Answer:
0.249 is the required proportion.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 822
Number of people who preferred foreign cars over domestic, x = 205
We have to find the proportion of new car buyers who prefer foreign cars.
Formula:
Putting values, we get,
Thus, 0.249 is the proportion of the new car buyers who preferred foreign over domestic cars..
Hi there!
We can use discriminants to determine the value of k for which the equation would have complex solutions. (Those involving i)
If b² - 4ac < 0, then the equation will have complex solutions. Therefore:
Plug in the given values of b and a to solve:
7² - 4(2)(k) < 0
Simplify:
49 - 8k < 0
Solve the inequality:
49 < 8k
6.125 < k
k > 6.125. Anything greater than 6.125 would result in complex solutions.
2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Step-by-step explanation:
The given is,
Initial investment - $5000
Future amount - $6000
Interest rate - 7.5% (compounded quarterly)
Step:1
Formula to calculate the Future amount with compound interest,
...................................(1)
Where, F - Future amount
P - Initial amount
r - Rate of interest
n - No. of compounding in a year
t - Time period
From given,
F = $6000
P = $5000
r = 7.5%
n = 4 (compounded quarterly)
Equation (1) becomes,
Take log on both sides,
Substitute log values,
0.07918 = 4(t) (0.0080676)
= (t) (0.0322705)
= 2.45
t ≅ 2.5 years
Result:
2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.