13)."
To calculate the probability, we need to determine the total number of seats and the number of seats at round tables.
There are 8 rectangular tables with 6 chairs each, so the total number of seats at rectangular tables is 8 * 6 = 48.
There are 5 round tables with 4 chairs each, so the total number of seats at round tables is 5 * 4 = 20.
The total number of seats in the community center is 48 + 20 = 68.
The probability of the first freshman being seated at a round table is the number of seats at round tables (20) divided by the total number of seats (68), which gives us 20/68 = 5/17.
Therefore, the correct answer is option C: 5/17.
In conclusion, the probability that the first freshman to arrive will be seated at a round table is 5/17. This is obtained by dividing the number of seats at round tables by the total number of seats in the community center.
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Which of the following inequalities is true?
A. 8<115 <9
B.9 <115 < 10
C.10 <115 <11
D. 11 <115 < 12
None of the inequalities is true.
Explain inequalities
Inequalities are mathematical expressions that compare two quantities or values using inequality symbols, such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to). They represent relationships where one quantity is larger, smaller, or not equal to the other, and can be solved using algebraic manipulation and logical reasoning.
According to the given information
Since 115 is an integer, we can see that it cannot be strictly between any two consecutive integers.
A: 8 < 115 < 9 is not true because 115 is not less than 9.
B: 9 < 115 < 10 is not true because 115 is not less than 10.
C: 10 < 115 < 11 is not true because 115 is not less than 11.
D: 11 < 115 < 12 is not true because 115 is not less than 12.
Therefore, none of the given inequalities is true.
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Philip is downloading applications (apps) and songs to his tablet. He
downloads 7 apps and 6 songs. Each song takes an average of 0.8 minutes
longer to download than each app. If it takes 21.7 minutes for his
downloads to finish, which of the following systems could be used to
approximate a, the average number of minutes it takes to download one
app, and s, the average number of minutes it takes to download one song?
Answer:
a + s = 21.7
7a = 6s - 0.8
Step-by-step explanation:
I just used pattern recognition in my head and stuff i dont know how to explain
Un medicamento tiene ciertos compuestos en las cantidades indicadas en la siguiente tabla:
Compuesto Cantidad en miligramos
A 0,6
B 0,402
C 0,08
D 0,46
Al ordenar la cantidad de compuesto que contiene dicho medicamento de menor a mayor, ¿Cuál es el orden correcto?
The correct order of the compounds in the medicine from least to greatest is: C, B, D, A.
To order the compounds in the medicine from least to greatest, we need to compare their amounts.
First, we can compare compounds A and C. Compound A has an amount of 0.6 milligrams, which is greater than the amount of compound C, which is only 0.08 milligrams. Therefore, we know that compound C is the smallest amount in the medicine.
Next, we can compare compounds B and D. Compound B has an amount of 0.402 milligrams, which is smaller than the amount of compound D, which is 0.46 milligrams. Therefore, we know that compound B is the second smallest amount in the medicine.
Finally, we can compare compounds A and D. Compound A has an amount of 0.6 milligrams, which is greater than the amount of compound D, which is only 0.46 milligrams. Therefore, we know that compound D is the third smallest amount in the medicine.
Therefore, the correct order of the compounds in the medicine from least to greatest is: C, B, D, A.
It's important to note that the amount of each compound in the medicine may have different effects on the patient's health, and that the order of the compounds from least to greatest may not necessarily reflect their importance or efficacy in treating a particular condition. The ordering of the compounds is simply a matter of comparing their relative amounts in the medicine.
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120 people seated in the first 5 rows at a concert how many were between the ages of 11 and 17
please help this is my chapter 7 practice test
Answer:
90
Step-by-step explanation:
Research on the major types of businesses in your province. Based from the data you have gathered, create 1 revenue problem involving quadratic functions.
The top industries are agriculture, mining, tourism, and manufacturing.
The quadratic equations are as given.A manufacturing company in my fiefdom produces and sells ceramic pots.
The company has fixed costs of$ 10,000 per month and variable costs of$ 5 per pot. The company's profit is given by the quadratic function R( x) = -0.2 x2 50x, where x is the number of pots produced and vended in a month.
