Area of square = where,
is the side length of the square.
s must be positive since it is a side length, so the negative root of 81 is rejected.
Perimeter=
Perimeter=
A student council president wants to learn about the preferred theme for the upcoming spring dance. Which of the following sampl
2 answers:
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(a) The explicit rule to model the sequence formed by the number of seats in each row is
(b) The 35th row has 120 seats
Step-by-step explanation:
The rule of the nth term of an arithmetic sequence is
, where
- a is the the first term
- d is the common difference between each two consecutive terms
∵ There are 18 seats in the 1st row
∵ There are 21 seats in the 2nd row
∵ 21 - 18 = 3
∵ The number of seats is increased by 3 with each additional row
- The number of seats in each row represents an arithmetic
sequence because there is a common difference between
each two consecutive rows
∴ The number of seats in each row formed an arithmetic sequence
∵ The number of seats in the first row = 18 seats
∴ a = 18
∵ The number of seats in a row continues to increase by 3 with each
additional row
∴ d = 3
- Substitute the values of a and d in the rule of nth term
∴
- Simplify the right hand side
∴
- Add like terms
∴
(a) The explicit rule to model the sequence formed by the number of seats in each row is
∵ There are 120 seat in a row
- Substitute by 120 in the rule above
∴ 120 = 15 + 3n
- Subtract 15 from both sides
∴ 105 = 3n
- Divide both sides by 3
∴ n = 35
∴ The number of the row is 35
(b) The 35th row has 120 seats
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Answer:
The diameter that separates the bottom 9% is 5.02 millimeters.
The diameter that separates the top 9% is 5.2 millimeters.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 5.11 millimeters and a standard deviation of 0.07 millimeters.
This means that
Bottom 9%:
The 9th percentile, which is X when Z has a pvalue of 0.09. So X when Z = -1.34.
The diameter that separates the bottom 9% is 5.02 millimeters.
Top 9%:
The 100 - 9 = 91th percentile, which is X when Z has a pvalue of 0.91. So X when Z = 1.34.
The diameter that separates the top 9% is 5.2 millimeters.