Juan is making a fruit salad. He has grapes, watermelon, apples, pineapple, bananas, mangoes, honeydew, and cantaloupe. He wants
1 answer:
The number of ways that he can make the fruit salad if it must contain watermelon is 35.
<h3>What is Permutation and combination?</h3>Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.
The salad contains water melon, now we have to select 4 more fruits out of 7.
Using combination
= n! / r! (n-r)!
= 7!/ 4! (7-4)!
= 7*6*5*4! / 4! * 3*2
= 35
Hence, number of ways that he can make the fruit salad if it must contain watermelon is 35.
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Answer:
cylinder, has the least surface area
Step-by-step explanation:
We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.
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We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.
<h3>Rectangular Prism</h3>The relevant formulas are ...
V = LWH
A = 2(LW +H(L +W))
for length L, width W, and height H.
<u>a)</u><u> prism 1</u>
The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...
V = (8 in)(8 in)(5 in) = 320 in³
A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²
<u>b)</u><u> prism 2</u>
The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...
V = (10 in)(8 in)(4 in) = 320 in³
A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²
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<h3>Cylinder</h3>The relevant formulas are ...
V = πr²h
A = 2πr(r +h)
for radius r and height h.
c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...
V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³
A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²
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<h3>Square Pyramid</h3>The relevant formulas are ...
V = 1/3s²h
A = s(s +2H)
for base side dimension s, vertical height h, and slant height H.
d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...
V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³
A = (10 in)(10 in + 2×14 in) = 380 in²
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<h3>Summary</h3>The proposed figures have volume and area (rounded to the nearest unit) as follows:
The proposed <em>cylinder</em> requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.
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<em>Additional comment</em>
For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.
The missing figure is attached down
Answer:
Container A is filling more quickly
Step-by-step explanation:
<em>Let us explain the linear relation</em>
The linear equation is y = m x + b, where
- m is the slope of the line which represents the rate of change (change in y/change in x)
- b is the y-intercept which means the initial amount of y (at x = 0)
<em>If a line represents the amount of water over time, then it represents the rate of filling of the water</em>
∵ There are two containers A and B that have the same size
∵ The two lines represent the amount of water over time in
containers A and B
∴ The slopes of the lines represent the rat of water in the tanks
→ That means the greater slope represents the greater rate
∵ The greater the slope, the steeper the line
∴ The container that represented by the steeper the line is filling quickly
→ The line represents container A is steeper more than the line
represents container B
∴ Container A is filling more quickly
