Answer:
72 spheres are formed
Step-by-step explanation:
We start by calculating the volume of the metallic cylinder
Mathematically, we have this as;
V = pi * r^2 * h
V = pi * 21 * 14^2
V = 4116 π cm^3
The volume of each small sphere is;
V = 4/3 * pi * r^3
= 4/3 * π * 7/2^3 = 57.167 π cm^3
To get the number of small spheres, we simply divide the volumes
That will be 4116 pi / 57.167 pi = 72
<h3>
Answer:</h3>
unshaded area = 25(4 -π) in^2 ≈ 21.46 in^2
<h3>
Step-by-step explanation:</h3>
Each of the shaded circles has a diameter of (20 in)/4 = 5 in, which also is the width of the enclosing rectangle. Then each circle has a radius of 2.5 in, and an area of ...
A = πr^2 = π(2.5 in)^2 = 6.25π in^2
The four circles together have an area of ...
4A = 4·(6.25π in^2) = 25π in^2
The area of the rectangle is the product of its length and width:
A = LW = (20 in)(5 in) = 100 in^2
Since the circles are shaded, the unshaded area is the difference between the rectangle area and the total area of the four circles:
unshaded area = (100 in^2) - (25π in^2) = 25(4 -π) in^2 ≈ 21.46 in^2
Answer:
see explanation
Step-by-step explanation:
sum the parts of the ratio, 5 + 6 + 3 = 14 parts
Divide number of members by 14 to find the value of one part of the ratio.
560 ÷ 14 = 40 ← value of 1 part of the ratio
(i)
number of women = 6 × 40 = 240
(ii)
number of children = 3 × 40 = 120
The histogram is attached. Every column shows on the bottom the range of age and on the left the number of cars of that particular age.
In order to find the percentage of cars with less than 20 years or more than 40 years, you have to sum up the numbers of cars in the first two columns from left (age 0-9 and 10-19) and the last two (age 40-49 and 50-59).
The number of cars of requested age is: 3 + 2 + 0 + 3 = 8
Now, you need to calculate the total number of cars (sum the cars of every column): 3 + 2 + 8 + 4 + 0 + 3 = 20
Lastly, you need to calculate the ration between the cars of requested age and the total number of cars, and transform it into a percentage:
8 ÷ 20 = 0.40 = 40%
Therefore, your answer is
40%.
4x - 2y ≤ 6 <em>subtract 4x from both sides</em>
-2y ≤ -4x + 6 <em>change the signs</em>
2y ≥ 4x - 6 <em>divide both sides by 2</em>
<h3>y ≥ 2x - 3</h3>
y = 2x - 3 - it's a linear function. We need only two points to plot the graph.
Choose any two values of x and calculate the values of y:
for x = 0 → y = 2(0) - 3 = 0 - 3 = -3 → (0, -3)
for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1)
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<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded to left
>, ≥ - shaded to right