3. Boxes are being loaded with apples. All of the boxes are the same size but have differing
numbers of apples in them. Each box is weighed and the weight is compared to the number
of apples in the box. The results are shown in the scatter plot below.
Answers
a. See image below
b. This is a positive association between the number of apples and the weight
c. The estimate of the y-intercept of my line of best fit to the nearest half-pound is 2 pounds
What is a Positive Association?In mathematics, a positive association refers to a relationship between two variables where an increase in the value of one variable is accompanied by an increase in the value of the other variable. This means that as one variable increases, the other variable also tends to increase.
Thus, as the pound increased, so did the number of apples, so this is a positive association
c. The estimate: when x= 0, the y-intercept is 2.0 pounds
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Related Questions
PLEASE I NEED HELP ON THIS QUESTION
Answers
Answer:
A: -1 B: 2 C: -4 1/2
Step-by-step explanation:
Which of the following rational functions is graphed below?
Answers
Answer:
The vertical asymptote is at x = -3, and the horizontal asymptote is at y = 1, so the correct answer is C.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
Plot the points on the graphing calculator, and then determine the linear regression equation: y = -.7222x + 7.2111
The closest equation is A.
Jenna threw a disc 18 yards to Karl, who threw it 11 yards in the same direction to Alice.
Start at 0 on the number line and move _____ to the right to represent Jenna throwing the disc to Karl.
Then move ______ to the right to represent Karl throwing the disc to Alice the result shows that.
Answers
In total the disc thrown 29 yards.
Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.
Then move 11 yards to the right to represent Karl throwing the disc to Alice.
The result shows that Jenna threw the disc 29 yards (18 + 11) in the same direction to Alice.
Therefore, in total the disc thrown 29 yards.
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The Indian cricket team won 50% of the matches played in the first two weeks of the
NatWest series in Australia. However, at the end of the series its success rate was 75%. If
the team had played 6 matches in the first two weeks and they then won all the matches
they played after the first two weeks, how many matches did they play after the first
two weeks?
Answers
Answer:
the Indian cricket team played 13 matches after the first two weeks.
Step-by-step explanation:
Let's assume that the Indian cricket team played x matches after the first two weeks.
We know that the team won 50% of the matches played in the first two weeks. So, out of the 6 matches played in the first two weeks, they won 0.5*6 = 3 matches.
We also know that at the end of the series, their success rate was 75%. This means that out of the total number of matches played in the entire series, they won 75% of them. Let's say the total number of matches played in the series is y. Then, we can write:
Number of matches won = 0.5*6 + x (matches won in the first two weeks + matches won after the first two weeks)
Total number of matches played = 6 + x (matches played in the first two weeks + matches played after the first two weeks)
According to the given information, the success rate at the end of the series was 75%. So we can write:
Number of matches won / Total number of matches played = 75/100
Substituting the values, we get:
(0.5*6 + x) / (6 + x) = 75/100
Simplifying this equation, we get:
12 + 4x = 25 + 3x
x = 13
Therefore, the Indian cricket team played 13 matches after the first two weeks.
Supplementary angles
Answers
Answer:
∠AGB or ∠EGD.
Step-by-step explanation:
∠AGB & ∠EGD make a straight line with ∠BGD which means they're supplementary.
Answer: ∠BGA
Step-by-step explanation:
Starting Angle: ∠BGD
Supplement: ∠BGA
Find the value that makes each equation true.
A. 110%n=11 n=
B.
(328 x 128) x k = 328 x (82 x 128)
K=
Answers
Answer:
A. [tex]n=100[/tex]
B. [tex]k=0[/tex]
Step-by-step explanation:
A. The equation "110% n = 11" can be solved as follows:
110% n = 11
To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).
(110% n) / 110% = 11 / 110%
n = 11 / 0.110
n = 100
So, the solution for n in the equation "110% n = 11" is n = 100.
B. The given equation is:
(328 x 128) x k = 328 x (82 x 128) x k
To solve for k, we can simplify the equation using the properties of multiplication.
