The probabilities regarding a person spending are given as follows:
a) More than 28: 0.2033 = 20.33%.
b) Between 9 and 21: 0.3608 = 36.08%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 23, \sigma = 6[/tex]
The probability of a person spending more than 28 is one subtracted by the p-value of Z when X = 28, hence:
Z = (28 - 23)/6
Z = 0.83
Z = 0.83 has a p-value of 0.7967.
1 - 0.7967 = 0.2033 = 20.33%.
The probability of spending between 9 and 21 is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 9, hence:
Z = (21 - 23)/6
Z = -0.33
Z = -0.33 has a p-value of 0.3707.
Z = (9 - 23)/6
Z = -2.33
Z = -2.33 has a p-value of 0.0099.
Hence:
0.3707 - 0.0099 = 0.3608 = 36.08%.
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A 10ft pole casts a 30ft shadow. What is the angle of elevation of the sun? For full credit, you must draw the triangle, label the sides and angle, and determine the answer. You may use a calculator for this problem.
18.43°
Given:A 10ft pole casts a 30ft shadow.To find:The angle of elevation of the sun.Diagram:Let AC be the height of the pole and BC be its shadow cast on the ground by the pole.Now, AB represents the ray of the sun. Angle ABC is the angle of elevation of the sun.Measurement:We have AC = 10ft, BC = 30ft.Let x be the angle of elevation of the sun. Then we have, tan(x) = opposite side/adjacent side = AC/BC = 10/30 = 1/3.To find the value of x, we have to take an inverse tangent of 1/3 on the calculator. We have,x = tan-1(1/3)x = 18.43°Therefore, the angle of elevation of the sun is 18.43°.
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b) Which number is smaller: -15 067 or -51 706 ?
Answer:
-51706
Step-by-step explanation:
when working with negative numbers, the number of greater size will be smaller.
Which function has the given properties below?
The domain is the set of all real numbers.
One x-intercept is (2 pi, 0).
The amplitude is 4.
The point (StartFraction pi over 2 EndFraction, negative 4 EndFraction) is on the graph.
The y-intercept is (0, 0).
y = –4sin(x)
y = –4cos(x)
y = 4sin(x)
y = 4cos(x)
The given data are:
A function that:
The domain is the set of all real numbers
One x-intercept
The amplitude is 4
The y-intercept is (0,0)
From the choices, the functions containing "cosine" can be eliminated since the described function passes through (0,0). So, we are left with two choices:
[tex]y = -4sin(x)[/tex] and [tex]y = 4sin (x)[/tex]
Given the amplitude of 4, the answer must be [tex]y = 4 sin(x)[/tex]
Work out the size of angle x give reasons for your answer
Answer:
x° = 80
Step-by-step explanation:
Remember a line is 180°
Because B is = 100°
B and x are interior angles meaning B + x = 180°
100° + x = 180°
x = 80°
Answer:
80 °
Step-by-step explanation:
[tex]\frac{360-2*100}{2} = 80[/tex]
FLOORING miguel is putting hardwood flooring in a hallway that measures 5 feet by 18 feet. The wood he has chosen is $5.48 per square foot. What is the range of the actual cost of putting the flooring in the hallway
Answer:
The cost of putting in the flooring is $493.20
Step-by-step explanation:
First you have to find the area
area = length times width
area = 5 x 18
a = 90 feet
The cost will be 90 x 5.48 = 493.20
Helping in the name of Jesus.
The sides of a triangle are 54, 31, and 69. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
The triangle is acute since a² + b² < c² ( 2916 + 961 < 4761.
Is the triangle is right, acute, or obtuse?To determine whether the triangle is right, acute, or obtuse, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
We can start by finding the longest side of the triangle, which is the hypotenuse.
hypotenuse = 69
Now we can use the Pythagorean Theorem to check whether the triangle is right:
a² + b² = c²
where a and b are the lengths of the other two sides of the triangle.
Plugging in the values we know, we get:
54² + 31² = 69²
Simplifying, we get:
2916 + 961 = 4761
3877 = 4761
Since this equation is not true, we know that the triangle is not a right triangle.
To determine whether the triangle is acute or obtuse, we need to compare the sum of the squares of the lengths of the shorter sides to the square of the length of the longest side:
a² + b² < c² => the triangle is acute
a² + b² > c² => the triangle is obtuse
c² = 69² = 4761
Plugging in the values we know, we get:
54² + 31² = 2916 + 961 = 3877
Since 3877 < 4761, we can conclude that the triangle is acute.
