Getaway Travel Agency surveyed a random sample of 45 of their clients about their vacation plans. Of the clients surveyed, 21 ex
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Answer:
Step-by-step explanation:
We have the two functions:
And we wish to find:
First, let’s find f(2) first. So, we will substitute 2 for x for f(x):
Hence, we can now substitute 3 for f(2):
Now, we can find g(6). Substitute 6 for t for g(t):
Therefore:
Answer:
Only d) is false.
Step-by-step explanation:
Let be the characteristic polynomial of B.
a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)
b) Remember that . 0 is a root of p, so we have that
.
c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.
d) det(B)=0 by part c) so B is not invertible.
e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.
Answer: $454.55
Step-by-step explanation:
Tito's weekly salary is always $ 500 per week.
But your weekly commission income depends on the sales you make. Your commissions are 55%.
If we call x the dollar amount of all sales made by Tito in a week, then his income z(x) is given by the following equation:
We wish that .
Then we equate the equation to 750 and solve for the variable x.
Total sales made by Tito must be $454.55