Answer: False, there are actually 900 different three-digit numbers
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Explanation:
The three digit numbers span from 100 to 999, including both endpoints.
This means we have 999-100+1 = 900 different three-digit numbers.
You subtract the endpoints (large-small) and add 1 to include the lower endpoint.
Here's a smaller example of why this works: say you had the set {1,2,3,4} and we wanted to count the number of items in this set. Clearly there are 4 items. Note how subtracting the endpoints 4-1 gets us 3 instead, so we add on 1 to include that left endpoint.
The angles are supplementary, therefore totaling them at 180°.
And because I'm bored, I'll solve for x for you!
(x + 25) + (9x + 10) = 180
10x + 35 = 180
Subtract 35 from both sides.
10x = 145
Divide by 10 on both sides.
x = 14.5
<u>Answer-</u>
<em>After 76 swings</em><em> the angle through which it swings less than 1°</em>
<u>Solution-</u>
From the question,
Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.
So the angle of the second swing = 
Then the angle of third swing = 
So, this follows a Geometric Progression.
a = The initial term = 30
r = Common ratio = 
As we have to find the number swings when the angle swept by the pendulum is less than 1°.
So we have the nth number is the series as 1, applying the formula
Putting the values,
Taking logarithm of both sides,
Therefore, after 76 swings the angle through which it swings less than 1°
Answer:
124.8
Step-by-step explanation:
52 divided by 5 = 10.4
then, multiply by 12 = 124.8
If it takes 125 gallons to go 5034 miles, then to find how far 1 gallon goes, we divide 5034/125=40.272 miles. Therefore your answer is 40.272miles a gallon
