Answer:
∠ PQR = 55°
Step-by-step explanation:
∠ QPR = 74° ( vertical angles )
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180°
∠ PQR = 180° - (74 + 51)° = 180° - 125° = 55°
The answer is the mean, mode, and median increases by 4, the range of times is the same.
Week 1: Week 2:
Student - Hours Student - Hours<span>
Bob 19 </span>Bob 23<span>
James 10 </span>James 14<span>
Karen 15 </span>Karen 19<span>
Rosario 17 </span>Rosario 21<span>
Antoine 10 </span>Antoine 14<span>
Julio 16 </span>Julio 20<span>
Maria 13 </span>Maria 17<span>
The mean is the sum of all values divided by the number of values:
Week 1: (19 + 10 + 15 + 17 + 10 + 16 + 13)/7 = 100/7 = 14.28
Week 2: (23 + 14 + 19 + 21 + 14 + 20 + 17)/7 = 128/7 = 18.28
The difference in means between Week 2 and Week 1 is 4 (18.28 - 14.28 = 4)
The median is the middle value. To calculate, first rearrange values from the lowest to the highest and then find the middle value:
Week 1: 10, 10, 13, 15, 16, 17, 19 - The median is 15.
Week 2: 14, 14, 17, 19, 20, 21, 23 - The median is 19.
The difference in medians between Week 2 and Week 1 is 4 (19 - 15 = 4)
The mode is the value that occurs most frequently.
</span>Week 1: 10, 10, 13, 15, 16, 17, 19 - The mode is 10.
Week 2: 14, 14, 17, 19, 20, 21, 23 - The mode is 14.
The difference in modes between Week 2 and Week 1 is 4 (14 - 10 = 4)
The range of times is the difference between the highest and the lowest value.
Week 1: 10, 10, 13, 15, 16, 17, 19 - The range of times is 9 (19 - 10 = 9).
Week 2: 14, 14, 17, 19, 20, 21, 23 - The median is 9 (23 - 14 = 9).
The difference in the ranges of times between Week 2 and Week 1 is 0 (9 - 9 = 0)
The question is incomplete. The complete question follows.
A company makes windows for use in homes and commercial builidings. The standards for glass thickness call for the glass to average 0.325 inch with a standard deviation equal to 0.065 inch. Suppose a random sample of n=44 windows yield a sample mean of 0.337 inch. Complete parts a and b.
a. What is the probability of x ≥ 0.337 if the windows meet the standards?
b. Based on your answer to part a, what would you conclude about the population of windows? Is it meeting the standards? (A result is unusual if it has a probability less than 0.05)
Answer and Step-by-step explanation: To answer this question, use <u><em>Central Limit Theorem</em></u>: it states regardless of the original population distribution, if the sample size is large enough, the sample mean distribution will approach a normal distribution.
The calculations for the CLT is given by normalizing the distribution, i.e.:
where
z is z-score
x is the sample mean
μ is population mean
σ is standard deviation of the population
n is the number of individuals in the sample
Calculating z-score for the window maker company:
z = 1.22
Using the z-score table, we found the probability:
P = 0.8888
As it is a "more than situation":
P(x≥0.337) = 1 - 0.8888
P(x≥0.337) = 0.1112 or 11.12%
a. Probability of x≥0.337 if the windows meet the standards is 11.12%.
b. Comparing results, probability of x≥0.337 is bigger than 0.05:
0.1112 > 0.05
So, we can conclude that the random sample of n=44 is meeting the standards estipulated.
The value is x= -5/4
<h3>What is LCD?</h3>
The least common denominator is the smallest number of all the common multiples of the denominators when 2 or more fractions are given.
Given:
1/x = 1/5+ 5/4x
1/x = 4x + 25 / 20x
20= 4x +25
4x= -5
x= -5/4
Learn more about this concept here:
brainly.com/question/2605216
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