Answer:
Step-by-step explanation:
We are given the formula:
where is centimeters and
is inches.
We know that Henry is 170 centimeters tall. Therefore, we can substitute 170 in for
We want to find out how tall Henry is, in inches. We must isolate the variable for inches, , on one side of the equation.
is being multiplied by 2.54. The inverse of multiplication is division. Divide both sides of the equation by 2.54
Round to the nearest tenth. The 2 in the hundredth place tells us to leave the 9 in the tenth place.
Henry is about 66.9 inches tall.
Answer:
$7,544.58
Step-by-step explanation:
We will use the compound interest formula provided to solve this:
<em>P = initial balance</em>
<em>r = interest rate (decimal)</em>
<em>n = number of times compounded annually</em>
<em>t = time</em>
<em />
First, change 3.3% into its decimal form:
3.3% -> -> 0.033
Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:
The balance after 1 year will be $7,544.58
Answer:
1)
the mean rate of return is 17 %
the standard deviation of return is 17.06055
2)
the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325
Step-by-step explanation:
Given the data in the question;
1)
For the portfolio, the mean return and standard deviation are computed as follows;
Mean = Return = 0.65 × 10 + 0.35 × 30
= 6.5 + 10.5
= 17 %
Therefore, the mean rate of return is 17 %
Standard deviation will be;
σp = √( 0.65² × 15² + 0.35² × 40² )
= √( 0.4225 × 225 + 0.1225 × 1600 )
= √( 95.0625 + 196 )
= √291.0625
= 17.06055
Therefore, the standard deviation of return is 17.06055
2)
probability that Marvin's portfolio will make at least 20% over the next 12 months.
P( X > 20 )
we convert to a standard normal variable;
Z = )
Z = 0.17
from z table, p-value is;
p( X < 20 ) = 0.5675
P( X > 20 ) 1 - 0.5675 = 0.4325
Therefore, the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325