Answer: she invested $3250 in 5% interest account and $6750 in 8% interest account.
Step-by-step explanation:
Let P be the amount Maria invested in an account with 5% interest , then 10,000-P denote the amount invested in account with 8% interest.
The simple interest on amount P with rate r % in time t is given by:-
![I=P\frac{r}{100}t](https://tex.z-dn.net/?f=I%3DP%5Cfrac%7Br%7D%7B100%7Dt)
Interest in 5% account in 1 year=![P(\frac{5}{100})(1)=0.05P](https://tex.z-dn.net/?f=P%28%5Cfrac%7B5%7D%7B100%7D%29%281%29%3D0.05P)
Similarly,
Interest in 8% account in 1 year=![(10,000-P)(\frac{8}{100})(1)=800-0.08P](https://tex.z-dn.net/?f=%2810%2C000-P%29%28%5Cfrac%7B8%7D%7B100%7D%29%281%29%3D800-0.08P)
According to the question,
![0.05P+800-0.08P=702.50\\\Rightarrow-0.03P=702.50-800\Rightarrow\ -0.03P=-97.5\\\Rightarrow\ P=\frac{97.5}{0.03}\\\Rightarrow\ P=3,250\\\\10,000-3250=6750](https://tex.z-dn.net/?f=0.05P%2B800-0.08P%3D702.50%5C%5C%5CRightarrow-0.03P%3D702.50-800%5CRightarrow%5C%20-0.03P%3D-97.5%5C%5C%5CRightarrow%5C%20P%3D%5Cfrac%7B97.5%7D%7B0.03%7D%5C%5C%5CRightarrow%5C%20P%3D3%2C250%5C%5C%5C%5C10%2C000-3250%3D6750)
Thus, she invested $3250 in 5% interest account and $6750 in 8% interest account.
Answer:
13 is 135
14 is 293.3
15 is 14208
16 is 400
17 is 125 percent of 44
18 is 137.5 percent of 56
19 is 25 percent
20 is 2 percent
Step-by-step explanation:
![\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%3D41.50%20%5C%5C%20b%3D35.78%20%5C%5C%20B%3D40.76%5Ctext%7B%20%5Cdegree%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
Explanation
Step 1
a) let
![\begin{gathered} A=49.23\text{ \degree} \\ c=54.8\text{ \degree} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D49.23%5Ctext%7B%20%5Cdegree%7D%20%5C%5C%20c%3D54.8%5Ctext%7B%20%5Cdegree%7D%20%5Cend%7Bgathered%7D)
b) b value
to find the measure of side b we can use cosine function
![\begin{gathered} cos\theta=\frac{adjacent\text{ side}}{hypotenuse} \\ replace \\ cos\text{ 49.23=}\frac{b}{54.8} \\ b=54.8*cos49.23 \\ b=35.78 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20cos%5Ctheta%3D%5Cfrac%7Badjacent%5Ctext%7B%20side%7D%7D%7Bhypotenuse%7D%20%5C%5C%20replace%20%5C%5C%20cos%5Ctext%7B%2049.23%3D%7D%5Cfrac%7Bb%7D%7B54.8%7D%20%5C%5C%20b%3D54.8%2Acos49.23%20%5C%5C%20b%3D35.78%20%5Cend%7Bgathered%7D)
c) angle B
to find the measure of Angle B we can use sine function
![\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ replace \\ sin\text{ B=}\frac{35.78}{54.8} \\ sin\text{ B= 0.65}\Rightarrow inverse\text{ function to isolate B} \\ B=\sin^{-1}(0.65) \\ B=40.76 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20sin%5Ctheta%3D%5Cfrac%7Bopposite%5Ctext%7B%20%20side%7D%7D%7Bhypotenuse%7D%20%5C%5C%20replace%20%5C%5C%20sin%5Ctext%7B%20B%3D%7D%5Cfrac%7B35.78%7D%7B54.8%7D%20%5C%5C%20sin%5Ctext%7B%20B%3D%200.65%7D%5CRightarrow%20inverse%5Ctext%7B%20function%20to%20isolate%20B%7D%20%5C%5C%20B%3D%5Csin%5E%7B-1%7D%280.65%29%20%5C%5C%20B%3D40.76%20%5Cend%7Bgathered%7D)
d) side a
![\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ A=}\frac{a}{c}=\frac{\placeholder{⬚}}{\placeholder{⬚}} \\ sin\text{ 49.23=}\frac{a}{54.8} \\ multiply\text{ both sides by 54.8} \\ 54.8s\imaginaryI n\text{49.23=}\frac{a}{54.8}*54.8 \\ 41.50=a \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20sin%5Ctheta%3D%5Cfrac%7Bopposite%5Ctext%7B%20side%7D%7D%7Bhypotenuse%7D%20%5C%5C%20sin%5Ctext%7B%20A%3D%7D%5Cfrac%7Ba%7D%7Bc%7D%3D%5Cfrac%7B%5Cplaceholder%7B%E2%AC%9A%7D%7D%7B%5Cplaceholder%7B%E2%AC%9A%7D%7D%20%5C%5C%20sin%5Ctext%7B%2049.23%3D%7D%5Cfrac%7Ba%7D%7B54.8%7D%20%5C%5C%20multiply%5Ctext%7B%20both%20sides%20by%2054.8%7D%20%5C%5C%2054.8s%5CimaginaryI%20n%5Ctext%7B49.23%3D%7D%5Cfrac%7Ba%7D%7B54.8%7D%2A54.8%20%5C%5C%2041.50%3Da%20%5Cend%7Bgathered%7D)
so, the answer is
![\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%3D41.50%20%5C%5C%20b%3D35.78%20%5C%5C%20B%3D40.76%5Ctext%7B%20%5Cdegree%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
I hope this helps you
Answer: it would be -17 m8
Step-by-step explanation:
Answer:
It is neutral.so I think it is true
Step-by-step explanation:
It is neutral