A casserole recipe calls for 4 ounces of cheese. Adrian wants to use 1/2 of the amount of cheese in his casseroles. How many pou
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The equation of the parabola that similar to f(x) = but the vertex is (3, 5) in the standard form is y =
+ 5
The equation of the parabola
f(x) =
The standard vertex form of a parabola is
y = + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) =
The value of a = 7
Substitute the values in the vertex form of a parabola
y = + 5
Hence, the equation of the parabola that is similar to f(x) = but the vertex is (3, 5) in the standard form is y =
+ 5
Learn more about vertex form here
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Answer:
The probability that the selected review was submitted in Word format is 0.56.
Step-by-step explanation:
We are given that Data on recent reviews indicates that 50% of them are short, 30% are medium, and the other 20% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 70% are in Word, whereas 50% of medium reviews are in Word and 30% of long reviews are in Word.
Let the probability that there are short reviews = P(S) = 0.50
The probability that there are medium reviews = P(M) = 0.30
The probability that there are long reviews = P(L) = 0.20
Let W = event that the reviews are submitted in either Word or LaTeX
So, the probability that short reviews are submitted in Word = P(W/S) = 0.70
The probability that medium reviews are submitted in Word = P(W/M) = 0.50
The probability that long reviews are submitted in Word = P(W/L) = 0.30
(a) The probability that the selected review was submitted in Word format is given by = P(W)
P(W) = P(S) P(W/S) + P(M)
P(W/M) + P(L)
P(W/L)
= (0.50 0.70) + (0.30
0.50) + (0.20
0.30)
= 0.35 + 0.15 + 0.06
= 0.56
Hence, the probability that the selected review was submitted in Word format is 0.56.
(b) Now, if the selected review was submitted in Word format, the posterior probabilities of it being short is given by = P(S/W)
P(S/W) =
=
= = <u>0.625</u>
Similarly, if the selected review was submitted in Word format, the posterior probabilities of it being medium is given by = P(M/W)
P(M/W) =
=
= = <u>0.268</u>
Also, if the selected review was submitted in Word format, the posterior probabilities of it being long is given by = P(L/W)
P(L/W) =
=
= = <u>0.107.</u>