There are two data sets x and y.
X includes = 14 25 19 35 20 12 5
Y includes = 360 293 315 212 315 331 404
to solve for the correlation coefficient, we need to get the following values step by step
Step 1: Find the mean of each set.
The mean of X = 18.571
The mean of Y = 318.571
Step 2: Subtract the mean of X from every value X value
(denote this with letter a). Do the same for y (denote this with letter b).
The mean of X subtracted from every X value (a):
14 - 18.571 = -4.571
25 - 18.571 = 6.429
19 - 18.571 = 0.429
35 - 18.571 = 16.429
20 - 18.571 = 1.429
12 - 18.571 = -6.571
5 - 18.571 = -13.571
The mean of Y subtracted from every value of Y (b):
360 - 318.571 = 41.429
293 - 318.571 = -25.571
315 - 318.571 = -3.571
212 = 318.571 = -106.571
315 - 318.571 = -3.571
331 - 318.571 = 12.429
404 - 318.571 = 85.429
Step 3: Calculate: a *
b, a^2 and b^2 of every value.
For a*b
-189.388
-164.388
-1.531
-1750.816
-5.102
-81.673
-1159.388
Sum: -3352.286
For a²
20.898
41.327
0.184
269.898
2.041
43.184
184.184
Sum: 561.714
For b²
1716.327
653.898
12.755
11357.469
12.755
154.469
7298.041
Sum: 21205.714
Step 4: Solve using this formula
r = ∑a * b / √((a²)(b²))
r = -3352.286 /
√((561.714)(21205.714))
= -0.9713
The correlation coefficient is -0.971
Answer:
Larger number:
16
Smaller number
3
Step-by-step explanation:
Larger number: 16
Smaller number: 3
Explanation:
Suppose the larger number is
a
and the smaller number is
b
.
You solve the following system of equations:
a⋅b=48
a−13=b
Since b is a −13, you can plug that into a⋅b=48, so...a⋅(a−13)=48
a 2−13a=48
a2−13a−48=0
Factor the polynomial:
(a−16)(a+3)=0
a=16 or a=−3a is positive so a=16.
We can now solve for b by plugging in a, so...16−13=b3=b We have a=16 and b=3, meaning that the larger number is 16 and the smaller number is 3.
Answer:
There are 12 circles and 6 of them are shaded. You have to find the ratio of how many circles are shaded and 6 circles are shaded and because, 6 is half of 12 the answer is 1 over 2=0.5
Answer:
a. x = 7
b. x = 36/5
Step-by-step explanation:
<u>Points to remember</u>
The ratio of of corresponding sides of similar triangles are equal.
<u>a). To find the value of x</u>
From the figure 1 we get two similar triangles, ΔABC and ADE
We can write,
AB/AD = AC/AE
3/6 = x/(x + 7)
3(x + 7) = 6 * x
3x + 21 = 6x
6x - 3x = 21
3x = 21
x = 21/3 = 7
<u>b). To find the value of x</u>
From the figure b we get
ΔABC ~ ΔEDF
AB/DE = BC/DF
4/5 = x/9
x = (4 * 9)/5 = 36/5
We can factor a 12 out of both terms. This leaves us with the expression 12(3x + 1), which is equivalent.
