Dimensions of the enclosure that is most economical to construct are approximately L = 6.79 feet and W = 29.43 feet, rounded to two decimal places.
Describe method to calculate dimensions of the enclosure that is most economical to construct?Let's assume that the rectangular area to be enclosed has dimensions length "L" and width "W", respectively.
We know that the area of the rectangle is 200 square feet:
L x W = 200
We also know that we need to enclose three sides of the rectangle with material that costs 6 dollars per foot, and one side with material that costs 14 dollars per foot.
The total cost, C, of the fencing can be expressed as:
C = 6(2L + W) + 14L
where 2L + W represents the length of the three sides that cost 6 dollars per foot, and L represents the length of the fourth side that costs 14 dollars per foot.
We can simplify this equation to:
C = 26L + 6W
using the equation L x W = 200.
Now we can use the method of calculus to find the minimum value of C. We take the derivative of C with respect to L, set it equal to zero, and solve for L.
dC/dL = 26 = 0
L = 0
This result means that the value of L that minimizes C is L = 0, which is obviously not a valid solution. This implies that the minimum value of C occurs at a critical point where dC/dL is undefined.
To find this critical point, we can use the equation L x W = 200 to eliminate one variable. Solving for W in terms of L, we get:
W = 200/L
Substituting this expression for W into the equation for C, we get:
C = 26L + 6(200/L)
Now we can take the derivative of C with respect to L and set it equal to zero:
dC/dL = 26 - 1200/L² = 0
Solving for L, we get:
L = √(46.15)
Substituting this value for L back into the equation for W, we get:
W = 200/√(46.15)
Therefore, the dimensions of the enclosure that is most economical to construct are approximately L = 6.79 feet and W = 29.43 feet, rounded to two decimal places.
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y is inversely proportional to the cube of x.
Complete the table.
Answer:
see attached
Step-by-step explanation:
You want the values that complete the table when y is inversely proportional to the cube of x.
RelationA proportional relation has the form ...
y = kx
where k is the constant of proportionality.
If y is inversely proportional to x, that is the same as saying y is proportional to the inverse of x:
y = k(1/x)
Here, y is proportional to the inverse of the cube of x:
y = k/x³
The value of k can be found as ...
k = x³·y = (10³)(0.6) = 600
So the relation to use with the table is ...
y = 600/x³
Missing yThe y-value can be found using the equation ...
y = 600/x³
y = 600/5³ = 600/125 = 24/5
y = 4.8
Missing xSolving the proportion for x gives ...
x³ = k/y
x = ∛(k/y) = ∛(600/75) = ∛8
x = 2
TableNow, we can fill the table as in the attachment.
THIS WAS DUE LAST WEEK
Answer:
A is correct.
A'B' = (1/2)(34) = 17
The measure of angle A stays the same, 28°.
The scale that maps Figure A A onto Figure B B is 1 : 7 1 4 1:7 4 1 . Enter the value of x x.
The value of x is 21.75 unit.
We have,
Scale Factor = 1 : 7 1/4 = 1 : 29/4
and, the dimension of Figure A = 3 unit
Now, Using the scale factor
x/3 = 29/4
4x = 87
x= 87/4
x = 21.75 unit
Thus, the dimension of Figure B is 21.75 unit.
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Find the exact and ordinary interest for a 280-day loan of $125,000 with a rate of 5% to the nearest cent. What is the difference between the 2 interest amounts? Assume it is not a leap year
a. $68.92
b. $67.78
c. $66.59
d. $69.56
The difference between the 2 interest amounts is $62.50
what is simple interest?Simple interest is a non-compounded loan where the interest is calculated off the remaining principal balance of the loan.
It does not include compounding interest and applies to both loans and savings accounts held by banks
Number of days 28 and 29 days
Principal = $125,000
rate = 5%
The simple interest formula
A = P(1 + rt)
can be used to calculate total principal plus simple interest on an investment/savings. This formula is derived from A = P + I, where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods.
A = P(1 + rt)
A= 125000(1+0.05*28)
A= 125000(2.4)
A= 300000
and A = P(1 + rt)
A= 125000(1+0.05*29)
A= 125000(2.45)
A= 306250
Therefore the difference the 2 interest amounts is $( 306250-300000) = $62.50
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about 650,000 people live in a circular region with a 6-mile radius. find the population density in people per square mile
The population density is 5750.2 people per square mile.
The radius of the circular region is 6 mile
Area of the circular region [tex]A =\pi r^2[/tex] sq. units.
Now, put the value of radius in above formula
[tex]A = \pi(6)^2[/tex]
A = 3.14 × 36
A = 113.04 [tex]mile^2[/tex]
Calculate the population density
The population of the circular region is
The formula for the population density of the region is : [tex]\frac{Population}{Area}[/tex]
Substitute 650,000 for population and area as 113.04 [tex]mile^2[/tex]
So, Population density = 650000/113.04
Population density = 5750.2 people per square mile
Hence, population density is 5750.2 people per square mile.
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quotient of the rational expression below? 3x/2x+5 divided by 2x/x+5
The quotient of the rational expression is 3(x + 5)/2(2x+5)
The quotient of the rational expressionFrom the question, we have the following parameters that can be used in our computation:
3x/2x+5 divided by 2x/x+5
Express properly
So, we have
3x/2x+5 ÷ 2x/x+5
Express as products
So, we have
3x/2x+5 * x+5/2x
Cancel out x
So, we have
3/2x+5 * x+5/2
Evaluate the products
3(x + 5)/2(2x+5)
Hence. the solution is 3(x + 5)/2(2x+5)
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How many degrees counterclockwise about the origin is △STU rotated to produce △S'T'U'?
Answer:
180°
Step-by-step explanation:
We Know
Each square represents 90°
We see the △STU rotate counterclockwise about the origin through 2 squares. So, the △STU rotated 180° counterclockwise to produce △S'T'U.
We can check by using the rule rotate about the origin 180° state that:
(x , y) → (-x , -y)
Pick point U (-2,1)
(-2,1) → (2, -1)
This meet the rule, so rotate 180° is the correct answer.
Hey, Siri halve to communities ask residence which candidate they supported for a local election. The survey data are shown in the relative frequency table what percentage of the Cherry Hill residence pool supported Gartman
a) 32 percentage of the Cherry Hill residents polled supported Zhang.
The relative frequency table shows the results of a survey in two communities, Cherry Hill and Mountain View, regarding their preferred candidate for a local election. The table displays the percentage of residents in each community who support the two candidates, Gartman and Zhang.
To find the percentage of Cherry Hill residents who supported Zhang, we need to look at the second row of the table, which shows the percentages of Zhang supporters in each community. The percentage for Cherry Hill is 0.38 or 38%. Therefore, the answer is A) 32%.
Correct Question :
A survey of two communities asked residents which candidate they supported for a local election. The survey data are shown in the relative frequency table Gartman 0.30 0.18 Total 0.62 Chemy Hill Mountain View Tota Zhang 0.32 0.20 0.,38 1.0 What percentage of the Cherry Hill residents polled supported Zhang?
a) 32%
b) 30%
c) About 6280
d) About 52%
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I want 25 percent of my order to be to tropicals and the rest monster
Answer: Incomplete question
(i think)
Step-by-step explanation:
f(x)=x^2 {x >_ 0} , g(x) = square root of x y=x c. For each function you listed in part b, give a domain restriction that will make the function one-to-one, thus allowing it to have an inverse function. Make sure that your domain restrictions are as large as possible.
The requried domain restriction for both functions is x ≥ 0.
a. f(x) = x² {x ≥ 0}
To make f(x) one-to-one, we need to restrict the domain so that each output (y-value) of the function fits only one input (x-value). The domain is x ≥ 0, which means that the function starts from the point (0,0) and goes up as x increases. Therefore, the domain restriction for f(x) to be one-to-one is x ≥ 0.
b. g(x) = √x
The square root function g(x) is already one-to-one for x ≥ 0. To make certain that the inverse function also exists, we can restrict the domain to x ≥ 0.
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sin(7r/6)=——————
it’s not r but the little r thing in trigonometry
(b) The formula for the total cost (C) of q rulers and s erasers is C = 40g + 15s
Work out the total cost of 7 rulers and 4 erasers.
Answer:
350
Step-by-step explanation:
C = 40g + 15s
C = 40(7) + 15(4)
C = 280 + 70
C = 350
paul wants to go to a concert. the concert ticket costs $125. paul earns $30 for each lawn he mows and $15 for each car he washes. how many lawns can paul mow and how many cars can he wash to have enough money to buy a concert ticket?
If Paul mows 3 lawns, he needs to wash at least 3 cars to earn enough money to buy the concert ticket.
Let's assume that Paul mows x lawns and washes y cars. Using the unitary method, we can find how much money Paul earns from mowing one lawn and washing one car.