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Please please PLEASE HELP!!!
Answer:
47.5
Step-by-step explanation:
We know that a semicircle is half the area of a circle so to answer this question we can simply find the area of a circle with a diameter of 11cm and then half it!
The area of a circle can be found using the equation: πr²
The radius of the circle would be 5.5cm as we have to be half the diameter.
This means to work it out we would be doing...
π × 5.5² = 95.0331777711Now we have to half it...
95.0331777711 ÷ 2 = 47.5165888855 or 47.5 rounded to 1d.pHope this helps, have a lovely day! :)
please help!! answers needed now-- work only NEEDS to be shown for question 3
use the triangle to answer the questions:
1. What is the exact length of the base of the triangle, y?
2. What is the exact height of the triangle, x?
3. What is the exact area of the triangle? Leave your answer in radical terms.
Show your work
4. What is the area of the triangle to the nearest hundredth of a square in?
Answer:
1. y = 5
2. x = 8√11
3. A = 20√11
4. 20√11 = 66.33
Step-by-step explanation:
1. sin(30) = y/10
=> 1/2 = y/10
y = 5
2. Pythagorean theorem: c^2 = a^2 + b^2
10^2 = x^2 + y^2
10^2 = x^2 + 5^2
x^2 = 100 - 25
x^2 = 75
x = √75 = 8√11
3. Are of right △: A=ab/2 = xy/2 = 5 x 8√11 x 1/2 = 20√11
4. 20√11 = 66.33
Carrie missed 9.6% of the problems on a test. The test had a total of 125 problems. Which of the following is the best estimate of the number of problems Carrie missed?
The best estimate οf the number οf problems she missed is 12
What are number problems ?When sοlving a number prοblem, yοu are provided with hints about one or more numbers, and you must use these hints to create an equation. The Problem-Solving Strategy can be practised with number problems, which don't occur frequently but are a gοod starting point.
To find the best estimate οf the number of problems Carrie missed, we can start by calculating what 9.6% of 125 is:
9.6% οf 125 = 0.096 x 125 = 12
This means that Carrie missed apprοximately 12 problems on the test. Therefore, the best estimate of the number of problems she missed is 12.
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Complete Questiοn:
Carrie missed 9.6% οf the problems on a test. The test had a total of 125 problems. Which of the following is the best estimate of the number of problems Carrie missed? F 123 G 13 H2 3 113 OPEN ENDED QUESTION This is a proportion question: What numbers would you fill into the ratios? 6 d a= b= C= ulube d='
A 3-pack of baseball caps costs $4.93. What is the unit price, rounded to the nearest cent?
Answer:
$1.64
Step-by-step explanation:
To find the unit price, we need to divide the total cost by the number of units. In this case, we have 3 caps in a pack, so the unit price is:
$4.93 / 3 = $1.64333333...
Rounding to the nearest cent, the unit price is $1.64.
What is wrong with step 3 and 6?
Step 3 is incorrect because it states that if all the sides of two figures are proportional then those two figures are similar.
Step 6 is incorrect because it states that if needed, we should reflect A B C D over segment WX. This is incorrect because reflection is not required to prove two figures are similar.
What is a segment?A segment is part of a market that is specifically targeted for a product or service. It is defined by characteristics such as demographics, geography, buying behavior, and interests. Segmentation helps companies to identify their target market and direct their marketing activities accordingly.
We can prove two figures are similar using a sequence of transformations that includes translations, rotations, and dilations, but not reflections. Reflection may be used to help visualize similar figures, but it is not necessary to prove that they are similar.
from the question:
Step 3 is erroneous since it implies that two figures are identical if all of their sides are proportionate. This isn't always the case because two figures can resemble one another without having sides that are proportional. When two figures of the same shape, such as two squares or two circles, proportional sides can only ensure that the two figures are identical.
Step 6 is erroneous because it instructs us to reflect A, B, C, and D over segment WX if necessary. This is false since the similarity between two figures can be established without thought. Using a series of transformations that includes translations, rotations, and dilations but not reflections, we may demonstrate the similarity of the two figures. Reflection may be employed to aid in seeing related figures, but it is not required to establish their similarity.
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The point Q(4,-3) is rotated 180° clockwise around the origin. What are the coordinates of the resulting point, Q'?
