What are the solutions of the equation x2 + 5x + 6 = 0? A. −3, 2 B. 6, −1 C. 6, 1 D. −3, −2
1 answer:
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Answer:
Step-by-step explanation:
To create a password, you need to select 8 characters (not necessarily different) from the set {1,3,5,7,9,a,b,c,...,z}. Now, this set has 31 elements: the 26 lowercase letters from the alphabet and the 5 odd numbers (1,3,5,7,9).
Now, there are 31 ways to choose the first character, it can be any element from our set. The second character can also be chosen in 31 ways, because there are not restrictions (repetitions, specific characters, etc). Similarly, the third, fourth, fifth, sixth, seventh and eighth characters have 31 possibilities each one.
The number of passwords is the number of ways of selecting the 8 characters, then by the multiplication principle the number of passwords is 31×31×31×31×31×31×31×31=31^8.
Answer:
A)sample proportion = 0.17, the sampling distribution of p can be calculated/approximated with normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281
B) 0.869
C)0.9668
Step-by-step explanation:
A) p ( proportion of population that spends more than $100 per week) = 0.17
sample size (n)= 800
the sample proportion of p = 0.17
standard error of p = = 0.013281
the sampling distribution of p can be calculated/approximated with
normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281
B) probability that the sample proportion will be +-0.02 of the population proportion
= p (0.17 - 0.02 ≤ P ≤ 0.17 + 0.02 ) = p( 0.15 ≤ P ≤ 0.19)
z value corresponding to P
Z =
at P = 0.15
Z = (0.15 - 0.17) / 0.013281 = = -1.51
at P = 0.19
z = ( 0.19 - 0.17) / 0.013281 = 1.51
therefore the required probability will be
p( -1.5 ≤ z ≤ 1.5 ) = p(z ≤ 1.51 ) - p(z ≤ -1.51 )
= 0.9345 - 0.0655 = 0.869
C) for a sample (n ) = 1600
standard deviation/ error = 0.009391 (applying the equation for calculating standard error as seen in part A above)
therefore the required probability after applying
z = at p = 0.15 and p = 0.19
p ( -2.13 ≤ z ≤ 2.13 ) = p( z ≤ 2.13 ) - p( z ≤ -2.13 )
= 0.9834 - 0.0166 = 0.9668