The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.
2 answers:
Answer:
C. 14 cm
Step-by-step explanation:
According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the measure of the third side.
Given,
The longest side of an isosceles obtuse triangle measures 20 centimeters.
Let x be the measure of the other two congruent sides,
By the above property,
20 < x + x
20 < 2x
10 < x
Thus, the measure of congruent sides must be greater than 10 cm,
Now, In an isosceles obtuse triangle, the square of the longest side is greater than the sum of squares of the other two congruent sides.
Since, √2 = 1.41421356≈ 1.41
Hence, the greatest possible whole-number value of the congruent side lengths is 14.
Option C is correct.
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Answer:
0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38
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 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
37% of the company's orders come from first-time customers.
This means that
A random sample of 225 orders will be used to estimate the proportion of first-time-customers.
This means that
Mean and standard deviation:
What is the probability that the sample proportion is between 0.26 and 0.38?
This is the pvalue of Z when X = 0.38 subtracted by the pvalue of Z when X = 0.26.
X = 0.38
By the Central Limit Theorem
has a pvalue of 0.6217
X = 0.26
has a pvalue of 0.0003
0.6217 - 0.0003 = 0.6214
0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38