Check the picture below.
A cylinder has a diameter of 10 inches and a height of 18 inches. What is the
volume of the cylinder?
OA. 8107
OB. 450TT
O C. 1800T
O D. 1807
After answering the presented question, we can conclude that As a cylinder result, option C. 1800 is the correct answer.
what is cylinder?A cylinder is a three-dimensional geometric shape made up of two parallel congruent circular bases and a curving surface connecting the two bases. The bases of a cylinder are always perpendicular to its axis, which is an imaginary straight line passing through the centre of both bases. The volume of a cylinder is equal to the product of its base area and height. A cylinder's volume is computed as V = r2h, where "V" represents the volume, "r" represents the radius of the base, and "h" represents the height of the cylinder.
volume of the cylinder is:
[tex]V = \pi r^2h\\V = \pi (5^2)(18)\\V = \pi (25)(18)\\V = 450\pi cubic inches\\V =450 x 3.14\\V =1413.00 cubic inches\\[/tex]
As a result, option C. 1800 is the correct answer.
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*see image* The number of wolves in a forest
increases by 25% each year.
This year, there are 400 wolves in the
forest.
Calculate the number of wolves that there
will be in the forest
a) after 1 year.
b) after 2 years.
Answer:
Below
Step-by-step explanation:
After 1 year there will be 25 % more than 400 or 1.25 * 400 = 500 wolves after two years there will be 25 % more than 500 wolves
= 1.25 * 500 = 625 wolves
How many different ways can the letters of "notebook" be arranged?
There are 40,320 different ways to arrange the letters of the word "notebook".
The word "notebook" contains 8 letters.
To calculate the number of different ways the letters can be arranged,
we can use the formula for permutations,
which is: n! / (n-r)!
where, n is the total number of items and r is the number of items selected.
For "notebook",
We want to find the number of permutations of all 8 letters,
So, n = 8 and r = 8.
Plugging these values into the formula,
we get: 8! / (8-8)! = 8!
Simplifying, 8! is equal to: 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Therefore, there are 40,320 different ways to arrange the letters of the word "notebook".
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Alonzo is sitting in a movie theater, 21 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 17°, and the angle of
depression from his line of sight to the bottom of the screen is 38°. Find the height of the entire screen.
Do not round any intermediate computations. Round your answer to the nearest tenth.
Note that the figure below is not drawn to scale.
The access to a full is [tex]23[/tex] m in height.
What kind of height is that?Height is a measurement of vertical distance, or how high or some someone is (how tall they were) "The altitude of an aircraft in flight is around 10,000 m," for instance.
How can I determine my height?Ensure that your shoulders are level, arms are at your sides, and legs are straight. The youngster or adolescent should maintain a straight gaze that is parallel to the ground. Measure the kid or adolescent when they are standing with their head, shoulders, buttocks, & heels on a flat surface.
The calculation of the total screen height is displayed below;
[tex]= a + b[/tex]
where
[tex]a = 21 * tan 17[/tex] degrees
[tex]= 21 * 0.305[/tex]
[tex]= 6.4 m[/tex]
And
[tex]b = 21 * tan 38[/tex] degree
[tex]= 21 * 0.781[/tex]
[tex]= 16.4 m[/tex]
So, the height of the entire screen is
[tex]= 6.4 m + 16.4 m[/tex]
[tex]= 22.8 m[/tex]
[tex]= 23 m[/tex]
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Figure ABCD has vertices A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2). What is the area of Figure ABCD?
a
5 square units
b
20 square units
c
25 square units
d
40 square units
After using the formula of a trapezoid, we know that the area is 25 units².
What is the area?The size of a patch on a surface is determined by its area.
Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The shape can also be placed on a grid, and the number of squares can be counted: The area of the rectangle is 15.
For instance, if each square is 1 meter in size, the area is 15 m² (15 square meters).
So, we have the vertices as follows:
A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2)
See, the plotted vertices on the graph.
The figure is a trapezoid.
The area of a trapezoid is as follows:
A = 1/2(AD+BC)AB
Now, find the distance:
AD = 4
BC = 6
AB = 5
Substitute as follows:
A = 1/2(4+6)5 = 25 units²
Therefore, after using the formula of a trapezoid, we know that the area is 25 units².
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In December, The Corner Coffee Spot had an average inventory of $123, 456 and retail sales of $196, 450. Find the stock
turnover at retail. Round to the nearest tenth.
