Answer:
The point is not a solution for both inequalities, so the point is not a solution for the system of inequalities.
Step-by-step explanation:
To find the relationship of the point and the system of inequalities, let's use the value of the point (x and y values) in the inequalities:
First inequality: y ≤ 3x + 2
Using x = 1 and y = -5, we have:
-5 ≤ 3*1 + 2
-5 ≤ 3 + 2
-5 ≤ 5 (True)
Second inequality: y > –2x – 3
Using x = 1 and y = -5, we have:
-5 > -2*1 - 3
-5 > -2 - 3
-5 > -5 (False)
The point is not a solution for both inequalities, so the point is not a solution for the system.
Graphically, the point is not inside the area generated by the system of inequalities (check the image attached).
Answer: The number of kittens= 500.
Step-by-step explanation:
Given, A random sample of cats at the SPCA shows that 25 out of the 40 cats are kittens.
i.e. ratio of kitten to cats =
We assume that , the ratio will remains same.
Let x be the number of kitten out of 800 , then we have
Hence, the number of kittens out of 800 cats= 500.
Answer:
Probability that the sample will have a mean that is greater than $52,000 is 0.0057.
Step-by-step explanation:
We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.
We select a random sample of 1,000 people.
<em>Let </em><em> = sample mean</em>
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean = $50,000
= population standard deviation = $25,000
n = sample of people = 1,000
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample will have a mean that is greater than $52,000 is given by = P( > $52,000)
P( > $52,000) = P(
>
) = P(Z > 2.53) = 1 - P(Z
2.53)
= 1 - 0.9943 = 0.0057
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.</em>
Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.