Answer:
The interest rate is 7.58%
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
A = P
, where
- A is the future value of the investment, including interest
- P is the principal investment amount (the initial amount)
- r is the interest rate in decimal
- t is the time the money is invested for
∵ Angus has $3,000 he want to invest
∴ P = 3000
∵ The interest rate is compounded continuously
∵ Angus has $5,500 in 8 years
∴ A = 5500
∴ t = 8
→ Substitute them in the rule above to find r
∵ 5500 = 3000
→ Divide both sides by 3000
∴ 
=
→ Insert ㏑ in both sides
∵ ㏑( ) = ㏑()
→ Remember ㏑(
) = n
∴ ㏑( ) = 8r
→ Divide both sides by 8
∴ 0.07576697545 = r
→ Multiply it by 100% to change it to a percentage
∴ r = 0.07576697545 × 100%
∴ r = 7.576697545 %
→ Round it to the nearest hundredth
∴ r ≅ 7.58
∴ The interest rate is 7.58%
The sales person is making 3% so, we would simply multiply $1400 by .03
1400*.03
=$42
They made $42 dollars on a $1400 sale, pretty lousy if you ask me.
Answer:
ℝ - {(-2/3),(3/2)}
Step-by-step explanation:
We want the domain of f(g(x)). So, firstly, we have to find the domain for g(x) and, then, for f(g(x)).
- Domain of g(x): Since the expression is a fracion, we must exclude the values of x that make null the denominator. Hence,
- Domain of f(g(x)): We'll find its expression:
Now, once again, we have to exclude the values of x that make the denominator equals to zero. Thus,
Lastly, we may write the domanin of f(g(x)):
![D(f(g(x)) = \left]-\infty,-\dfrac{2}{3}\right[\cup\left]-\dfrac{2}{3},\dfrac{3}{2}\right[\cup\left]\dfrac{3}{2},\infty\right[](https://tex.z-dn.net/?f=D%28f%28g%28x%29%29%20%3D%20%5Cleft%5D-%5Cinfty%2C-%5Cdfrac%7B2%7D%7B3%7D%5Cright%5B%5Ccup%5Cleft%5D-%5Cdfrac%7B2%7D%7B3%7D%2C%5Cdfrac%7B3%7D%7B2%7D%5Cright%5B%5Ccup%5Cleft%5D%5Cdfrac%7B3%7D%7B2%7D%2C%5Cinfty%5Cright%5B)
or, just writing in a shorter way:
Answer:
y = 4x -1
Step-by-step explanation:
You use the equation y = mx + b
m is the slope, so you just substitute 4 for m, and b is the y-intercept, so you substitute -1 for b
700 times 5 = 3500 or 726 times 5 estimated =4000 hope this helps