2.1
1.9
1.6
1.3
Answer:
1.6
Step-by-step explanation:
The stock turnover at retail is a measure of how many times a business sells its average inventory during a period of time. We can calculate the stock turnover by dividing the retail sales by the average inventory.
Stock turnover = Retail Sales / Average Inventory
Given the values :
Average Inventory = $123,456Retail Sales = $196,450Substituting these values
Stock turnover at retail = 196,450 / 123,456 = 1.6 (rounded to the nearest tenth)
Help with all please
A scatter plot of the data is shown below.
An equation of a reasonable trend line is y = x - 0.1.
The arm span of someone who is 1.6 m tall is 1.5 meter.
The arm span of someone who is 2.2 m tall is 2.1 meters.
How to write an equation of the line of best fit for the data?In order to write a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the heights would be plotted on the x-axis of the scatter plot while the arm span would be plotted on the y-axis of the scatter plot.
At point (2.0, 1.9), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 1.9 = (2.0 - 1.9)/(2.1 - 2.0)(x - 2.0)
y - 1.9 = (x - 2.0)
y = x - 0.1.
For someone who is 1.6 m tall, their arm span is given by;
y = x - 0.1
y = 1.6 - 0.1.
x = 1.5 meter.
For someone who is 2.2 m tall, their arm span is given by;
y = x - 0.1
y = 2.2 - 0.1.
x = 2.1 meters.
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Please help I really struggle with these !!!
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =312 \end{cases}\implies s=\cfrac{(312)\pi (4)}{180}\implies s=\cfrac{104\pi }{15}\implies s\approx 21.8[/tex]
a local university reports that 3% of their students take their general education courses on a pass/fail basis. assume that fifty students are registered for a general education course. what is the expected number of students who have registered on a pass/fail basis?
The expected number of students who have registered for the course on a pass/fail basis is 1.5.
To answer the given question, we can use the formula for expected value:
Expected Value = (Probability of Event Occurring) x (Number of Trials)
Here, the event is students taking the course on a pass/fail basis, and the number of trials is the total number of students registered for the course.
We are given that the probability of a student taking the course on a pass/fail basis is 3%, or 0.03.
Using this information,
we can substitute the values into the formula and calculate the expected number of students taking the course on a pass/fail basis:
Expected Value = (0.03) x (50)
Expected Value = 1.5.
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pressure=Force/area A brake pad has an area of 0.35m² and has a force of 140 N applied to it. Calculate the pressure on the brake pad in N/m². If you answer is a decimal, give it to 1 d.p.
Answer:
Step-by-step explanation:
140/0.35squared
=1142.857142
to 1 d,p=1142.9
Divide and simplify. Please show all steps to simplifying.
(1/x+4) ÷ (x-3/ x²+7x+12)
The polynomial fraction division (1/x + 4) ÷ (x - 3/x² + 7x + 12) = (x + 3)/(x - 3)
What is a polynomial?A polynomial is a mathematical expression in which the least power of the unknown is 2.
Since we are given the polynomial expression
(1/x + 4) ÷ (x - 3/x² + 7x + 12).
We proceed to divide and simplify as follows.
(1/x + 4) ÷ (x - 3/x² + 7x + 12) = (1/x + 4) × (x² + 7x + 12)/(x - 3)
= (x² + 7x + 12)/(x - 3)(x + 4)
To simplify further, we factorize the numerator. So, we have that
x² + 7x + 12 = x² + 4x + 3x + 12
Factorizing, we have that
x² + 4x + 3x + 12 = x(x + 4) + 3(x + 4)
= (x + 3)(x + 4)
So, we have that
x² + 7x + 12 = (x + 3)(x + 4)
So, substituting this into the fraction, we have that
(x² + 7x + 12)/(x - 3)(x + 4) = (x + 3)(x + 4)/(x - 3)(x + 4)
Cancelling out (x + 4), we have that
(x² + 7x + 12)/(x - 3)(x + 4) = (x + 3)/(x - 3)
So, we have (1/x + 4) ÷ (x - 3/x² + 7x + 12) = (x + 3)/(x - 3)
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Ruben and Estelle just had business cards made. Ruben's printing company charged a one-time setup fee of $8 and then $18 per box of cards. Estelle, meanwhile, ordered hers online. They cost $6 per box. There was no setup fee, but she had to pay $20 to have her order shipped to her house. By coincidence, Ruben and Estelle ended up spending the same amount on their business cards. How much did each spend? How many boxes did each buy?