Step 1: Perform the multiplications inside the parentheses:
41984 x k = 328 x 10576 x k
Step 2: Rearrange the equation by applying the associative property of multiplication:
41984 x k = 328 x (10576 x k)
Step 3: Divide both sides of the equation by 328:
(41984 x k) / 328 = 10576 x k
Step 4: Cancel out the common factor of k on the left-hand side:
(41984 / 328) x k = 10576 x k
Step 5: Simplify the left-hand side:
128 x k = 10576 x k
Step 6: Subtract 10576 x k from both sides of the equation to isolate k:
128 x k - 10576 x k = 0
Step 7: Factor out k on the left-hand side:
k x (128 - 10576) = 0
Step 8: Simplify further:
k x (-10448) = 0
Step 9: Divide both sides of the equation by (-10448):
k = 0
So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.
Greta's neighborhood is having a picnic to celebrate the end of the school year. She has been
asked to prepare potato salad. Greta actually has to work at 2pm when the picnic is scheduled, so
she asks Lynn, the neighbor coordinating food, if she can drop off the potato salad at the park
when she goes into work at 10am. Lynn is not sure this will work. Describe why Lynn is hesitant
and what might happen if Greta's potato salad sits out in the sun until the picnic begins at 2pm.
Then offer at least one suggestion to solve Greta and Lynn's problem.
Answers
Answer:
Step-by-step explanation:
they do not have enough time
Step-by-step explanation:
they do not have enough time
PLEASE HELP I JUST HELP i dont know how to answer this please asap
Answers
Answer:
see picture
Step-by-step explanation:
found an answer by someone else on brainly
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Find the value of x. Assume that segments that appear to be tangent are tangent.
x =
(50 POINTs will give BRAINIEST FOR EFFORT)
Answers
Answer:
x = 28.27 units-------------------------
Tangent line is perpendicular to radius at the point of tangency.
It means the given is a right triangle.
Use Pythagorean theorem to find the missing side length.
One of legs is x, second leg is 15 units and the hypotenuse is the sum of 17 units and radius.
x² + 15² = (17 + 15)²x² + 225 = 1024x² = 1024 - 225x² = 799x = √799x = 28.27 units (rounded to the nearest hundredths)Determine the order of the matrix.
VA/L
1
5
-1 1 1 -5
-3 5 7
Answers
The order of a matrix is 2 x 5.
We have,
The order of a matrix is in the form of:
= number of rows x number of columns
Now,
The given matrix has 2 rows.
The given matrix has 5 columns.
Now,
= number of rows x number of columns
= 2 x 5
Thus,
The order of a matrix is 2 x 5.
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Given f(x)=3x^2−5 and g(x)=6x+1, what is the value of (g∘f)(2)?
Enter your answer, in simplest form, in the box.
Answers
If f(x)=3x²−5 and g(x)=6x+1, then the value of (g∘f)(2) = 43.
What is function?
A connection or statement involving one or more variables is called a function. A set of inputs and outputs are present.
First, we need to find f(2):
f(2) = 3(2)² - 5
f(2) = 3(4) - 5
f(2) = 7
Now we need to apply g to f(2):
g(f(2)) = g(7) = 6(7) + 1 = 43
Therefore, (g∘f)(2) = 43.
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HELP DUE ASAP!!!!!
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year. A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils. A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils. Which class lost the most pencils overall based on the data displayed? Mr. Simpson's class; it has a larger median value 14.5 pencils Mr. Johnson's class; it has a larger median of 11 pencils Mr. Simpson's class; it has a narrow spread in the data Mr. Johnson's class; it has a wide spread in the data
Answers
The spread of the data can also be considered, but it does not necessarily indicate which class lost the most pencils overall. Mr. Simpson's class has a narrower spread than Mr. Johnson's class, but this only means that the data in Mr. Simpson's class is more consistent, not that they lost fewer pencils overall.
Therefore, the answer is: Mr. Simpson's class; it has a larger median value 14.5 pencils.
If x = 5 and y = -6 find the value of 3(x - y) + xy
Answers
Answer:
The value of the given equation is 3.
