Answer:
7
Step-by-step explanation:
Since the goal is to draw three marbles of the same colour, regardless of which colour that is, the worst possible scenario would be drawing two marbles of each color in the first six picks (2 red, 2 white and 2 blue). At this point, with the 7th pick, no matter what colour marble the student picks will form three of the same kind.
Therefore, the minimum number of marbles which students should take from the box to ensure that at least three of them are of the same colour is 7.
Let the length and width be l and w, respectively. Then, perimeter = 2(l + w) = 40, and area = lw = 96. In other words:
l + w = 20
lw = 96
From here, we could guess and check to get that the length and width are 12 and 8, but let’s do this rigorously:
By the first equation, l = 20 - w
Substituting into the second equation:
(20 - w) * w = 96
w^2 - 20w + 96 = 0
w^2 - 20w + 100 = 4
(w - 10)^2 = 4
w - 10 = 2 or -2
w = 12 or 8
The rest is trivial.
<u>We are given</u>
- Radius of Earth; 6.4 x 100 meters = 640 meters
Clearly, the shape of the earth is a sphere. Thus, to determine the volume of the earth, we will use a formula that determines the volume of a sphere.
![\implies \text{Volume of sphere =} \ \dfrac{4\pi r^{3}}{3}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BVolume%20of%20sphere%20%3D%7D%20%5C%20%20%20%5Cdfrac%7B4%5Cpi%20r%5E%7B3%7D%7D%7B3%7D)
When we substitute the radius in the formula, we get;
![\implies\text{Volume of sphere} = \dfrac{4\pi (640)^{3}}{3}](https://tex.z-dn.net/?f=%5Cimplies%5Ctext%7BVolume%20of%20sphere%7D%20%3D%20%5Cdfrac%7B4%5Cpi%20%28640%29%5E%7B3%7D%7D%7B3%7D)
![\implies\text{Volume of sphere} = \dfrac{4\pi (640)(640)(640)}{3}](https://tex.z-dn.net/?f=%5Cimplies%5Ctext%7BVolume%20of%20sphere%7D%20%3D%20%5Cdfrac%7B4%5Cpi%20%28640%29%28640%29%28640%29%7D%7B3%7D)
Take π as 3.14
![\implies\text{Volume of sphere} = \dfrac{4\pi (640)(640)(640)}{3}](https://tex.z-dn.net/?f=%5Cimplies%5Ctext%7BVolume%20of%20sphere%7D%20%3D%20%5Cdfrac%7B4%5Cpi%20%28640%29%28640%29%28640%29%7D%7B3%7D)
![\implies \text{Volume of sphere} = \dfrac{4(3.14)(640)(640)(640)}{3}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BVolume%20of%20sphere%7D%20%3D%20%5Cdfrac%7B4%283.14%29%28640%29%28640%29%28640%29%7D%7B3%7D)
Simplify the numerator;
![\implies \text{Volume of sphere} = \dfrac{4(3.14)(640)(640)(640)}{3}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BVolume%20of%20sphere%7D%20%3D%20%5Cdfrac%7B4%283.14%29%28640%29%28640%29%28640%29%7D%7B3%7D)
![\implies \text{Volume of sphere} = \dfrac{3292528640}{3}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BVolume%20of%20sphere%7D%20%3D%20%5Cdfrac%7B3292528640%7D%7B3%7D)
Divide the numerator by 3;
![\implies \text{Volume of sphere} = \dfrac{3292528640}{3}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BVolume%20of%20sphere%7D%20%3D%20%5Cdfrac%7B3292528640%7D%7B3%7D)
![\implies \text{Volume of sphere} = \boxed{1097509546.67 \ \text{m}^{3} } \ \ \ (\text{Estimated})](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctext%7BVolume%20of%20sphere%7D%20%3D%20%5Cboxed%7B1097509546.67%20%5C%20%5Ctext%7Bm%7D%5E%7B3%7D%20%7D%20%5C%20%5C%20%5C%20%28%5Ctext%7BEstimated%7D%29)
You have little to no information here but i assume you are using the apex program and the only spiral i know of is made up of 45 right triangles if you have more information im glad to help sorry dude
A: Package A is a better deal. For example, if you get 5 car washes from each package, the results are $47 for package A and $56 for package B.
B:
Package A: 1-15, 2-1, 3-15, 4-1, 5-15, 6-1, 7-15, 8-1.
Package B: 1-28, 2-7, 3-7, 4-7, 5-7, 6-7, 7-7, 8-7.
C: Graph A represents Geometric growth and Graph B represents Arithmetic growth.
D: Package A
E: Package A
Hope this Helps! Let me know if anything is wrong!