We can only sum matrices with equal order, so we can't sum matrices A and B in the first exercise.
As for the second exercise, we have:
All of these answers depend on the fact that the sum/difference of two matrices is simply the sum/difference of the correspondent elements. So, if the element in the i-th row and the j-th column of A is and the element in the i-th row and the j-th column of B is
, we have
So, the sum between matrices inherits the properties of the sum between numbers: the order matters when you subtract (which is why a and f are false), the sum is commutative (which is why b, c, d are true) and associative (which is why e is true).
Answer:
Option C (1, 0)
Step-by-step explanation:
We have a system with the following equations:
The first equation is a parabola.
The second equation is a straight line
To solve the system, substitute the second equation in the first and solve for x.
Simplify
You must search for two numbers that when you add them, obtain as a result -2 and multiplying both results in 1.
These numbers are -1 and -1
Therefore
Finally the solutions are
We reject our null hypothesis, H₀, at a level of significance of =0.01 since the P-value is less than that threshold. There is compelling statistical data to indicate that since 1991, the proportion of drivers who love driving has decreased.
Given,
The Pew Research Center recently polled n=1048 U.S. drivers and found that 69% enjoyed driving their automobiles.
In 1991, a Gallup poll reported this percentage to be 79%. using the data from this poll, test the claim that the percentage of drivers who enjoy driving their cars has declined since 1991.
To report the large-sample z statistic and its p-value,
Null hypothesis,
H₀ : p = 0.79
Alternative hypothesis,
Ha : p < 0.79
Level of significance, α = 0.01
Under H₀
Test statistic,
Z₀ = -7.948
The alternative hypothesis(Ha) is left-tailed, so the P-value of the test is given by
P-value = P(z <-7.945)
= 0.000 (from z-table)
Since the P-value is smaller than given level of significance, α=0.01 we reject our null hypothesis, H₀, at α=0.0.1 level Strong statistical evidence to conclude that the percentage of drivers who enjoy driving their cars has declined since 1991.
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