The system of equation that has one solution is: (d) –2x+ 7y = –5 and 2x +7y = –9
<h3>What are systems of equations?</h3>
This is a group of equations which may have none, one or more solutions.
From the list of given options, the system of equations that has one solution is:
–2x+ 7y = –5 and 2x +7y = –9
This is so because, the solution is (-1,-1)
However, the other systems have infinite many solutions
Read more about system of equations at:
brainly.com/question/13729904
Answer:
x = 75
Step-by-step explanation:
Answer: 0.8413
Step-by-step explanation:
population mean = 3
population variance = 0.03
sd (standard deviation) = √0.03
Let x = sample mean
x has a mean of 3 and sd of √0.03/√3 = √0.01 = 0.1
And we can aprox the sample mean distribution using a normal distribution
Note: this approximation maybe is not so good (n = 3)
with mean = 3 and sd = 0.1
z = (x-3)/0.1 has a standard normal distribution
P(x<3.1) = P(z<(3.1-3)/0.1) = P(z<1) =0.8413
1. This question refers to conditional probability and is asking us to find the probability of Q occurring, given that R occurs. What this means is that we must divide the probability of Q and R occurring by the probability of R occurring (this is because we have the condition that R occurs). This may be written as such:
Pr(Q|R) = Pr(Q ∩ R) / Pr(R)
2. Now, the first step is to find Pr(Q ∩ R). This is given by the value in the centre of the Venn Diagram (ie. in the cross-over between the two circles) divided by the total of all the values:
Pr(Q ∩ R) = 3/(8 + 3 + 4 + 22)
= 3/37
3. The next step is to find Pr(R). This is given by the value in the circle denoted R (including the cross-over with Q) divided by the total of all the values.
Pr(R) = (4 + 3)/(8 + 3 + 4 + 22)
= 7/37
4. Thus, we can now subtitute the probabilities we defined in 2. and 3. into the formula for conditional probability we defined in 1.:
Pr(Q|R) = (3/37) / (7/37)
= 3/7
Thus, the answer is B.
Note that technically there is no need to write out the full probabilities before coming to this answer. The same exact answer could be found by using Pr(Q ∩ R) = 3 and Pr(R) = 7. This works because they are part of the same universal set - in other words, since the total of all the values in the Venn Diagram remains constant, the denominators of the two probabilities would be the same (given that no cancelling is done) and these denominators would be cancelled out when dividing Pr(Q ∩ R) by Pr(R). This can be particularly useful for a multiple choice question such as this one.
