Answer choices for A : 6, 5 , 5.5
1 answer:
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Answer:
a. f(n) = n(n+1)/2
b. 351
c. 19
d. no; n would not be an integer for f(n) = 17.
Step-by-step explanation:
a. The terms are 1, 3, 6, 10, ...
Each term has the term number added to the previous term. That is, first differences are 3-1 = 2, 6-3 = 3, 10-6 = 4. These differences have a constant difference of 1.
When the 2nd differences are constant, a 2nd degree polynomial can describe the sequence. It is a little bit of trouble to find that polynomial.
For the polynomial ...
We can substitute values for n and f(n) to get 3 equations in 3 unknowns:
Solving these equations by your favorite method gives ...
(a, b, c) = (1/2, 1/2, 0)
That is, the function representing the relationship is ...
f(n) = n(n+1)/2 . . . . the function describing the relationship
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b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26
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c. The number of the term having 190 squares can be found by solving ...
n(n +1)/2 = 190
n(n +1) = 380 = 19(20)
The 19th term will have 190 squares.
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d. Terms 5 and 6 are 15 and 21.
17 is not the value of one of the terms in this sequence.
Answer:
There is not sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women
Step-by-step explanation:
The correlation coefficient between the variables h(height in inches) and pulse rates (in beats per minute) is 0.202
Sample size n=40
Level of significane alpha = 0.01
Create null and alternate hypothesis as:
H0: r=0
Ha: r not equal 0
(Two tailed test at 1% significance level)
Sample r = 0.202
r difference = 0.202
test statistic t =
df =n-2 =38
t critical value for 0.01 and df =38 is 2.704
Since our test statistic lies below 2.704, we accept null hypothesis
There is not sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women