Orly uses 2 cups of raisins for every 9 cups of trail mix she makes. How many cups of trail mix will she make if she uses 12 cup
1 answer:
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Depends if you want
1. find how much he will earn, find the differnce between that and 18000
2. see how much to invest till he will get 18000
A=
A=futre amount
P=present amout
r=rate in decimal
n=number of times per year ccompounded
t=time in years
1.
A=?
P=9000
r=0.06
n=4 (quarter means 4 times per year)
t=2
?=
?=
?=
?=10138.4 will be earned
18000-10138.4=7861.6 needed
2.
A=18000
P=9000+x
r=0.06
n=4 (quarter means 4 times per year)
t=2
18000=
18000=
18000=
divide both sides by 1.015^8
15978.8=9000+x
minus 9000 both sides
6978.8 needed
if he willnot be investing any more, he needs $7861.6 more
if he will invest more he will need to invest $6978.8 more
1. find how much he will earn, find the differnce between that and 18000
2. see how much to invest till he will get 18000
A=
A=futre amount
P=present amout
r=rate in decimal
n=number of times per year ccompounded
t=time in years
1.
A=?
P=9000
r=0.06
n=4 (quarter means 4 times per year)
t=2
?=
?=
?=
?=10138.4 will be earned
18000-10138.4=7861.6 needed
2.
A=18000
P=9000+x
r=0.06
n=4 (quarter means 4 times per year)
t=2
18000=
18000=
18000=
divide both sides by 1.015^8
15978.8=9000+x
minus 9000 both sides
6978.8 needed
if he willnot be investing any more, he needs $7861.6 more
if he will invest more he will need to invest $6978.8 more
Answer:
1. Yes.
2. No.
3. Yes.
Step-by-step explanation:
Consider the following subsets of Pn given by
1.Let W1 be the set of all polynomials of the form , where a is in ℝ.
2.Let W2 be the set of all polynomials of the form , where a is in ℝ.
3. Let W3 be the set of all polynomials of the form , where a is in ℝ.
Recall that given a vector space V, a subset W of V is a subspace if the following criteria hold:
- The 0 vector of V is in W.
- Given v,w in W then v+w is in W.
- Given v in W and a a real number, then av is in W.
So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.
- First property:
Note that for W2, for any value of a, the polynomial we get is not the zero polynomial. Hence the first criteria is not met. Then, W2 is not a subspace of Pn.
For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.
- Second property:
W1. Consider two elements in W1, say, consider a,b different non-zero real numbers and consider the polynomials
.
We must check that p_1+p_2(t) is in W1.
Note that
Since a+b is another real number, we have that p1(t)+p2(t) is in W1.
W3. Consider two elements in W3. Say . Then
So, again, p1(t)+p2(t) is in W3.
- Third property.
W1. Consider an element in W1 and a real scalar b. Then
.
Since (ba) is another real scalar, we have that bp(t) is in W1.
W3. Consider an element in W3 and a real scalar b. Then
.
Since (ba) is another real scalar, we have that bp(t) is in W3.
After all,
W1 and W3 are subspaces of Pn for n= 2
and W2 is not a subspace of Pn.