How much would 500$ invested at 9% interest compounded annually be worth after 4 years?
1 answer:
Answer:
$705.79
Step-by-step explanation:
(see attached for reference)
the formula for compound interest is
A = P [1 + (r/n) ]^(nt)
Where:
P = Principal Amount = $500
r = annual interest rate = 9% = 0.09
t = 4 years
n = 1 (compounded annually)
A = 500 [1 + (0.09/1) ]^(1 x 4)
A = 500 [1 + 0.09 ]^(4)
A = 500 [1.09 ]^(4)
A = $705.79
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Answer: The time at which the distance between the two is 150 miles is 1.3 hr.
Step-by-step explanation:
Step 1: Sketch the problem as shown in the attached image.
The problem can be solved using Pythagoras theorem since the sketch is a right angled triangle.
It follows the equation x² + y² = 15².
The distance covered by Greg is given by <em>x mi</em>, and that of Erin is given by <em>y mi</em>.
Step 2: To derive the distance covered by Erin and Greg, we use the formula <em>Speed = distance ÷ time.</em>
Which by cross-multiplying gives <em>distance = speed × time</em>.
Let time taken to cover the distance be <em>t h</em>.
Given that Speed of Erin is 9 mph and that of Greg is 7 mph.
Hence, distance covered by Greg, x = 7 × t = 7t.
Distance covered by Erin, y = 9 × t = 9t.
Step 3: Insert the terms x and y into the Pythagoras equation x² + y² = 15² and solve for <em>time t.</em>
(7t)² + (9t)² = 15²
49t² + 81t² = 225
(49 + 81)t² = 225
t² = 225/(49 + 81)
t² = 225/130
t² = 1.730769231
t = √1.730769231
t = 1.315587029
t = 1.3hr
Hence the time at which the distance between the two is 150 miles is 1.3 hr.
Answer:
The sample size is
Step-by-step explanation:
From the question we are told that
The margin of error is E =4.266
The standard deviation is
From the question we are told the confidence level is 99% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the sample size is mathematically represented as
=>
=>