Paul earns $30 for each lawn he mows, so he earns $30/1 lawn or $30 per lawn.
Similarly, Paul earns $15 for each car he washes, so he earns $15/1 car or $15 per car.
Now, to find the total amount of money Paul earns by mowing x lawns and washing y cars, we can use the following equations:
Total money earned = (Money earned per lawn) x (Number of lawns mowed) + (Money earned per car) x (Number of cars washed)
Total money earned = ($30/lawn) x (x lawns) + ($15/car) x (y cars)
Total money earned = $30x + $15y
We need to find the values of x and y such that the total money earned is at least $125, which is the cost of the concert ticket. So we can write:
$30x + $15y ≥ $125
We can simplify this equation by dividing both sides by $5:
$6x + $3y ≥ $25
Now we can find the values of x and y that satisfy this inequality. One way to do this is to use trial and error. We can start by assuming different values of x and finding the corresponding value of y that satisfies the inequality. For example:
If x = 2, then 6x = 12 and the inequality becomes:
12 + 3y ≥ 25
3y ≥ 13
y ≥ 4.33
So if Paul mows 2 lawns, he needs to wash at least 5 cars to earn enough money to buy the concert ticket.
Similarly, if we assume x = 3, then 6x = 18 and the inequality becomes:
18 + 3y ≥ 25
3y ≥ 7
y ≥ 2.33
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Rewrite each equation without absolute value for the given conditions.
The equations without absolute value for the given conditions is shown below:
y = 2x - 5, if x > 5
y = -2x, if x < -5
y = |2x - 5|, if -5 < x < 5
How do we calculate?We take notice the three stated conditions and simplify with regards to that.
Condition 1: x > 5
Condition 2: x < -5
Condition 3: -5 < x < 5
For condition 1, where x > 5 the expression inside the absolute value bars will be simplified to:
y = x - 5 + x + 5 = 2x - 5.
Therefore, we have the expression as y = 2x - 5, if x > 5
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Four identical rectangles surround a square. The perimeter of each rectangle is 20 cm and the area of the square is 44 cm². What is the area of each rectangle?
Answer:
Let x be the length of one side of the square. Then, the perimeter of the square is 4x.
Each rectangle has two sides that are equal in length to the side of the square, and two sides that are equal in length to some other value y. Therefore, the perimeter of each rectangle can be expressed as:
2x + 2y = 20
Simplifying this equation, we get:
x + y = 10
We can use this relationship to solve for y in terms of x:
y = 10 - x
The area of each rectangle is given by:
Area = x*y
Substituting y = 10 - x, we get:
Area = x*(10-x)
Area = 10x - x²
To find the area of each rectangle, we need to solve for x. We know that the area of the square is 44 cm², so:
x² = 44
x ≈ 6.63 cm
Now we can find the area of each rectangle:
Area = 10x - x²
Area = 10(6.63) - (6.63)²
Area ≈ 38.85 cm²
Therefore, each rectangle has an area of approximately 38.85 cm².
what values of t place 85% of the area in the middle of the distribution? (use technology. round your answers to two decimal places.)
The values of t that place 85% of the area in the middle of the distribution are between -3.379 and 3.379.
To find the values of t that place 85% of the area in the middle of the distribution, we need to find the t-scores that correspond to the 7.5th and 92.5th percentiles of the t-distribution with 46 degrees of freedom.
We can use a t-table or a statistical software to find these values. Using a t-table, we can look up the critical t-values for the two tails of the distribution that include 7.5% and 92.5% of the area.
For a two-tailed test at the 5% significance level with 46 degrees of freedom, the critical t-value is approximately 2.013.
To find the t-scores for the 7.5th and 92.5th percentiles, we need to multiply the critical t-value by the corresponding t-multiplier for the degrees of freedom. For 46 degrees of freedom, the t-multiplier is approximately 1.678.
Thus, the t-score that corresponds to the 7.5th percentile is -2.013 x 1.678 = -3.379, and the t-score that corresponds to the 92.5th percentile is 2.013 x 1.678 = 3.379.
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The given question is incomplete, the complete question is:
Consider a t distribution with 46 degrees of freedom. What values of t place 85% of the area in the middle of the distribution?
individuals who smoke one pack of cigarettes per day have a 1 in 250 lifetime probability of developing lung cancer. what kind of analysis is this?
The statement "individuals who smoke one pack of cigarettes per day have a 1 in 250 lifetime probability of developing lung cancer" is an example of statistical analysis.
