MUCH lower. And that is the truth! We have done several of them here and CLEP exams cost about $80 for the exam and maybe $40 for the study guide. Compare that with a $500 class. MUCH lower.
Three main functions are protection regulation and sensation. Protection is primary I️ believe.
Answer: There is a weak, positive correlation between the weight Lucy lost and the number of weeks.
Explanation:
The correlation coefficient is used to measure the relationship between two variables in terms of how they move in relation to one another.
If two variables are said to have a positive correlation, it means that they increase at the same time and decrease at the same time for example, there is a positive correlation between the amount of food a family buys and how much money they have because the more money they have, the more food they buy.
Negative correlations are the reverse for instance Ice cream sales and cold temperatures. The colder it is, the less people buy ice cream.
The Correlation coefficient ranges from -1 to +1 with +1 (-1) meaning that the variables are perfectly positively(negatively) correlated. The closer the value is to 0, the weaker the correlation.
Generally, for a correlation coefficient between the numbers 0 and +0.3, there is a weak positive correlation.
With a correlation coefficient of 0.0502, there is therefore a weak, positive correlation between the weight Lucy lost and the number of weeks.
Solution. To check whether the vectors are linearly independent, we must answer the following question: if a linear combination of the vectors is the zero vector, is it necessarily true that all the coefficients are zeros?
Suppose that
x 1 ⃗v 1 + x 2 ⃗v 2 + x 3 ( ⃗v 1 + ⃗v 2 + ⃗v 3 ) = ⃗0
(a linear combination of the vectors is the zero vector). Is it necessarily true that x1 =x2 =x3 =0?
We have
x1⃗v1 + x2⃗v2 + x3(⃗v1 + ⃗v2 + ⃗v3) = x1⃗v1 + x2⃗v2 + x3⃗v1 + x3⃗v2 + x3⃗v3
=(x1 + x3)⃗v1 + (x2 + x3)⃗v2 + x3⃗v3 = ⃗0.
Since ⃗v1, ⃗v2, and ⃗v3 are linearly independent, we must have the coeffi-
cients of the linear combination equal to 0, that is, we must have
x1 + x3 = 0 x2 + x3 = 0 ,
x3 = 0
from which it follows that we must have x1 = x2 = x3 = 0. Hence the
vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer. The vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
