Answer:
72.4%
Step-by-step explanation:
The probability of A occurring given that B occurs = the probability of both A and B / the probability of B
P(A|B) = P(A∩B) / P(B)
This can be rearranged as:
P(A∩B) = P(B) P(A|B)
In this case:
A = biased coin is chosen
~A = fair coin is chosen
B = 4 heads then 1 tail
First, let's find P(A∩B).
P(A∩B) = P(B) P(A|B)
P(A∩B) = ½ × ₅C₄ (⅘)⁴ (⅕)¹
P(A∩B) = 0.2048
Next, find P(~A∩B).
P(~A∩B) = P(B) P(~A|B)
P(~A∩B) = ½ × ₅C₄ (½)⁴ (½)¹
P(~A∩B) = 0.078125
Therefore, the probability that the coin is biased is:
P = P(A∩B) / (P(A∩B) + P(~A∩B))
P = 0.2048 / (0.2048 + 0.078125)
P = 0.723866749
The probability is approximately 72.4%.
Answer:
-14+(-6)
-6+(-14)
Step-by-step explanation:
Given:
Rectangular prism
Length = 2.5x
Width = x
Height = 6 feet
Volume = 2,940 feet³
Volume = Length * Width * Height
2,940 ft³ = (2.5x) * x * 6ft
2,940 ft³ ÷ 6 ft = 2.5x²
490 ft² = 2.5 x²
490 ft² ÷ 2.5 = x²
196 ft² = x²
√196 ft² = √x²
14 ft = x
Width = x = 14 feet
Length = 2.5x = 2.5 * 14 ft = 35 feet
Answer:
- A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
Explanation:
To find a relationship modeled by the given function it is recommendable to factor it.
The function is:
The first step to factor it is to extract common factor 4x:
The second step is to factor the quadratic trinomial.
That is made by writting it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is:
Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
- x is the desired (unknown) length
- 4x is 4 times the desired length
- x - 10 is 10 less than the desired length
- x - 8 is 8 less than the desired length
Thus, the volume of the prism is the product of the three factors: