Answer:
The proof contains a simple direct proof, wrapped inside the unnecessary logical packaging of a proof by contradiction framework.
Step-by-step explanation:
The proof is rigourous and well written, so we discard the second answer.
This is not a fake proof by contradiction: it does not have any logical fallacies (circular arguments) or additional assumptions, like, for example, the "proof" of "All the horses are the same color". It is factually correct, but it can be rewritten as a direct proof.
A meaningful proof by contradiction depends strongly on the assumption that the statement to prove is false. In this argument, we only this assumption once, thus it is innecessary. Other proofs by contradiction, like the proof of "The square root of 2 is irrational" or Euclid's proof of the infinitude of primes, develop a longer argument based on the new assumption, but this proof doesn't.
To rewrite this without the superfluous framework, erase the parts "Suppose that the statement is false" and "The fact that the statement is true contradicts the assumption that the statement is false. Thus, the assumption that the statement was false must have been false. Thus, the statement is true."
Answer:
The minimum score of those who received C's is 67.39.
Step-by-step explanation:
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.
In this problem, we have that:
If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?
This is X when Z has a pvalue of 1-0.695 = 0.305. So it is X when Z = -0.51.
The minimum score of those who received C's is 67.39.
may i please get brainlyest She can make 42 identical packages which contains 2 chocolate chip cookies and 1 sugar cookies.
86 / 2 = 43 chocolate chips cookies
42 / 1 = 42 sugar cookies
Though the chocolate chip cookies can make 43 packs, the sugar cookies cannot fulfill the extra pack for it only has 42 pieces. That is why the maximum number of package that has identical content is 42 packages.
Answer:
b > -6 or b < 6
Step-by-step explanation:
The absolute value operator always returns a positive number, with |b| = b if b > 0, and |b| = -b if b 0. With this in mind, consider the following inequality:
Because of the absolute value operator, this is valid for b values larger than 6 and less than -6. As a result, the compound inequality that this circumstance illustrates is:
