Given y- x ≥ 2 and y ≤ -3x+2

Mathematics

1 answer:

sukhopar [10]3 years ago

3 0

Answer:

Picture 3

Step-by-step explanation:

The easiest method is to see if (0,0) is the solution.

1. The line y ≤ -3x + 2 is the line pointing down, and y - x ≥ 2 is the line pointing up, since negative slopes go bottom-right.

2. y - x ≥ 2 --> plug in numbers: 0 - 0 ≥ 2 --> Not true --> the line pointing up's shading will go up, to avoid (0,0) --> Picture 3 is right.

3 (not needed in this situation). y ≤ -3x + 2 --> 0 ≤ 0 + 2 --> True --> The line pointing bottom right has (0,0) --> Picture 2 or 3 is right.

The overlap of possible answers is picture 3.

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The comprehensive strength of concrete is normally distributed with μ = 2500 psi and σ = 50 psi. Find the probability that a ran

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Answer:

The probability that the diameter falls in the interval from 2499 psi to 2510 psi is 0.00798.

Step-by-step explanation:

Let's define the random variable, $X =$ "Comprehensive strength of concrete". We have information that $X$ is normally distributed with a mean of 2500 psi and a standard deviation of 50 psi (or a variance of 2500 psi). In other words, $X \sim N(2500, 2500)$ .

We want to know the probability of the mean of X or $\bar{X}$ that falls in the interval $[2499;2510]$ . From inference theory we know that :

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Now we can find the probability as follows:

$P(2499 \leq \bar{X} \leq 2510) \Rightarrow P(\frac{2499 - 2500}{500} \leq \frac{\bar{X} - 2500}{500} \leq \frac{2499 - 2500}{500} ) \Rightarrow\\\Rightarrow P(-0.002 \leq \frac{\bar{X} - 2500}{500} \leq 0.02 ) \Rightarrow P(-0.002 \leq Z \leq 0.02 )$