What is the equation of a line perpendicularto y=-2/5x-1 that passes through(2,-8)
1 answer:
<h2>Answer: y = ⁵/₂ x - 13 OR y + 8 = ⁵/₂ x - 5 </h2><h3>Step-by-step explanation:</h3>
<u>Find the slope of the perpendicular line</u>
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are <em>negative-reciprocal</em>s of each other.
⇒ if the slope of this line = - ²/₅
then the slope of the perpendicular line (m) = ⁵/₂
<u>Determine the equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-8) = ⁵/₂ (x - 2)
∴ y + 8 = ⁵/₂ (x - 2)
We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y + 8 = ⁵/₂ (x - 2)
y = ⁵/₂ x - 13
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Answer:
0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games
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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
The home team therefore wins 50% of its games
This means that
Determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games
Sample of 80 means that and, by the Central Limit Theorem:
This probability is 1 subtracted by the pvalue of Z when X = 0.65. So
By the Central Limit Theorem
has a pvalue of 0.9963
1 - 0.9963 = 0.0037
0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games