Here is the answer for the 1st one. I have a picture of the second one but I’m not sure if I can post the picture of it
Given
investment = $1200
earned in interest = $ 66
Time = one year
Find out the interest rate .
To proof
FORMULA
here
Principle =$ 1200
Simple interest =$66
Time = 1 year
put these value in the above formula
we get
Rate = 5.5 %
The interest rate is 5.5 %
Hence proved
The 100th term of the sequence is 2130.
<h3>How to calculate the value?</h3>
a3 = a + 2d = 93
a5 = a + 4d = 135
Compute both equations
(4d - 2d) = (135 - 93)
2d = 42
d = 42/2 = 21
a + 2d = 93
a + 2(21) = 93
a + 42 = 93
a = 94 - 42 = 51
100th term will be:
= a + 99d
= 51 + 99(21)
= 51 + 2079
= 2130
Learn more about sequence on:
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Answer:
<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>
Step-by-step explanation:
1. Let's review all the information provided for solving this question:
Eastbound train speed = x
Westbound train speed = x + 3 miles per hour (The speed of the westbound train is 3mph greater than the speed of the eastbound train)
Duration of trip = 3 hours
Distance between trains after 3 hours = 468 miles
2. Let's find the speed of each train, using the following equation:
3x + 3(x + 3) = 468
3x + 3x + 9 = 468
6x + 9 = 468
6x = 468 - 9 (Subtracting 9 at both sides)
6x = 459
x = 459/6 (Dividing by 6 at both sides)
x = 76.5 miles per hour
<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>
3. Proof that x = 76.5 is correct
3x + 3(x + 3) = 468
3 (76.5) + 3 (76.5 + 3) = 468
229.5 + 238.5 = 468
<u>468 = 468</u>
<u>The value of x = 76. 5 is correct. And now we know that the Eastbound train has traveled 229.5 miles since the departure from Cleveland and the Westbound train 238.5 miles.</u>