This statement uses an observed relationship between smoking and lung cancer to estimate the probability of developing lung cancer over a lifetime of smoking one pack of cigarettes per day. This estimate is based on statistical data collected from studies that have observed the association between smoking and lung cancer over many years.
This type of analysis is often used in epidemiology and other areas of public health to estimate the risk of various health outcomes based on observed relationships between risk factors and outcomes.
These estimates can be used to inform public health policies and interventions aimed at reducing the prevalence of risk factors and improving health outcomes.
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A teacher asked 18 students how many book they read last summer. The dot represents one student. The midst frequent response was...
The most frequent response was 1 book. 6 students said that they read 1 book.
What was the most frequent response?In the histogram provided, we can see that 3 students read 0 books while 6 students read 1 book. 4 students read 2 books and 1 student read 3 books. 1 student read 4 books and 2 students read 5 books.
Finally, 1 student read 10 books. In the provided data, it is clear that the most frequent response was the 6 students who said that they read 1 book each. This figure was greater than the other responses.
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The cashier at a box office sold 200 more adult tickets at $11 each than children’s at $18 each. What is the minimum number of each type to be at least $5000?
The minimum number of children's tickets sold is 97 and the minimum number of adult tickets sold is 297.
How to calculate the minimum number of each type to be at least $5000Let's start by setting up two equations based on the given information:
Let x be the number of children's tickets sold.
Then, the number of adult tickets sold is x + 200.
The revenue from the children's tickets is 18x, and the revenue from the adult tickets is 11(x + 200).
The total revenue is the sum of these two:
Total revenue = 18x + 11(x + 200)
Simplifying this expression:
Total revenue = 18x + 11x + 2200
Total revenue = 29x + 2200
We also know that the total revenue is at least $5000. So, we can set up an inequality:
Total revenue ≥ 5000
Substituting the expression for the total revenue, we get:
29x + 2200 ≥ 5000
Subtracting 2200 from both sides:
29x ≥ 2800
Dividing both sides by 29:
x ≥ 96.55
Since we can't sell a fraction of a ticket, we need to round up to the nearest whole number, which gives us:
x ≥ 97
So, the minimum number of children's tickets sold is 97.
x + 200 = 97 + 200 = 297
Therefore, the minimum number of children's tickets sold is 97 and the minimum number of adult tickets sold is 297.
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El área de una caja de arena rectangular de la escuela de David es de 108 pies cuadrados.
La caja tiene un ancho de 9 pues.
Cuanto mide de largo, en pies, la caja de arena?
Answer: perdon, no se
Step-by-step explanation:
hich of the following are most likely to be dependent samples? multiple choice a study that compares the mean wait times at two different hospital emergency rooms a study that compares the salaries earned by men and women in the same job position a study that compares the weight gain for puppies who eat two different brands of food a study that compares standardized test scores before and after a course is taken
The statement which most likely represent "dependent-samples" is (d) study which compares standardized "test-scores" before and after course is taken.
The scores obtained before and after are linked, as they are obtained from the same group of individuals, and are therefore dependent samples.
For example, suppose a group of students is given a standardized test before and after taking a preparation course.
The scores obtained before the course are likely to be related to the scores obtained after the course, as they are both measures of the same group of students.
If the course has a significant impact on the scores, the before-and-after scores will likely be correlated, and the samples will be dependent.
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
Which of the following are most likely to be dependent samples?
(a) A study that compares the mean wait times at two different hospital emergency rooms
(b) A study that compares the salaries earned by men and women in the same job position
(c) A study that compares the weight gain for puppies who eat two different brands of food
(d) A study that compares standardized test scores before and after a course is taken.
Please help me with this homework
Answer:
62
Step-by-step explanation:
180-70-48=62
Angles in a triangle add up to 180.
What is the measure of angle QVR?
The measure of angle QVR is 24°
What are angles on parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Since angle UWT and QVR are on indirectly opposite to each other , they will be equal.
This means that UWT = QVR
= 3x+12 = x+20
collecting like terms;
3x-x = 20-12
2x = 8
divide both sides by 2
x = 8/2
x = 4
angle QVR = x+20
therefore QVR = 4+20
= 24°
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Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1
an = n - 3
What is the radius of a hemisphere with a volume of 66 cm³, to the nearest tenth of
a centimeter?
The radius of the hemisphere with a volume of 66 cm³ is 3.2 cm.
What is the radius of the hemisphere?A hemisphere is gotten when a sphere is cut into two equal halves.
The volume of a hemisphere is expressed as;
V = (2/3) × πr³
Where r is the radius and π is pi ( π = 3.14 ).