Ruben ordered 0 boxes of cards and Estelle ordered 2 boxes of cards. Ruben spent $8 and Estelle spent $20 + $6(2) = $32.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's start by setting up equations for the total cost of Ruben and Estelle's business cards. Let R be the number of boxes of cards Ruben ordered and E be the number of boxes Estelle ordered. Then we have:
Ruben's cost = 8 + 18R
Estelle's cost = 6E + 20
We know that Ruben and Estelle spent the same amount, so we can set their costs equal to each other and solve for R and E:
8 + 18R = 6E + 20
18R - 6E = 12
3R - E = 2
This equation tells us that Ruben ordered two more boxes of cards than Estelle. We can use trial and error to find the values of R and E that satisfy this equation and give us the same cost:
If R = 4 and E = 2, then Ruben's cost = 8 + 18(4) = 80 and Estelle's cost = 6(2) + 20 = 32, which are not equal.
If R = 3 and E = 1, then Ruben's cost = 8 + 18(3) = 62 and Estelle's cost = 6(1) + 20 = 26, which are not equal.
If R = 2 and E = 0, then Ruben's cost = 8 + 18(2) = 44 and Estelle's cost = 6(0) + 20 = 20, which are not equal.
If R = 1 and E = -1, then Ruben's cost = 8 + 18(1) = 26 and Estelle's cost = 6(-1) + 20 = 14, which are not equal.
If R = 0 and E = -2, then Ruben's cost = 8 + 18(0) = 8 and Estelle's cost = 6(-2) + 20 = 8, which are equal.
Therefore, Ruben ordered 0 boxes of cards and Estelle ordered 2 boxes of cards. Ruben spent $8 and Estelle spent $20 + $6(2) = $32.
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Joules and calories are two different units of energy. The equation j=0. 239c
relates the measures, where c
stands for calories and j
stands for joules
If the equation j=0. 239c, the food that contains 200 calories provides 47.8 joules of energy.
To convert the energy in calories to joules using the equation j = 0.239c, we can simply substitute the given value of c (200 calories) into the equation and solve for j:
j = 0.239c
j = 0.239 x 200
j = 47.8 joules
It's important to note that joules are the standard unit of energy in the International System of Units (SI), while calories are more commonly used in nutrition and food science.
The conversion factor between joules and calories is not exact, as it depends on the definition of the calorie used.
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Complete question is:
Joules and calories are two different units of energy. The equation j=0. 239c relates the measures, where c stands for calories and j stands for joules. If a food contains 200 calories, how many joules of energy does it provide?
Determine the indicated probability for a Poisson random variable with the given values of λ and t. Λ = 0. 8, t = 5, P(More than 3)
The probability of obtaining more than 3 events in a Poisson random variable with a mean of λ = 0.8 and a time period of t = 5 is approximately 0.3272 or 32.72%.
To determine the probability of obtaining more than 3 events in a Poisson random variable with a mean of λ = 0.8 and time period of t = 5, we can use the Poisson probability distribution formula, which is:
P(X > k) = 1 - P(X ≤ k)
= 1 - e^(-λ) * ∑(i=0 to k) (λ^i / i!)
where X is the Poisson random variable, k is the number of events, λ is the mean or expected number of events, and e is the mathematical constant approximately equal to 2.71828.
In this case, we want to find P(X > 3), which means we need to compute P(X ≤ 3) first:
P(X ≤ 3) = e^(-λ) * ∑(i=0 to 3) (λ^i / i!)
= e^(-0.8) * [1 + 0.8 + (0.8^2 / 2!) + (0.8^3 / 3!)]
= 0.6728
Then, we can find P(X > 3) using the formula:
P(X > 3) = 1 - P(X ≤ 3)
= 1 - 0.6728
= 0.3272
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Marisol burned 670 calories while exercising on Monday. If Ling burned x fewer calories while exercising than Marisol did, which of the following represents the number of calories Ling burned while exercising?
Choose 1 answer:
The answer is option C. (670 - x)
What is an expression?An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, among others. It is a mathematical phrase that represents a value or a set of values when evaluated. It can be simple or complex.
The number of calories Ling burned while exercising can be represented as:
Ling's calories burned = Marisol's calories burned - x
Since Marisol burned 670 calories, we can substitute this value:
Ling's calories burned = 670 - x
Therefore, the answer is 670 - x.
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Complete question-
The surface area of this rectangular prism is 94 square feet. What is the volume
The volume of the rectangular prism is 60 cubic feet.
What is a rectangular prism?
A rectangular prism is a three-dimensional geometric shape with six faces, where each face is a rectangle. It is also known as a rectangular cuboid. A rectangular prism has 8 vertices, 12 edges, and 6 rectangular faces. The opposite faces of a rectangular prism are congruent and parallel to each other. The length (l), width (w), and height (h) of a rectangular prism are the three dimensions that determine its size and shape.
The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
In this case, we have l = r, b = 5ft, h = 3ft, and SA = 94 sq ft. Substituting these values into the formula, we get:
94 = 2(r)(5) + 2(r)(3) + 2(5)(3)
94 = 10r + 6r + 30
94 = 16r + 30
64 = 16r
r = 4
So, the length of the rectangular prism is 4 feet.
Now, we can use the formula for the volume of a rectangular prism:
V = lwh
Substituting the values for l, w, and h, we get:
V = (4)(5)(3) = 60 cubic feet
Therefore, the volume of the rectangular prism is 60 cubic feet.
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An auditorium has 288
seats distributed evenly in
6 rows. Find the unit rate of seats per row.
Answer: To find the unit rate of seats per row, we can divide the total number of seats by the number of rows:
288 seats ÷ 6 rows = 48 seats per row
Therefore, the unit rate of seats per row is 48.
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Una empresa procesadora de cafe produce 4000 kilogramos diarios de cafe tradicional obteniendo una ganancia diaria de 13500 dolares y una ganancia marginal de 4 dolares por kilo 1. Un administrador propone cambiar la produccion de cafe tradicional a cafe excelso, el administrador afirma que la funcion de ganancia diaria asociada a la produccion de cafe excelso es:
G(x) = Zx+1
1
t
2 + 1
t
dt
The function representing the daily profit based on production of premium coffee is given by ,
T = [tex]\int_{1}^{x}[/tex] [(t² + 1 ) / t² ] dt + (13,500 + (1/x) - x)
Function for daily profit associated with the production of excel so coffee is equal to,
G(x) =[tex]\int_{1}^{x}[/tex] [(t² + 1 ) / t² ] dt
Let's assume that the profit per kilogram of premium coffee is p dollars.
And total production of premium coffee is y kilograms per day.
Total profit from premium coffee is P = p × y
Company produces a total of 4000 kilograms of coffee per day.
⇒ y = 4000 - x
x = production of traditional coffee in kilograms per day.
Total profit for the company is,
T = G(x) + P
Substituting the expressions for P and y,
T = G(x) + p × (4000 - x)
Company's daily profit from producing traditional coffee = $13,500
⇒ 13,500 = G(x) + 4 × x
Substituted the marginal profit of $4 per kilogram for traditional coffee.
Profit per kilogram of premium coffee, p, in terms of x is equal to,
⇒ T = G(x) + p × (4000 - x)
⇒ 13,500 = G(x) + p×(4000 - x)
⇒ 13,500 = [tex]\int_{1}^{x}[/tex][(t² + 1 ) / t² ] dt + p×(4000 - x)
⇒ 13,500 = [x - (1/x)] + p× (4000 - x)
⇒13,500 = x - (1/x) + 4000p - px
⇒ 13,500 = (1-p)x - (1/x) + 4000p
p = (13,500 + (1/x) - x)/(4000 - x)
Function for daily profit associated with the production of premium coffee is,
T = G(x) + (13,500 + (1/x) - x)/(4000 - x) × (4000 - x )
Simplifying we get,
⇒ T = G(x) + (13,500 + (1/x) - x)
Therefore, the function for daily profit associated with the production of premium coffee is equal to
T = [tex]\int_{1}^{x}[/tex] [(t² + 1 ) / t² ] dt + (13,500 + (1/x) - x)
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The above question is incomplete , the complete question is:
A coffee processing company produces 4,000 kilograms of traditional coffee per day, obtaining a daily profit of 13,500 dollars and a marginal profit of 4 dollars per kilo 1. An administrator proposes to change the production of traditional coffee to premium coffee, the administrator affirms that the function of daily profit associated with the production of excel so coffee is:
G(x) = [tex]\int_{1}^{x}[/tex] [(t² + 1 ) / t² ] dt