Step-by-step explanation:
QUESTION :If :
x = 5 y = -6Find the value of 3(x - y) + xy
SOLUTION :[tex] \longrightarrow{\sf{3(x - y) + xy}}[/tex]
Substituting the given values in the equation :
[tex] \longrightarrow{\sf{3 \bigg(5 - (-6) \bigg) + 5 \times - 6}}[/tex]
[tex] \longrightarrow{\sf{3 \bigg( 5 + 6 \bigg) - 30}}[/tex]
[tex] \longrightarrow{\sf{3 \bigg( 11 \bigg) - 30}}[/tex]
[tex] \longrightarrow{\sf{ 33 - 30}}[/tex]
[tex]\longrightarrow{\sf{\underline{\underline{ 3}}}}[/tex]
Hence, the value of the given equation is 3.
————————————————Question 6(Multiple Choice Worth 1 points)
(05.03 MC)
Solve the system of equations using elimination.
-2x + 3y = 13
x + y = 11
(-5, 1)
(-3, 3)
(3,8)
(4,7)
Answers
(4,7 ) are solution of linear equations .
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Solve the system of equations using elimination.
-2x + 3y = 13
x + y = 11
Multiply by 2
-2x + 3y = 13
2x + 2y = 22
5y = 35
y = 7
put in equation
x + y = 11
x = 11 - 7 = 4
so (x,y) = (4,7 )
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answer this math question
Answers
The table in this problem is completed as follows:
8 pints for 1 gallon.40 pints for 5 gallons.64 pints for 8 gallons.What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
The constant for the relationship is:
k = 16/2
k = 8.
Hence the equation is:
y = 8x.
In which:
x is the number of gallons.y is the number of pints.Then the numeric values are:
x = 1, y = 8 x 1 = 8.x = 5, y = 8 x 5 = 40.x = 8, y = 8 x 8 = 64.More can be learned about proportional relationships at https://brainly.com/question/7723640
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Amy works in a bakery that bakes all types of breads. She sells a loaf of yeast bread for five dollars and a loaf of brown bread for two dollars. She needs to sell over 100 loaves of bread and make at least $350.
If x represents the loaves of bread sold, and y represents the loaves of yeast bread sold, which of the following graphs represent the situation above?
Answers
The equations that represent both scenarios are x + y > 100 and 2x + 5y ≥ 350
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
Let x represents the loaves of bread sold, and y represents the loaves of yeast bread sold.
She needs to sell over 100 loaves of bread, hence:
x + y > 100
Also, she needs to make at least $350, hence:
2x + 5y ≥ 350
Plotting both equations gives the graph attached.
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For a confidence level of 99% with a sample size of 19, find the critical t value.
Answers
Using a t-distribution table with 18 degrees of freedom (19 - 1 = 18), we can find the critical t value for a two-tailed test at a 99% confidence level to be approximately 2.878.
Therefore, the critical t value for a confidence level of 99% with a sample size of 19 is 2.878 (rounded to three decimal places).
I hope this is right
Question 1 of 10
All else being equal, a study with which margin of error would give you the
most confidence in the results?
OA. ±20 percentage points
OB. +5 percentage points
O C. 15 percentage points
D. ±10 percentage points
Answers
Answer:
±5 percentage points
Step-by-step explanation:
i can't really understand what was equal, because there isn't data about it.
But in case you really don't know it, the lower the margin of error of something is, the more confident you are it is correct, because the lower the error is, the more accurate it is to the theoretical result, so in this case it is ±5.
Eli decides to estimate the volume of a coffee cup by modeling it as a right cylinder.
Eli measures its circumference as 18.3 cm and its volume as 221 cubic centimeters.
Find the height of the cup in centimeters. Round your answer to the nearest tenth if
necessary.
Answers
the height of the cup is approximately 6.2 centimeters. Rounded to the nearest tenth, this is 6.2 centimeters.
what is Rounded to the nearest tenth ?
Rounded to the nearest tenth means to round a number to the nearest value that has one decimal place. To do this, we look at the digit in the second decimal place (the tenths place) and round up or down depending on whether that digit is greater than or less than 5.
In the given question,
We know that the volume (V) of a right cylinder is given by the formula:
V = πr²h
where r is the radius of the cylinder and h is its height.
