A negative linear relationship implies that larger values of one variable will result in smaller values in the second variable.
1 answer:
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Answer:
The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4 " is represented by the graph ⇒ D
Step-by-step explanation:
To find the answer let us find the equation of each line
Blue line:
∵ The line passes through points (5 , 0) and (0 , 2.5)
- Find the slope of the line
∵ m = Δy/Δx
∴
∴ m = -0.5
- The form of the equation is y = m x + b, where b is the
y-intercept (value y at x = 0)
∵ y = 2.5 at x = 0
∴ b = 2.5
- Write the equation of the line
∴ y = - 0.5 x + 2.5
- Multiply both sides by 2
∴ The equation of the blue line is 2 y = - x + 5
- The shading is under the line and the line is solid, that means
2 y is less than or equal - x + 5
∴ The inequality of the blue line is 2 y ≤ - x + 5
Red line:
∵ The line passes through points (3 , -5) and (0 , 4)
- Find the slope of the line
∴
∴ m = -3
∵ y = 4 at x = 0
∴ b = 4
- Write the equation of the line
∴ y = -3 x + 4
∴ The equation of the red line is y = -3 x + 4
- The shading is below the line and the line is solid, that means
y is less than or equal -3 x + 4
∴ The inequality of the red line is y ≤ -3 x + 4
Let us find which answer is the same with this system of inequalities
∵ 2 y ≤ - x + 5
- Add x to both sides
∴ x + 2 y ≤ 5 ⇒ same as the first inequality of answer D
∵ y ≤ -3 x + 4
- Add 3 x to both sides
∴ 3 x + y ≤ 4 ⇒ same as the second inequality of answer D
The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4" is represented by the graph
Answer:
Traditional method
We can find a critical value in the chi square distribution with df =16 who accumulates of the area on each tail and we got:
Since the calculated value is between the two critical values we don't have enough evidence to conclude that the true deviation is NOT significantly different from 3.5 cm
Confidence level method
We can find the p value like this
Since the p value is higher then the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is NOT significantly different from 3.5 cm
Step-by-step explanation:
Data provided
represent the sample selected
represent the significance
represent the sample variance
represent the value to check
Null and alternative hypothesis
We want to verify if the new production method has lengths with a standard deviation different from 3.5 cm, so the system of hypothesis would be:
Null Hypothesis:
Alternative hypothesis:
The statistic for this case is given by:
The degrees of freedom are:
Traditional method
We can find a critical value in the chi square distribution with df =16 who accumulates of the area on each tail and we got:
Since the calculated value is between the two critical values we don't have enough evidence to conclude that the true deviation is significantly different from 3.5 cm
Confidence level method
We can find the p value like this
Since the p value is higher then the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is significantly different from 3.5 cm