Complete the equation to represent finding x, the greater integer. x(x – ) = 143 What is the greater integer?
1 answer:
Answer:
Where
Step-by-step explanation:
Given
Required
Complete the blank
The complete question implies that the product include 2 consecutive odd numbers.
Two numbers whose products equal 143 are: 11 and 13
i.e.
So, we have:
By comparison, we have:
Collect like terms
Substitute 13 for x
So, the complete equation is:
Where
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Answer:
P(A | Y = 8) = 0.633
Step-by-step explanation:
It is really a simple and interesting question, as it involves the Poisson distribution and probability.
First of all, let's try to understand the problem statement clearly. It says that there are two process by which beams are made, namely A and B.
It further states that, beam made by process A has = 10 flaws per meter.
Beam made by process B has = 5 flaws per meter.
Finally, it says that from a yard containing equal numbers of process A and process B beans, one beam is randomly selected and 1 - meter of it is inspected. And they have found 8 flaws in it.
We now, have to find out the probability that the inspected beam is from process A.
For this,
Let's suppose, Y is no. of flaws
So,
P (Y=8|A) =
where , e = Euler's Constant = 2.71828
P (Y=8|A) = 0.11
Similarly for process B
P (Y=8|B) =
P (Y=8|B) = 0.06
As, we know from the problem statement that there are equal numbers of process A and process B beams.
So, the probability of A = Probability of B = 0.5
P(A) = 0.5
P(B) = 0.5
We need to find, P(A|Y=8) and for this we need to find the P(Y=8) first.
Using the law of total probability:
P(Y=8) = P(Y = 8 |A) P(A) + P(Y = 8|B) P(B)
Plug in the values:
P(Y=8) = (0.11 x 0.5) + (0.06 x 0.5)
P(Y=8) = 0.088
Now, by applying Bayes Theorem, we can find the required probability:
P(A | Y = 8) = P(Y = 8 | A) P(A) / P(Y = 8)
8 flaws are found, the probability the inspected beam was fabricated using process A is :
P(A | Y = 8) = 0.11 x 0.5 / 0.088
P(A | Y = 8) = 0.633
Furthermore,
8 flaws are found, the probability the inspected beam was fabricated using process B is :
P(B | Y = 8) = 1-P(A | Y = 8)
P(B | Y = 8) = 1 - 0.633
P(B | Y = 8) = 0.367
Answer:
18:19
Step-by-step explanation:
Given that,
The radius of circle A = 9 cm
The diameter of circle B = 19 cm
We know that,
Radius = diameter/2
The radius of circle B = 19/2 cm
The circumference of circle A is :
....(1)
And that of circle B is :
....(2)
Dividing equation (1) and (2) :
Hence, the ratio of circumferences of Circle A and Circle B is 18:19.