A 168-m long fence is to be cut into pieces to make three enclosures, each of which is square. How should the fence be cut up in order to minimize the total area enclosed by the fence?

Q: If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the…

A: Let dimesnion of the region is x and ysince, the farmer has 162 feet of fencingtherefore,…

Q: A cable that has 50 cm is divided into two parts. One part is used to make an equilateral triangle…

A: Length of cable = 50 cm

Q: An open box will be made by cutting a square from each corner a 5-ft by 8-ft piece of cardboard and…

A:

Q: A 216 m2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by…

A:

Q: A piece of wire 16m long is cut into two pieces. One piece is bent into a square and the other is…

A:

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

A: Let the length of square is x. Then each side of the square will be x4. The circumference of the…

Q: A 100 cm piece of wire is going to be cut in two pieces. One will be bent into a square, and the…

A:

Q: What is the longest dimension of an open top rectangular box of greatest volume that can be…

A:

Q: A farmer builds a rectangular grid of pens with 1 row and 5 columns using 550 feet of fencing. What…

A: Given problem:- A farmer builds a rectangular grid of pens with 1 row and 5 columns using 550 feet…

Q: a rectangular plot of land is to be enclosed by a fence. Furthermore an additional section of fence…

A:

Q: A landscape architect wishes to enclose a rectangular garden of area 1000 m2 on one side by a brick…

A:

Q: An athletes runs with velocity 11 km/h for 4 minutes, 14 km/h for the next 2 minutes, and 17 km/h…

A: Use the velocity distance formula given below, d=v×t where d is the distance, v is the velocity (in…

Q: The Philippine Postal Service will accept a box for domestic shipment only if the sum of its length…

A:

Q: A long rectangular sheet of metal 30 inches wide is to be made into a gutter by turning up strips…

A: Let the length of the vertical strips along the tow sides is x inches. Then the length of the base…

Q: An open box is to be made from a 6 ft by 16 ft reetangulas card board by cutting out equaL squares…

A:

Q: A rectangular field is to be covered by 800-meter of hog wire in such a way that one side has a…

A: Area of a rectangle with length x and breadth y is given by x.y. Perimeter of a rectangle with…

Q: If 1800 feet is available to build 5 adjacent pens, find the dimension of the pens that will…

A: Given:The perimeter of all 5 pens is 1800 ft.Calculation:Let x and y be the length and thge width of…

Q: An open box is made from a 16 inch by 16 inch piece of cardboard by cutting equal squares from each…

A: This question is based on application of derivative.

Q: A 480-m long fence is to be cut into pieces to make three enclosures, each of which is square. How…

A: We will use Lagranges multiplier to solve this question.

Q: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four…

A: Solution: Let x be the width of the rectangle and y the height. we can form the equation  5x +…

Q: A 120-m long fence is to be cut into pieces to make three enclosures, each of which is square. How…

A: Given: The length of the fence is 120 m. The fence is to be cut into pieces to make three square…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Let x be the width and y be the length of the rectangle.From the given statement, the three side…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given  Total length of the fence=2500 m Letl=length of the plotb=width of the plot

Q: The maximum possible volume of a rectangular box with the sum of its twelve edges 60 cm is

A: Given 12 edges sum is 60, let C=60So, 4x+4y+4z=CV=xyz    =xy(14C-x-y)    =14Cxy-x2y-xy2 for x>0,…

Q: An airline policy states that all baggage must be box-shaped with a sum of the length, width, and…

A: Given data is: The sum of the length, width, and height not exceeding 120 inches. To find the…

Q: 4. A farmer with 160 ft of fence wishes to use the fence to enclose a rectangular area and then…

A:

Q: You have to cut four equal squares from each corner of the 8.5" x 11" paper in order to make an open…

A: The volume of a cuboid is given by the formula V=l×w×h. Here, l is the length of the box, w is the…

Q: Find the total rebound distance of a ball that is dropped from a height of 7 m, with each rebounds…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given length of wire is 700 m. rectangular plot's three sides are bounded by electric fence.

Q: Find the dimensions of a rectangle with area 1000m2 whose perimeter is as small as possible.

A:

Q: Three equally sized corrals are constructed next to a river. if the area to be enclosed is 19600…

A: Use concept of minimizing of fencing

Q: A farmer wants to fence in an area of 200 square feet in a rectangular field and then divide it in…

A: Given Area of rectangular field =200 square feet

Q: A 10-ft wire is to be formed into an equilateral triangle and a square. What is the measure of the…

A: Given;+ A 10-ft wire is to be formed into an equilateral triangle and a square. To find What is the…

Q: A one-story building having a rectangular floor space of 13200 ft2 is to be constructed where a 22ft…

A:

Q: How many small cubes with edge of 20 cm each can be just accomodated in a cubical box of 2 m edge

A:

Q: A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is…

A: the total length of a wire is 14m  let the length of a square be x m so, the length of a circle will…

Q: A rectangle whose width is less than its length by 3 and its area is 4, then its length is

A: Please refer the attached image for complete solution.

Q: A farmer with 750 ft of fencing wants to enclose a rectangular region and then divide it into four…

A: Solve for the lager rectangle dimension and area of large rectangle

Q: A square piece of green origami paper that is 6 inches on a side is being made into a gift box (with…

A: Maximizing the surface.

Q: What are the dimensions of a rectangle that will maximize the area given its imeter is 100 units?

A: Given: Perimeter of rectangle is 100 units   To Find: Dimensions of a rectangle that will maximize…

Q: A 27-inch by 72-inch piece of cardboard is used to make an open-top box by removing a square from…

A: The numerical is interpreted as shown in the drawing below;

Q: A 10ft board is to be cut into three pieces, two equal-length ones and the third 3 in. Shorter than…

A: Calculation:It is given that the length of a board is 10ft which has to be cut into three…

Q: If the farmer has 648 feet of fencing, what are the dimensions of the region which enclose the…

A: x = length of the rectangle y = width of the rectangle fencing =648 ft hence 2x + 3y = 648 x…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Let a and b be the sides of a retangular fence.

Q: If a cube has edges that are each three times as long as a second cube, then its volume will be nine…

A: Volumes

Q: Find the edge of a cube if its total area is numerically equal to three times its volume.

A:

Q: Suppose an airline policy states that all baggage must be rectangular with a sum of length, width,…

A:

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: Consider the given information.

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.