Given that:
Volume of the hemisphere V = 66 cm³,Radius r = ?To solve for the radius r, plug the value of V into the above formula and solve for r.
V = (2/3) × πr³
66 cm³ = (2/3) × πr³
66 cm³ = (2/3) × 3.14 × r³
r³ = (66 cm³) / (2/3)3.14
[tex]r^3=\frac{66 cm^3}{(2/3)3.14} \\\\r = \sqrt[3]{\frac{66 cm^3}{(2/3)3.14} } \\\\r = 3.2[/tex]
r = 3.2 cm
Therefore, the radius is 3.2 centimeters.
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Write a linear function f with the values f(3)=-4 and f(5)=-4
To write a linear function f(x) with the values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation:
f(x) - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Using the two given points, we have:
f(3) = -4 and f(5) = -4
This means that (3, -4) and (5, -4) are two points on the line.
To find the slope, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
m = (-4 - (-4)) / (5 - 3)
m = 0 / 2
m = 0
Therefore, the slope of the line is 0.
Using the point-slope form with the point (3, -4) and the slope m = 0, we get:
f(x) - (-4) = 0(x - 3)
f(x) + 4 = 0
f(x) = -4
So, the linear function f(x) that passes through the points (3, -4) and (5, -4) is f(x) = -4.
A girl leaves a history classroom and walks 20 meters north to a drinking fountain then she turns and walks 30 meter south to an art classroom what is the girl’s total displacement from the history classroom to the art classroom
Answer:
50 m
Step-by-step explanation:
BC if she walked 20 metres from the history class and 30 for the art it's 50 m
Find the 13th term of the arithmetic sequence whose common difference is d=-8 and whose first term is a1=25 .
If the "arithmetic-sequence" which has "first-term" as 25, then it's 13th term will be -71.
The first-term of the "arithmetic-sequence" is denoted as "a₁" is 25,
The common-difference denoted as "d" is -8,
We can use the formula for the nth term of an arithmetic sequence to find the 13th term. The formula is : aₙ = a₁ + (n - 1)d;
where, n is = number of the term we want to find,
We have to find the 13th term, so, n is = 13,
Substituting the values,
We get;
a₁₃ = 25 + (13 - 1)(-8)
a₁₃ = 25 + 12(-8)
a₁₃ = 25 - 96
a₁₃ = -71
Therefore, the 13th term of arithmetic sequence is -71.
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Based on the table, which statement is true?
A. About 40% of the students prefer Chocolate.
B. About 30% of the students prefer Mint.
C. About 20% of the students prefer Orange.
D. About 50% of the students prefer Orange.
Based on the table, statement which is true is C) About 20% of the students prefer Orange.
To find the correct answer, we need to calculate the total number of students surveyed and the number of students who prefer each flavor.
The total number of students surveyed is:
34 + 35 + 36 + 38 + 27 + 35 = 205
The number of students who prefer Chocolate is:
34 + 38 = 72
The number of students who prefer Mint is:
35 + 27 = 62
The number of students who prefer Orange is:
36 + 35 = 71
So, the correct statement is:
C. About 20% of the students prefer Orange.
To calculate this, we can use the following formula:
Percentage of students who prefer Orange = (Number of students who prefer Orange / Total number of students surveyed) x 100
= (71 / 205) x 100
= 34.63% (rounded to the nearest whole number)
Since the percentage is closest to 20%, we can conclude that about 20% of the students prefer Orange. Therefore, option C is correct.
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a moving company packs two boxes: box a and box b. each box has a volume of 4 cubic feet. box a weighs 24.6 pounds. box b weighs 37.4 pounds. to the nearest whole number, what is the difference in density, in pounds per cubic foot, between box a and box b?a.2b.3c.4d.5
The difference in density, in pounds per cubic foot, between the box A and box B to the nearest whole number is 3. So, correct answer is option b.
The density of the body is the mass per unit volume and to find the difference in density we have to find density of each box.
Density of box A = Mass of box A / Volume of box A
= 24.6 pounds / 4 cubic feet
= 6.15 pounds per cubic foot
Density of box B = Mass of box B / Volume of box B
= 37.4 pounds / 4 cubic feet
= 9.35 pounds per cubic foot
The difference in density,
Density box A - density box B.
= (9.35- 6.15)pounds per cubic foot
= 3.2 pounds per cubic foot
To the nearest whole number, the difference in density is 3. Therefore, the answer is (b) 3.
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