Mathematics, 25.12.2019 00:31 ciralove2004

Annual high temperatures in a certain location have been tracked for several years. let xx represent the year and yy the high temperature. based on the data shown below, calculate the correlation coefficient (to three decimal places) between xx and yy. use your calculator! x y4 43.655 40.746 38.537 37.228 33.019 30.610 29.8911 27.1812 25.8713 23.5614 22.2515 18.6416 18.3317 16.9218 13.8119 9.9

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Answer from: shred360

r =-0.996

Step-by-step explanation:

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

In order to calculate the correlation coefficient we can begin doing the following table:

n x y xy x*x y*y

1 4 43.65 174.6 16 1905.323

2 5 40.74 203.7 25 1659.748

3 6 38.53 231.18 36 1484.561

4 7 37.22 260.54 49 1385.323

5 8 33.01 264.08 64 1089.660

6 9 30.61 275.49 81 936.972

7 10 29.89 298.9 100 893.412

8 11 27.18 298.98 121 738.752

9 12 25.87 310.44 144 669.257

10 13 23.56 306.28 169 555.0974

11 14 22.25 311.50 196 495.063

12 15 18.64 279.60 225 347.450

13 16 18.33 293.28 256 335.989

14 17 16.92 287.64 289 286.286

15 18 13.81 248.58 324 190.716

16 19 9.9 188.10 361 98.01

$n =16 \sum x \sum y \sum xy \sum x^2 \sum y^2$

n=16 $\sum x = 184, \sum y = 430.11, \sum xy=4232.89, \sum x^2 =2456, \sum y^2 =13071.6$

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{16(4232.89)-(184)(430.11)}{\sqrt{[16(2456) -(184)^2][16(13071.600) -(430.11)^2]}}=-0.996$

So then the correlation coefficient would be r =-0.996

Answer from: Quest

answer: $\frac{sin40^{\circ}}{x} = \frac{sin60^{\circ}}{12}$

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

$\frac{sin40^{\circ}}{x} = \frac{sin60^{\circ}}{12}$

which is the required equation for finding the value of x,

$\frac{x}{sin40^{\circ}}= \frac{12}{sin60^{\circ}}$

$x= 12\times \frac{sin40^{\circ}}{sin60^{\circ}}$

$x= 12\times 0.74222719896$

$x= 8.90672638762\approx 8.967$

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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