What's the maximum profit that the company can induce in a month: To break this problem, we can use the formula for chancing the maximum value of a quadratic function, which is given by x = - b/ 2a. In this case, the measure of the x2 term is-0.2, and the measure of the x term is 50. Plugging these values into the formula, we get x = -50/( 2 *(-0.2)) = 125 Hence we obtain the quadratic equation.
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A business has a savings account that earns a 3% annual interest rate. At the end of 1996, the business had $4,000 in the account. The
formula F
+
100
is used to determine the amount in the savings account.
p(1
a)
. Fis the final amount,
⢠p is the initial investment amount,
. Ris the annual interest rate, and
. Tis the time in years.
To the nearest dollar, how much did the business initially invest in 1991?
To the nearest dollar, the business initially invested approximately $3,449 in 1991.
To determine the initial investment in 1991, we can use the formula F = P(1 + R/100)^T, where F is the final amount, P is the initial investment amount, R is the annual interest rate, and T is the time in years.
In this case, F = $4,000 (the amount in the account at the end of 1996), R = 3% (the annual interest rate), and T = 5 years (1996 - 1991). We need to solve for P, the initial investment amount.
First, let's rewrite the equation: P = F / (1 + R/100)^T
Now, we can plug in the known values: P = 4000 / (1 + 3/100)^5
Next, we calculate the denominator: (1 + 0.03)^5 = 1.159274
Then, we divide the final amount by the denominator to find the initial investment: P = 4000 / 1.159274
Lastly, rounding to the nearest dollar, we get: P ≈ $3,449
So, the business initially invested approximately $3,449 in 1991.
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questions.
1) Choose the correct name for the set of numbers.
{..., -3, -2, 1, 0, 1, 2, 3, ...}
erc
The set of numbers is an example of the integers.
What is the best name for the set of numbers?The set of numbers is an example of the integers. Integers are whole numbers (positive or negative) and zero. They are often represented by the symbol "Z". In this set, we have all the whole numbers from negative infinity to positive infinity, including negative and positive 3, 2, 1, 0, and all the numbers in between. The use of ellipses indicates that the set goes on indefinitely in both directions. It is worth noting that 1 appears twice in the set, indicating that sets of integers may have repeated elements. Overall, the set of numbers shown is an infinite set of integers.
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a fast food restaurant executive wishes to know how many fast food meals teenagers eat each week. they want to construct a 85% confidence interval with an error of no more than 0.06 . a consultant has informed them that a previous study found the mean to be 4.9 fast food meals per week and found the standard deviation to be 0.9 . what is the minimum sample size required to create the specified confidence interval? round your answer up to the next integer.
The minimum sample size which is need to to create the given confidence interval is equal to 467.
Sample size n
z = z-score for the desired confidence level
From attached table,
For 85% confidence level, which corresponds to a z-score of 1.44.
Maximum error or margin of error E = 0.06
Population standard deviation σ = 0.9
Minimum sample size required to construct a 85% confidence interval with an error of no more than 0.06,
Use the formula,
n = (z / E)^2 × σ^2
Plugging in the values, we get,
⇒ n = (1.44 / 0.06)^2 × 0.9^2
⇒ n = 466.56
Rounding up to the next integer, we get a minimum sample size of 467.
Therefore, the minimum sample size required to construct a 85% confidence interval with an error of no more than 0.06 is 467.
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A car-detailing service estimates that its daily cost of waxing a cars is C(q) = 0.06q²+37q + 360, If the service collects $65 for each car waxing, find the number of cars the service should wax daily in order to maximize profit
The service should wax approximately 233 cars daily to maximize profit.
To maximize profit, we need to find the number of cars (q) that would result in the highest profit. Profit function P(q) can be calculated as:
P(q) = Revenue - Cost
P(q) = 65q - (0.06q² + 37q + 360)
Now, to find the optimal value of q, we can calculate the derivative of the profit function with respect to q and set it to zero:
dP(q)/dq = 65 - (0.12q + 37)
0 = 65 - 0.12q - 37
Solve for q:
0.12q = 28
q = 28 / 0.12
q ≈ 233.33
Since the number of cars must be a whole number, we can round q to the nearest integer. Therefore, the service should wax approximately 233 cars daily to maximize profit.
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