660 feet
given distance varies directly with time (t) then
d = kt ( k is the constant of variation )
find k using the condition d = 264 when t = 0.5
k = =
= 528
thus d = 528t
when t = 1.25
d = 528 × 1.25 = 660 feet
Tony Soprano has a collection of five-dollar and one-dollar bilis in his shirt pocket. He has 100 bills in all worth a total of
1 answer:
Answer:
Step-by-step explanation:
From the question we are told that:
Five-dollar bill x
One-dollar bill y
Total number of bills
Worth of bills
Generally the equation for Total number of bills is mathematically given by
Since it is made up of five and one dollar bills
Therefore
Hence the Equation for Total worth of bills is
The System of equations used is
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Answer:
0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months
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 can be 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
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
In this problem, we have that:
What is the probability that the sample mean would differ from the true mean by less than 1.11 months?
This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So
X = 120.1
By the Central Limit Theorem
has a pvalue of 0.7517
X = 117.9
has a pvalue of 0.2483
0.7517 - 0.2483 = 0.5034
0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months