We also know that the circumference (C) of a right cylinder is related to its radius (r) by the formula:
C = 2πr
From the given information, we can use the circumference to find the radius of the cylinder:
C = 2πr
18.3 = 2πr
r = 18.3 / (2π) ≈ 2.91
Now we can use the radius and the volume to find the height of the cylinder:
V = πr²h
221 = π(2.91)²h
h = 221 / (π(2.91)²) ≈ 6.2
Therefore, the height of the cup is approximately 6.2 centimeters. Rounded to the nearest tenth, this is 6.2 centimeters.
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Refer to the set of data values for Diamonds below
PRICE: 6958,5885,6333,4299,9539,6921,4426,6885,5826,3670,7176,74975170,5547,13596,7521,7260,8139,12196, 14998,9736,9859,12393,25522, 11008,38794,66730,46769,28800,28868
CARATIWEIGHT):1,1,1.01,1.01,1.02,104,104,107,1.07,111,1.12,1 16,1 2,1 23,1.25,129,1.5,1.51,1.67,1.72,1.76,1.8,188,2.03,2.03,2.06,3,4.01,4.01.4.05
COLOR: 3,5, 4, 5, 2, 4, 5, 4, 5, 9,2,5,6,7,1,6,6,6,3,4,8, 5, 6, 2,8,2,1,3,6,7
(a) Use the paired data consisting of the carat weight (x) and the price (y). What is the best predicted price of a diamond with a weight of 1.6 carats?
(b) Use the paired color (x) and the price (y) data. What is the best predicted price of a diamond with a color rating of 37
Answers
linear regression equations can be used to accurately predict the price of a diamond given its carat weight or color rating.
By fitting a line to the paired data, the slope of the line can be used to determine the rate of change in price for a given increase in carat weight or color rating. This can then be used to accurately predict the price of a diamond with a given carat weight or color rating.
What is Equation?
An equation is a mathematical statement that states the equality of two expressions. It is made up of two parts—the left side and the right side—that are separated by an equal sign (=). The left side of an equation is made up of terms, which are numbers and/or variables, and the right side is made up of a single number or variable. Equations are used to solve for unknown values in mathematics, science, and engineering.
The best predicted price of a diamond with a weight of 1.6 carats can be found by using a linear regression equation. This equation uses the paired carat weight (x) and the price (y) data to produce a line that best fits the data. The slope of the line will help determine the rate at which the price changes as the carat weight increases. The equation can then be used to calculate the predicted price of a diamond with a weight of 1.6 carats.
The best predicted price of a diamond with a color rating of 3 can be found by using the paired color (x) and the price (y) data. Using the data, a linear regression equation can be used to produce a line that best fits the data. The slope of the line will help determine the rate at which the price changes as the color rating increases. The equation can then be used to calculate the predicted price of a diamond with a color rating of 3.
In conclusion, linear regression equations can be used to accurately predict the price of a diamond given its carat weight or color rating. By fitting a line to the paired data, the slope of the line can be used to determine the rate of change in price for a given increase in carat weight or color rating. This can then be used to accurately predict the price of a diamond with a given carat weight or color rating.
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Kylie, a youth leader at a summer camp, is making clear slime for an activity with the kids. She is placing the slime in 2-ounce plastic containers with lids. If Kylie can mix up the slime and fill 75 containers in 50 minutes, how long will it take her to make the slime and fill up 450 of the 2-ounce plastic containers??
A. 6 hours
B. 5 hours
C. 4 hours
D. 9 hours
Answers
Answer: B
Step-by-step explanation:
First, you want to find out how many ounces of slime she filled per minute. So 75 containers that are 2 ounces each, 75 x 2 equals to 150 ounces. We know that she has filled 150 ounces in 50 minutes, so we'll divide this to figure out how many ounces she fills per minute. So 150 divided by 50 equals to 3 ounces filled per minute. Now we want to figure out how many ounces she would need to fill up the 450 containers. We'll multiply 450 by 2, which gives 900 ounces. We want to divide 900 ounces by 3 ounces per minute, in order to know how much time it would take to fill it up, which is 300 minutes. Because the answers are in hours, we'll divide 300 by 60 (total number of minutes in 1 hour) and the answer we get is 5. Therefore, it will take Kylie 5 hours to fill up 450 of the 2-ounce plastic containers.
