Answer:
The probability that the animal chosen is brown-haired is 0.6333.
Step-by-step explanation:
Denote the events as follows:
<em>A</em> : a brown-haired rodent
<em>B</em> : Litter 1
The information provided is:
![P (A|B) =\frac{2}{3}\\\\P(A|B^{c})=\frac{3}{5}](https://tex.z-dn.net/?f=P%20%28A%7CB%29%20%3D%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5CP%28A%7CB%5E%7Bc%7D%29%3D%5Cfrac%7B3%7D%7B5%7D)
The probability of selecting any of the two litters is equal, i.e.
![P(B)=P(B^{c})=\frac{1}{2}](https://tex.z-dn.net/?f=P%28B%29%3DP%28B%5E%7Bc%7D%29%3D%5Cfrac%7B1%7D%7B2%7D)
According to the law of total probability:
![P(X)=P(X|Y_{1})P(Y_{1})+P(X|Y_{2})P(Y_{2})+...+P(X|Y_{n})P(Y_{n})](https://tex.z-dn.net/?f=P%28X%29%3DP%28X%7CY_%7B1%7D%29P%28Y_%7B1%7D%29%2BP%28X%7CY_%7B2%7D%29P%28Y_%7B2%7D%29%2B...%2BP%28X%7CY_%7Bn%7D%29P%28Y_%7Bn%7D%29)
Compute the total probability of event <em>A</em> as follows:
![P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})](https://tex.z-dn.net/?f=P%28A%29%3DP%28A%7CB%29P%28B%29%2BP%28A%7CB%5E%7Bc%7D%29P%28B%5E%7Bc%7D%29)
![=[\frac{2}{3}\times\frac{1}{2}]+[\frac{3}{5}\times\frac{1}{2}]\\\\=\frac{1}{3}+\frac{3}{10}\\\\=\frac{10+9}{30}\\\\=\frac{19}{30}\\\\=0.6333](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B2%7D%7B3%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D%5D%2B%5B%5Cfrac%7B3%7D%7B5%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D%5D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B3%7D%7B10%7D%5C%5C%5C%5C%3D%5Cfrac%7B10%2B9%7D%7B30%7D%5C%5C%5C%5C%3D%5Cfrac%7B19%7D%7B30%7D%5C%5C%5C%5C%3D0.6333)
Thus, the probability that the animal chosen is brown-haired is 0.6333.
A. The Area of one triangular face would be 320 ft². B. The total surface area, in square feet, of the square pyramid is 2,304 ft².
<h3>What is the area of the triangle?</h3>
The Area of one triangular face can be calculated as;
A = area of triangle = ½ x b x h
Where,
b = 32 ft
h = 20 ft
A = ½ x 32 x 20 = 16 x 20
A = 320 ft²
Area of 1 triangular face = 320 ft²
B.
Total surface area = area of the 4 triangular faces + area of the base of the square pyramid
T.S.A = 4(320) + (s²)
Where,
s = 32 ft
T.S.A = 4(320) + (32²)
T.S.A = 1,280 + 1,024
= 2,304 ft²
A. The Area of one triangular face would be 320 ft². B. The total surface area, in square feet, of the square pyramid is 2,304 ft².
Learn more about pyramids here:
brainly.com/question/22213308
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Answer:
hmmmm im not the smart one but i think its k+2^(h-x)a=y
Step-by-step explanation:
Answer:
11 1/4
Step-by-step explanation:
13 5/6- 1 2/6= 12 1/2
12 1/2- 1 1/4= 11 1/4
Answer:
There is no value of x to fit this requirement.
Step-by-step explanation:
The 2 perimeters in terms of x are:
4(x + 3) for the square and
2(x+1) + 2(x +4) for the rectangle
and these need to be equal so
we equate these 2 and solve for x:
4(x + 3) = 2(x+1) + 2(x +4)
4x + 12 = 2x + 2 + 2x + 8
4x + 12 = 4x + 10
4x - 4x = 10 - 12
0 = -2 which is of course absurd so there is no solution to this equation.