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Francis makes a trip to the mall to purchase clothes. He has a $100
2 answers:
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Answer:
C'A' = 10units (A)
Question
A complete question related to this found at brainly(question ID 2475535) is stated below.
Triangle ABC was dilated using the rule Dy, 5/4
If CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
Step-by-step explanation:
Given:
Scale factor = 5/4
CA = 8units
Find attached the diagram for the question.
This is a question on dilation. In dilation, figures have the same shapes but different sizes.
Y is the center of dilation
Lengths of ∆ABC: CB, AB, CA
Lengths of ∆A'B'C': C'B', A'B', C'A'
C'B' = scale factor × CB
A'B' = scale factor × AB
C'A' = scale factor × CA
C'A' = 5/4 × 8
C'A' = 40/4
C'A' = 10units (A)
Answer:
15.87% probability that the average of 100 randomly selected beams is greater than 30.2 kN/mm
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 normally distributed samples are 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the average of 100 randomly selected beams is greater than 30.2 kN/mm?
This probability is 1 subtracted by the pvalue of Z when X = 30.2. So
By the Central Limit Theorem
has a pvalue of 0.8413.
1 - 0.8413 = 0.1587
15.87% probability that the average of 100 randomly selected beams is greater than 30.2 kN/mm