What is the perimeter of parallelogram HIJK? Round to the nearest hundredth.
1 answer:
Answer:
Perimeter of the parallelogram = 26.64 units
Step-by-step explanation:
The perimeter of parallelogram = 2(a + b)
Here a = KJ = 7 units.
b = HK
We need to find the HK using the distance formula.
Distance formula =
H = (-4, 3) and k = (-2, -3)
Now plug in x1 = -4, y1 =3, x2 = -2, y2 = -3 in the distance formula
HK =
=
=
=
HK = b = 6.32 units
Now plug in a = 7 and b = 6.32 in the perimeter formula, we get
Perimeter = 2(7 + 6.32)
= 2(13.32)
= 26.64 units
Thank you.
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Answer:
0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
The mean per capita consumption of milk per year is 131 liters with a variance of 841.
This means that
Sample of 132 people
This means that
What is the probability that the sample mean would be less than 133.5 liters?
This is the p-value of Z when X = 133.5. So
By the Central Limit Theorem
has a p-value of 0.8389
0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.