6. An entry window consisting of a rectangle topped with a semi-circle is to have a perimeter of 20 feet. Find the radius of the semicircle if the area of the window is to be maximized. K- 2r

Q: a. A rectangular pen is built with one side against a barn. If 2500 m of fencing are used for the…

A: Let the width of the pen = x ft So length = (2500-2x)ft So area of the pen is: Answer(a):

Q: a. A rectangular pen is built with one side against a barn. If 1500 m of fencing are used for the…

A: Note:- As per our guidelines, we'll answer the first one as both are different question. Please…

Q: a. A rectangular pen is built with one side against a barn. If 200 m of fencing are used for the…

A: As per the guidelines we are supposed to answer only first question and rest can be reposted..

Q: A rectangular corral of 486 square meters is to be fenced off and then divided by a fence into two…

A:

Q: 1. A cable wire 100 meters long is to be cut into two pieces. One of the pieces will be bent into…

A: Let length of one part is x  Therefore length of another part is (100-x)

Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

A:

Q: 12. Show that a rectangle with given perimeter has maximum area when it is a square.

A:

Q: A rectangular corral of 726 square meters is to be fenced off and then divided by a fence into two​…

A: Given problem is : A rectangular corral of 726 square meters is to be fenced off and then divided…

Q: a. A rectangular pen is built with one side against a barn. If 1500 m of fencing are used for the…

A: a. Let the dimensions of the pen be x m and y m.  Now, the length of the perimeter to be covered by…

Q: a. A rectangular pen is built with one side against a barn. If 1400 m of fencing are used for the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. A rancher from above needs two equal adjacent rectangular pens that share a fence in the middle.…

A: Given that ,Rancher needs two equal adjacent rectangular pens with a fence in middle. this can be as…

Q: . A rectangular pen is built with one side against a barn. If 1400 m of fencing are used for the…

A: l+2w=1400; l=1400-2w; l=2(700-w); are=lw ; so, lw=2(700-w)w =(1400w-2w^2);  to maximize,…

Q: a. A rectangular pen is built with one side against a barn. If 1700 m of fencing are used for the…

A:

Q: A piece of sheet metal is rectangular, 5 feet wide and 8 feet long. Congruent squares are to be cut…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the dimensions of the rectangle of maximum area having two vertices on the x-axis and 2…

A: Let the rectangle has its two vertices on x-axis and remaining two vertices on the parabola y=4-x2.…

Q: (b) A wire of length 100 centimeters is cut into two pieces. One piece is bent to form a square. The…

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Q: If an isosceles triangle has perimeter P, how long must the legs of the triangle be to maximize its…

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Q: A farmer decides to enclose a rectangular field using the side of a barn as one side of the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 6. Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

A:

Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

A: Using Lagrange multiplier to find the dimension of rectangle whose area is maximum

Q: Suppose the feasible region has four corners at these points (0,0), (8,0), (0,12), and (4,8).  If…

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Q: is the find the areas of the other regular polygons listed on the chart, (Show your work) and then…

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Q: a. A rectangular pen is built with one side against a barn. If 300 m of fencing are used for the…

A: a) Let x represents the width of the pen and y represents the length of the pen. Given that, the…

Q: Given the area of a rectangle is A = LW. If three sides of the rectangle are fixed, for example, 2VW…

A: Given:- Given the area of a rectangle is A = LW If three sides of the rectangle are fixed, for…

Q: A rectangular pen is built with one side against a barn. If 1800 m of fencing are used for the other…

A: a) Assume that the length of the pen be x and width be y. Since the length of fencing on three sides…

Q: 9. The backyard of a property is to be fenced off in a rectangular design. Fencing is only needed on…

A:

Q: Two chicken coops are to be built adjacent to one another using 120 ft of fencing. a. What…

A: Total fence needed is: (x+x+x)+y+y+y+y=3x+4y So, 3x+4y=120

Q: -2 Albert wants to make an open box from a rectangular piece of cardboard by cutting squares out of…

A: We have to find the following.  Let the side of cutting square be x

Q: (3) A rancher plans to make 4 identical and adjacent rectangular pens against a barn (see figure…

A:

Q: A rectangular building covering 16000m2  is to be built on a lot shown in this picture. If the…

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Q: 13. A rectangular dog pen of 800 sq. feet is to be constructed as shown. The cost is $5 per running…

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Q: A piece of wire of length 67 is cut, and the resulting two pieces are formed to make a circle and a…

A:

Q: 3. Prove that of all rectangles with a given area, the one with smallest perimeter is a square. (Let…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A first class radio-telephone operator wishes to cut the wire 100 meters long into two pieces. One…

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Q: 5. Crunchy Coco Hunks cereal comes in a rectangular box that must be exactly 4 inches deep. If the…

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Q: 4-Find the length and width of a rectangle with perimeter 100 m that maximize the a

A: I have solved the 4th question for you since you have marked it. As per guidelines, we are supposed…

Q: Solve the given item on a separate sheet of paper. A rectangular box with open top and has a square…

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Q: 17. A Norman window is a rectangle with a semi-circle on top. If the perimeter of the window is 24…

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Q: A box (with no top) is to be constructed from a piece of cardboard with sides of length A and B by…

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Q: a. A rectangular pen is built with one side against a barn. If 2500 m of fencing are used for the…

A: Part (a) The diagram of the field is shown below. Given that, the total length of fencing is 2500…

Q: . A rectangular pen is built with one side against a barn. If 2300 m of fencing are used for the…

A:

Q: An isosceles triangle has a perimeter of 30cm. What is the length of the base if its area is to be…

A:

Q: A farmer wants to rope off an area for a new garden using 3300 yards of rope. What dimensions of a…

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Q: 2. A rectangular area is enclosed with fencing on three sides, with the fourth side along a house.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and…

A: Let x be the length of the wire cut for the circle then the length of the wire cut for the square.If…

Q: 6] [3M] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle…

A: Let the dimensions be length = x and breadth =y.  Area of rectangle A(x,y) = xy  Perimeter of…

Q: The area of a rectangle is A = LW. If three sides of the rectangle are fixed, 2W + L = 40, what are…

A: "Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: a. A rectangular pen is built with one side against a barn. If 1200 m of fencing are used for the…

A:

Q: A piece of wire of length 69 is cut into two pieces. One piece is bent into a square and the other…

A: Here we have to find the length of the square and circle such that the sum of areas of  square and…

Q: A rectangular building covering 6,000m2 is to be built on a lot as shown in the figure. If the…

A: Minimize area

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.