brainly Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to creat
1 answer:
Answer:
Step-by-step explanation:
Since each town he has allows him to create 1.13 times as many villagers as he had in the one before.
The population of the next village will be a multiplication of the population of the previous village by 1.13.
This forms a sequence in which the next term is obtained by multiplication of the previous term by a constant. This type of sequence us called a Geometric Sequence and the constant is called the Common ratio.
For any number of terms, the nth term of a Geometric Progression is determined using the formula:
Where a= First Term
r= common ratio
n= number of terms
The game gave Chase 4 villagers to start with.
Therefore, his first term a=4
The common ratio, r= 1.13
To predict the number of villagers in any specific town, we use the formula:
In the 17th town, i.e. n=17
The number of villagers that can be created will be found by substituting n=17 into the formula above.
Since number of villagers cannot be fractional, the number of villagers he can create to live in the 17th village is 28.
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Answer:
78.88% probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value
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 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.
In this problem, we have that:
What is the probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value?
This is the pvalue of Z when X = 2 + 0.1 = 2.1 subtracted by the pvalue of Z when X = 2 - 0.1 = 1.9. So
X = 2.1
By the Central Limit Theorem
has a pvalue of 0.8944
X = 1.9
has a pvalue of 0.1056
0.8944 - 0.1056 = 0.7888
78.88% probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value
Answer:
The total change that will likely occur in 2 years is mg/L
Step-by-step explanation:
Given : The first year, they found the chloride concentration changed by mg/L .
It is estimated that the chloride concentration will change mg/L the next year.
To find : What is the total change that will likely occur in 2 years?
Solution :
The chloride concentration changed by mg/L in first year.
The chloride concentration will change mg/L the next year.
The total change that will likely occur in 2 years is
In a mixed fraction - mg/L