Answer:
0.25 per gallon
slope: 0.25
Step-by-step explanation:
the train travels 25 miles per 100 gallons
this simplifies into 0.25 per 1 gallon
slope is y/x
y/x = 25/100 = 0.25
Answer:
Expression: Y = -10/3 X
Y = 10/3
Step-by-step explanation:
If Y varies directly as X, then;
Y∝X
Y = kX
k is the constant of variation
If Y = 10 and X = -3
10 = -3k
k = -10/3
Substitute k = -10/3 into the expression Y = kX
Y = -10/3 X
This gives the required expression
To get the value of Y when X = -1
Recall that Y = kX
Y = -10/3 (-1)
Y = 10/3
Hence the value of Y is 10/3
Choice A is a function.
Each input can only be there once
In order to determine the money you have to invest now to obtain $100,000 after 18 years, use the following formula:
![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
where,
P: principal = ?
A: amount after t years = 100,000
r: APR in decimal form = 0.11 (11%)
n: times of the compounded interest at year = 4 (quarterly)
t: time = 18 (years)
Solve the equation above for P, replace the values of the other parameters and simplify:
![\begin{gathered} 100000=P(1+\frac{0.11}{4})^{4*18} \\ 100000=P(1.0275)^{72} \\ P=\frac{100000}{(1.0275)^{72}} \\ P\approx14181.04 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20100000%3DP%281%2B%5Cfrac%7B0.11%7D%7B4%7D%29%5E%7B4%2A18%7D%20%5C%5C%20100000%3DP%281.0275%29%5E%7B72%7D%20%5C%5C%20P%3D%5Cfrac%7B100000%7D%7B%281.0275%29%5E%7B72%7D%7D%20%5C%5C%20P%5Capprox14181.04%20%5Cend%7Bgathered%7D)
Hence, you need to invest approimately $14,181.04 to obtain $100,000 after 18 years.