To put it into numbers:
75 x 2 = 150
150 ÷ 50 = 3
450 x 2 = 900
900 ÷ 3 = 300
300 ÷ 60 = 5
(You could also use the total amounts in order to get the answer for this question. We know that it takes 50 minutes to fill 75 containers, so we divide 450 by 75. In turn, we get 6, now we multiply 50 minutes by 6 which still gives us 300 minutes. Divide 300 minutes by 6 and again we get 5 hours.)
In all honesty, this question first confused me when I read it. For example, are we taking into account the time she used to mix the slime into the 50 minutes? However, I thought that something is better than no answer at all, so I tried to work out an answer that was included in the options given (A, B, C, D). But I cannot say with 100% certainty that this may be the correct answer. It's your choice whether you want to use this explanation for your problem, so I sincerely hope that this helped you out.
Congruent angles. Help me solve!
Answers
Answer: ∠FGE
Step-by-step explanation:
Congruent: Have the same angle measure
Starting Angle: ∠BGC
Angle Of Congruence: ∠FGE
Use the slope 2, and y-intercept 1, to complete the equation of the line in slope-intercept form, "x" will be "x."
y =
Answers
Answer:
y = 2x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = 2 and y- intercept c = 1 , then
y = 2x + 1 ← equation of line
A country with a population of 103 million has 19,261 traffic fatalities. Find the fatality
rate in deaths per 100,000 population.
Select one:
O A. 187 deaths per 100,000 people
O B. 1926 deaths per 100,000 people
O C. 1.87 deaths per 100,000 people
O D. 18.7 deaths per 100,000 people
Answers
Answer: C. 1.87 deaths per 100,000 people
Step-by-step explanation:
To find the fatality rate, we need to divide the number of traffic fatalities by the total population and then multiply by 100,000.
Fatality rate = (Number of traffic fatalities / Total population) x 100,000
Plugging in the values given in the question:
Fatality rate = (19,261 / 103,000,000) x 100,000 = 1.87 deaths per 100,000 people.
Therefore, the correct option is C.
K In a poll of 514 human resource professionals, 45.5% said that body piercings and tattoos were big personal grooming red flags. Complete parts (a) through (d) below. a. Among the 514 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big personal grooming red flags? 234 (Round to the nearest integer as needed.) b. Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags.
Answers
234 of them said that body piercings and tattoos were big personal grooming red flags and the 99% confidence interval is 0.412 to 0.498.
a) Among the 514 human resource professionals who were surveyed, the number who said that body piercings and tattoos were big personal grooming red flags is:
45.5% of 514 = 0.455 × 514 ≈ 234
Rounding to the nearest integer, we get 234.
b) To construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags, we can use the following formula:
CI = p ± z√(p(1-p)/n)
where p is the sample proportion, n is the sample size, z is the critical value from the standard normal distribution corresponding to the desired confidence level (99% in this case), and √(p(1-p)/n) is the standard error of the proportion.
Substituting the values from the given information, we have:
p = 0.455
n = 514
z = 2.576 (from standard normal distribution table)
Using these values, we can calculate the confidence interval:
CI = 0.455 ± 2.576√(0.455(1-0.455)/514)
≈ 0.412 to 0.498
Therefore, we can be 99% confident that the true proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags lies between 0.412 and 0.498.
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Does anyone have the answer for this?
Answers
Answer:
m<CAD=m<CBD - alternate interior angles
Step-by-step explanation:
I'm not sure what the question wants you to put, but the way to solve this question would be to prove the angles are congruent, and then use CPCTC (corresponding parts of congruent triangles are congruent) to prove that BD= CA. I hope this helped!
When a baseball is thrown upward, its height h, in feet, is the function of time t, in seconds. If this function is described by the formula h(t)=-16t^2+24t+5, what is the maximum height of the baseball reaches?
Answers
Answer:
the maximal height is 14.75 units of distance.
