Answer:
The probability of rolling a 3 and then a 5 is 1/36.
Step-by-step explanation:
Rolling a six sided die is an independent event. That means for each roll, you have the same chance of rolling a number as the previous roll. Since there are six different numbers on a die, then there are six different outcomes for each roll - 1, 2, 3, 4, 5 or 6. The chances that you would roll a '3' is 1 out of 6, or 1/6. The chances that you would roll a '5' is also 1 out of 6, or 1/5. However, when we combine these events, we need to take each probability and multiply them. So, the probability of rolling a '3' and then a '5' is 1/6 x 1/6 or 1/36.
So we know that the formula for the area of a rectangle is
.
Now both the length and width of the rectangle increase at 3 km/s, therefore,
![A(t) = (3t+l)*(3t+w). Since the initial length = initial width = 4 km, then the initial area = 16 [tex]km^2](https://tex.z-dn.net/?f=A%28t%29%20%3D%20%283t%2Bl%29%2A%283t%2Bw%29.%20Since%20the%20initial%20length%20%3D%20initial%20width%20%3D%204%20km%2C%20then%20the%20initial%20area%20%3D%2016%20%5Btex%5Dkm%5E2)
. We want to know the time when the area is four times its original area, therefore, our new formula is:
. Plugging in our known
values we have:
![64 [km^2] = (3t + 4 [km])*(3t + 4 [km])](https://tex.z-dn.net/?f=64%20%5Bkm%5E2%5D%20%3D%20%283t%20%2B%204%20%5Bkm%5D%29%2A%283t%20%2B%204%20%5Bkm%5D%29)
The area is four times its original area after <span>\frac{4}{3} s[/tex]</span>.
If the number of the edges of the polyhedron is 14 and the vertices are 9. Then the number of the faces of the polyhedron is 7.
<h3>What is a
polyhedron?</h3>
A polyhedron is a solid made composed of polygons in three dimensions. It has vertices, flat faces, and straight edges.
We know the Euler's formula
F + V - E = 2,
where, F = number of faces, V = number of vertices, and E = number of edges
Edges: 14
Vertices: 9
F + 9 - 14 = 2
F = 14 + 2 - 9
F = 16 - 9
F = 7
Then the number of the faces of the polyhedron is 7.
More about the polyhedron link is given below.
brainly.com/question/2321456
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