Consider the sequence of numbers 3/8,3/4, 1 1/8,1 7/8 Which statement is a description of the sequence?
2 answers:
The complete question in the attached figure
Let
for n=1
f(1)=3/8
for n=2
f(2)=3/4
for n=3
f(3)=1 1/8
for n=4
f(4)=1 1/2
for n=5
f(5)=1 7/8
we know that
f(2)-f(1)=3/4-3/8=3/8------> f(2)=f(1)+3/8
f(3)-f(2)=1 1/8-3/4----> 9/8-6/8----> 3/8-----> f(3)=f(2)+3/8
f(4)-f(3)=1 1/2-1 1/8-----> 12/8-9/8----> 3/8-----> f(4)=f(3)+3/8
f(5)-f(4)=1 7/8-1 1/2-----> 15/8-12/8---> 3/8-----> f(5)=f(4)+3/8
therefore
the answer is the option
The sequence is recursive and can be represented by the function f(n + 1) = f(n) + 3/8
Let
for n=1
f(1)=3/8
for n=2
f(2)=3/4
for n=3
f(3)=1 1/8
for n=4
f(4)=1 1/2
for n=5
f(5)=1 7/8
we know that
f(2)-f(1)=3/4-3/8=3/8------> f(2)=f(1)+3/8
f(3)-f(2)=1 1/8-3/4----> 9/8-6/8----> 3/8-----> f(3)=f(2)+3/8
f(4)-f(3)=1 1/2-1 1/8-----> 12/8-9/8----> 3/8-----> f(4)=f(3)+3/8
f(5)-f(4)=1 7/8-1 1/2-----> 15/8-12/8---> 3/8-----> f(5)=f(4)+3/8
therefore
the answer is the option
The sequence is recursive and can be represented by the function f(n + 1) = f(n) + 3/8
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Answer:
Step-by-step explanation:
We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find .
For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".
A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.
Then
(1)
We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.
Then
(2)
Having equations (1) and (2), we can form a system of two equations and two unknowns values:
(1)
(2)
Rearranging these two equations:
(1)
(2)
To solve this system of equations, we can multiply (1) by -1, and them sum the two resulting equation:
(1)
(2)
Summing both equations, we obtain the following equation:
Then
To find the value of the mean, we need to substitute the value obtained for the standard deviation in equation (2):
(2)