3x+2y=4 8x-3y=-6 solving systems of equations by substitution
1 answer:
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Answer:
1/5
Step-by-step explanation:
Well work can be defined as:
where rate=amount of work that can be done in one unit of time
let a = rate of work A does in a day
let b = rate of work B does in a day
this means that: where work=1 and it just means the entire job has been completed.
Since b can do it alone in 15 days, this means that:
If we divide by 15 here, we get the equation:
We can now use this definition to substitute it into the first equation we made.
Multiply the 10 and 1/15
subtract 2/3 from both sides
Now divide both sides by 10
Now multiply this by 6, since we a represents the amount of work that can be done in a day, we want to find how many parts of the work can be done by a in 6 days
Now divide both the numerator and denominator by 6
Answer:
0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.
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:
Find the probability that the average score of the 64 golfers exceeded 76.
This is 1 subtracted by the pvalue of Z when X = 64.
By the Central Limit Theorem
has a pvalue of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.