Step-by-step explanation:
We want to find the maximum height of the function
h(t) = -16*t^2 + 24*t + 5
In order to find the maximum, we need to find the value of t where the derivate of h(t) is equal to zero, then we evaluate our original function in that time.
The derivate of h(t) (or the vertical velocity) is:
h'(t) = 2*(-16)*t + 24 = -32*t + 24
we want to find the value of such:
0 = -32*t +24
32*t = 24
t = 24/32 = 0.75
Now we evaluate our height function in that value.
h(0.75) = -16*0.75^2 + 25*0.75 + 5 = 14.75 units
The maximum height of the baseball can be found by determining the vertex of the parabolic function h(t) = -16t^2 + 24t + 5.
The vertex of a parabola in the form of y = ax^2 + bx + c is given by the coordinates (-b/2a, c - b^2/4a).
In this case, a = -16, b = 24, and c = 5.
Therefore, the vertex of the parabola is at t = -b/2a = -24/(2*-16) = 0.75 seconds.
To find the maximum height, we substitute t = 0.75 into the equation for h(t):
h(0.75) = -16(0.75)^2 + 24(0.75) + 5 = 11.5 feet.
Therefore, the maximum height reached by the baseball is 11.5 feet.
A new apartment complex with 90 one bedroom apartment units and 100 two bedrooms apartment units was built near a lake. Rental prices that will provide full occupancy are estimated as $1200 for one bedroom unit and $1800 for two bedrooms unit. A market survey suggests that for every $20 increase in price of one bedroom unit one less customer will sign a lease and for every $60 increase in price of two bedrooms unit two less customers will sign a lease. What rental price should the manager charge to maximize revenue?
Rental Price for One bedroom ____
Rental Price for Two bedroom ____
Answers
The manager should charge $1200 for one bedroom unit and $1800 for two bedroom unit to maximize revenue.
To maximize revenue, the manager should charge the prices that will provide full occupancy. According to the market survey, for every $20 increase in price of one bedroom unit, one less customer will sign a lease.
Therefore, the manager should charge $1200 for one bedroom unit to maximize occupancy. Similarly, for every $60 increase in price of two bedrooms unit, two less customers will sign a lease.
Therefore, the manager should charge $1800 for two bedroom unit to maximize occupancy.
Therefore, the optimal rental price to maximize revenue is $1200 for one bedroom unit and $1800 for two bedroom unit.
Therefore, the manager should charge $1200 for one bedroom unit and $1800 for two bedroom unit to maximize revenue.
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A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its base is twice the width. Material for the base costs 20 dollars per square meter. Material for the sides costs 3 dollars per square meter. Find the cost of materials for the cheapest such container.
Answers
The cost of the materials for the cheapest container is when width = 1.5 m
Given data ,
Let's use "w" metres to represent the rectangular storage container's width. The length would be "2w" metres since the base's length is twice as long as its width.
The container's height is indicated by the letter "h" metres.
Volume is determined by the following formula:
20 = (2w)(w)(h) 20 = 2w²h
The equation may be rearranged to represent "h" in terms of "w":
h = 20 / (2w²)
The container's "w" and "h" surface area is the next item to discuss. The surface area would be made up of the base and the four sides as the container has an open top.
We are given that the cost of material for the base is $20 per square meter and the cost of material for the sides is $3 per square meter
Cost of base material = 20 x 2w² = 40w² dollars
Cost of side material = 3 x 4wh = 12wh dollars
Total cost of material = Cost of base material + Cost of side material = 40w² + 12wh dollars
Now we can substitute the expression for "h" that we derived earlier:
Total cost of material = 40w^2 + 12w(20 / (2w²)) = 40w² + 120 / w
To find the value of "w" that minimizes the cost of material, we can take the derivative of the total cost of material with respect to "w" and set it equal to zero, then solve for "w":
d/dw (40w² + 120 / w) = 0
80w - 120 / w² = 0
On multiplying by w² on both sides , we get
80w = 120
Divide by 80 on both sides , we get
w = 3/4 m
Hence , the width of the rectangular box is w = 1.5 meter
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