The equation of line AB is y = 2x + 4. What is the equation of a line parallel to line AB in slope-intercept form that contains
2 answers:
The equation of line parallel to y = 2x + 4 containing point (3, −2) is:
Step-by-step explanation:
Given equation is:
y = 2x + 4
The given equation is in slope-intercept form the co-efficient of x will be the slope of line is: 2
The slope of the line parallel to given line will also be 2 as the slopes of parallel lines are equal.
So,
m=2
Slope-intercept form of equation of line is:
Putting the value of slope
To find the value of b, putting (3,-2) in the equation
Putting the values of b and m
The equation of line parallel to y = 2x + 4 containing point (3, −2) is:
Keywords: Slope, Equation of line
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Answer:
0.5 = 50% probability that a random sample of 100 independent persons will cause an overload
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sum of n values of a distribution, the mean is and the standard deviation is
An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.
This means that
If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload
Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So
has a pvalue of 0.5
1 - 0.5 = 0.5
0.5 = 50% probability that a random sample of 100 independent persons will cause an overload