Two forces with magnitudes of 90 and 50 pounds act on an object at angles of 30° and 160°, respectively. Find the direction and
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Answer:
the 8% loan has a principal of $37500
the 12% loan has a principal of $12500
Step-by-step explanation:
Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).
Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":
Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:
This is our first equation in the variables x and y which are our unknowns.
Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:
We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:
Therefore the amount of the loan at 12% is $12500
Now to find the amount of the second loan "y" we use the equation for the totals of the loans:
Therefore, the loan at 8% is $37500
Answer:
40000
Step-by-step explanation:
Simple interest (I) is calculated as
I =
P is the amount borrowed , R is the interest and T the time in years
Here I = 2000 , R = 5 and T = 1 with P to be found , then
2000 = ( multiply both sides by 100 )
5P = 200000 ( divide both sides by 5 )
P = 40000
Answer:
(a) Number of sets B given that
- A⊆B⊆C: 2¹⁰. (That is: A is a subset of B, B is a subset of C. B might be equal to C)
- A⊂B⊂C: 2¹⁰ - 2. (That is: A is a proper subset of B, B is a proper subset of C. B≠C)
(b) Number of sets B given that set A and set B are disjoint, and that set B is a subset of set X: 2²⁰ - 2¹⁰.
Step-by-step explanation:
<h3>(a)</h3>Let denote the 20 elements of set X.
Let denote elements of set X that are also part of set A.
For set A to be a subset of set B, each element in set A must also be present in set B. In other words, set B should also contain .
For set B to be a subset of set C, all elements of set B also need to be in set C. In other words, all the elements of set B should come from .
.
For each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus possibilities for set B.
In case the question connected set A and B, and set B and C using the symbol ⊂ (proper subset of) instead of ⊆, A ≠ B and B ≠ C. Two possibilities will need to be eliminated: B contains all ten "maybe" elements or B contains none of the ten "maybe" elements. That leaves possibilities.
Set A and set B are disjoint if none of the elements in set A are also in set B, and none of the elements in set B are in set A.
Start by considering the case when set A and set B are indeed disjoint.
.
Set B might be an empty set. Once again, for each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus possibilities for a set B that is disjoint with set A.
There are 20 elements in X so that's possibilities for B ⊆ X if there's no restriction on B. However, since B cannot be disjoint with set A, there's only
possibilities left.