Which sets of measurements could be the side lengths of a triangle?
2 answers:
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Answer:
1.
2.
3.
Step-by-step explanation:
Standard form of a line is .
If a line passing through two points then the equation of line is
where, m is slope, i.e.,.
1.
The line passes through the points (7,-3) and (4,-8). So, the equation of line is
Therefore, the required equation is .
2.
We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to .
Slope of the line :
Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).
Equation of line is
Therefore, the required equation is .
3.
We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to .
From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).
Equation of line is
Therefore, the required equation is .
Answer:
Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Top 5%:
X when Z has a pvalue of 0.95. So X when Z = 1.645
Bottom 5%:
X when Z has a pvalue of 0.05. So X when Z = -1.645
Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.