Answer:
It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.
Step-by-step explanation:
Use the formula for continuous compounding
![X(t) = Pe^{rt}](https://tex.z-dn.net/?f=X%28t%29%20%3D%20Pe%5E%7Brt%7D)
where r stands for the (annual) interest rate, t for time in years, P for the initial principal (investment) and X is the amount after t years.
(this formula can be beautifully derived from just basic considerations, btw)
We are given t=5, and percent increase on the initial P, so we can solve for r
![X(5) = 1.5P=Pe^{r\cdot5}\\1.5=e^{r\cdot5}\\\ln 1.5=\ln e ^{5r}\\\ln 1.5=5r\\r = \frac{\ln 1.5}{5}=0.081\rightarrow 8.1\%](https://tex.z-dn.net/?f=X%285%29%20%3D%201.5P%3DPe%5E%7Br%5Ccdot5%7D%5C%5C1.5%3De%5E%7Br%5Ccdot5%7D%5C%5C%5Cln%201.5%3D%5Cln%20e%20%5E%7B5r%7D%5C%5C%5Cln%201.5%3D5r%5C%5Cr%20%3D%20%5Cfrac%7B%5Cln%201.5%7D%7B5%7D%3D0.081%5Crightarrow%208.1%5C%25)
It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.
Answer:△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.
Step-by-step explanation:
A rigid motion of the plane is a motion which maintain distance.
Translation is a kind of rigid motion used in geometry to trace a function that moves an object a particular distance.
A reflection is also a kind of rigid motion . It is mainly a 'toss' of a shape across the line of reflection.
So,△DEF is mapped to △D′E′F′ using the rule (x,y)→(x,y+1) ( which is a translation.) followed by (x,y)→(x,−y)(which is reflection),therefore it is a sequence of rigid motions.
I think it’s C I hope it helps
Answer:
d. f opens upward with a y-intercept at (0, 2); h opens downward with a y-intercept at (0, -2)
The cost of each song is Rs 1.75
<h3>How to solve algebra word problems?</h3>
Let the variable representing the cost of 1 song be x.
Now, since she was given a $50 gift card to a music downloading app. She purchased 18 songs from the app that all cost the same amount each. If she has $18.50 remaining on her gift card. Thus, we can express this as;
50 - 18x = 18.50
-18x = 18.50 - 50
-18x = -31.5
x = -31.5/-18
x = 1.75
Therefore, the cost of each song is Rs 1.75
Read more about Algebra Word Problems at; brainly.com/question/13818690
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