Answered

IDNLearn.com makes it easy to find accurate answers to your specific questions. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.

The following is a list of 4 measurements:

[tex]\[6, 7, 9, 20\][/tex]

Suppose that these 4 measurements are respectively labeled [tex]\[x_1, x_2, \ldots, x_4\][/tex]. Compute the following:

[tex]\[
\sum_{i=1}^4\left(x_i\right)^2
\][/tex]

Sagot :

GinnyAnsweridn
Let's proceed step-by-step to compute the sum of the squares of each measurement given.


First, label the measurements as follows:
- [tex]\( x_1 = 6 \)[/tex]
- [tex]\( x_2 = 7 \)[/tex]
- [tex]\( x_3 = 9 \)[/tex]
- [tex]\( x_4 = 20 \)[/tex]


We need to calculate:
[tex]\[ \sum_{i=1}^4 (x_i)^2 = x_1^2 + x_2^2 + x_3^2 + x_4^2 \][/tex]


Substitute the values of [tex]\( x_1, x_2, x_3, \)[/tex] and [tex]\( x_4 \)[/tex]:


[tex]\[ 6^2 + 7^2 + 9^2 + 20^2 \][/tex]


Now square each measurement:


[tex]\[ 6^2 = 36 \][/tex]
[tex]\[ 7^2 = 49 \][/tex]
[tex]\[ 9^2 = 81 \][/tex]
[tex]\[ 20^2 = 400 \][/tex]


Next, sum these squared values:


[tex]\[ 36 + 49 + 81 + 400 \][/tex]


Add them step-by-step:


[tex]\[ 36 + 49 = 85 \][/tex]
[tex]\[ 85 + 81 = 166 \][/tex]
[tex]\[ 166 + 400 = 566 \][/tex]


Therefore, the sum of the squares of the measurements is:


[tex]\[ \sum_{i=1}^4 (x_i)^2 = 566 \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.