Answer:
9 and 18
Step-by-step explanation:
Answers:
x = -8/5 or x = 8/5
Sum of the first ten terms where all terms are positive = 4092
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Explanation:
r = common ratio
- first term = 4
- second term = (first term)*(common ratio) = 4r
- third term = (second term)*(common ratio) = (4r)*r = 4r^2
The first three terms are: 4, 4r, 4r^2
We're given that the sequence is: 4, 5x, 16
Therefore, we have these two equations
Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.
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To find the sum of the first n terms, we use this geometric series formula
Sn = a*(1 - r^n)/(1 - r)
We have
- a = 4 = first term
- r = 2, since we want all the terms to be positive
- n = 10 = number of terms to sum up
So,
Sn = a*(1 - r^n)/(1 - r)
S10 = 4*(1 - 2^10)/(1 - 2)
S10 = 4*(1 - 1024)/(-1)
S10 = 4*(-1023)/(-1)
S10 = 4092
Answer:
ΔABC ~ ΔDEF
Step-by-step explanation:
If the given triangles ΔABC and ΔDEF are similar,
Their corresponding sides will be proportional.
By substituting the measures of the given sides,
2 = 2 = 2
Since, corresponding sides of both the triangles are proportional, both the triangles will be similar.
ΔABC ~ ΔDEF
Answer:
Option b, c and e are wonderful approaches to solve the problem.
Step-by-step explanation:
Option (b) is appropriate this is because the option is talking about Simple random sampling where random universities are chosen to remove bias.
Option (c) is correct because this is an example of Stratified sampling where two homogenous groups (private and public universities are considered) and samples are chosen at random to remove bias
Option (e) is correct because this again is an example of Simple random sampling where 60 random STEM majors are chosen at random.
