1 1/4 miles in 2 min and 4 seconds, or 1 3/16 miles in 1 min and 55 sec. Which is greater?
$1.60 for 5 min or $19.50 for 1 hour. Which is greater?
Look for a pattern in the expressions shown below. Use the pattern to write an expression for the sum of the whole numbers from 1 to n. then find the sum of the whole numbers from 1 to 50.
1+2=2•3/2. 1+2+3=3•4/2. 1+2+3+4=4•5/2.
1.25 / 124 = 0.0100806 miles/second
1.1875 / 115 = 0.010326 miles per second
The first is faster.
1.6/5 = $0.32 per minute
19.50/60 = 0.325 per minute
To determine which distance is greater, we need to compare the fractions as decimals.
For 1 1/4 miles in 2 minutes and 4 seconds, we can convert the time to decimal form. There are 60 seconds in a minute, so 2 minutes and 4 seconds is equivalent to 2 + 4/60 = 2.07 minutes. Now, we can find the speed:
Distance = 1 1/4 miles = 1.25 miles
Time = 2.07 minutes
Speed = Distance / Time = 1.25 miles / 2.07 minutes = 0.6039 miles/minute
For 1 3/16 miles in 1 minute and 55 seconds, we can convert the time to decimal form as well. 1 minute and 55 seconds is equivalent to 1 + 55/60 = 1.92 minutes. Now, we can find the speed:
Distance = 1 3/16 miles = 1.1875 miles
Time = 1.92 minutes
Speed = Distance / Time = 1.1875 miles / 1.92 minutes = 0.6182 miles/minute
Comparing the speeds, we can see that 0.6182 miles/minute is greater than 0.6039 miles/minute. Therefore, the distance of 1 3/16 miles in 1 minute and 55 seconds is greater than 1 1/4 miles in 2 minutes and 4 seconds.
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To determine which value is greater between $1.60 for 5 minutes and $19.50 for 1 hour, we need to calculate the rate of pay per minute for each scenario.
For $1.60 in 5 minutes, we can find the rate of pay per minute:
Amount of money = $1.60
Time = 5 minutes
Rate of pay per minute = Amount of money / Time = $1.60 / 5 minutes = $0.32/minute
For $19.50 in 1 hour, we need to convert the time to minutes. There are 60 minutes in 1 hour, so:
Amount of money = $19.50
Time = 1 hour = 60 minutes
Rate of pay per minute = Amount of money / Time = $19.50 / 60 minutes = $0.325/minute
Comparing the rates of pay per minute, we can see that $0.325/minute is greater than $0.32/minute. Therefore, $19.50 for 1 hour has a higher pay rate than $1.60 for 5 minutes.
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To find a pattern and write an expression for the sum of whole numbers from 1 to n, let's observe the given expressions:
1 + 2 = 2 * (3 / 2)
1 + 2 + 3 = 3 * (4 / 2)
1 + 2 + 3 + 4 = 4 * (5 / 2)
From these examples, we can see that the sum of the whole numbers from 1 to n can be written as n multiplied by (n + 1) divided by 2.
So, the expression for the sum of the whole numbers from 1 to n is (n * (n + 1)) / 2.
To find the sum of the whole numbers from 1 to 50, substitute n = 50 into the expression:
Sum = (50 * (50 + 1)) / 2
Sum = (50 * 51) / 2
Sum = 2550 / 2
Sum = 1275
Therefore, the sum of the whole numbers from 1 to 50 is 1275.
To compare the first two distances, we need to convert them to a common unit. Let's convert both distances to miles.
1 1/4 miles = 1.25 miles
2 minutes and 4 seconds = 2 + (4/60) minutes = 2.067 minutes
1 3/16 miles = 1.1875 miles
1 minute and 55 seconds = 1 + (55/60) minutes = 1.917 minutes
Now we can compare the distances:
1.25 miles > 1.1875 miles
Therefore, 1 1/4 miles in 2 min and 4 seconds is greater than 1 3/16 miles in 1 min and 55 sec.
Moving on to the second question, let's compare the two rates:
$1.60 for 5 minutes means the rate is $1.60/5 minutes = $0.32 per minute.
$19.50 for 1 hour means the rate is $19.50/60 minutes = $0.325 per minute.
Therefore, $19.50 for 1 hour has a greater rate than $1.60 for 5 minutes.
For the third question, we observe a pattern in the expressions:
1 + 2 = 2 * (3/2)
1 + 2 + 3 = 3 * (4/2)
1 + 2 + 3 + 4 = 4 * (5/2)
From these patterns, we can deduce that the sum of the whole numbers from 1 to n is n * (n+1) / 2.
To find the sum of the whole numbers from 1 to 50, substitute n = 50 into the expression:
Sum = 50 * (50+1) / 2 = 25 * 51 = 1275.
Therefore, the sum of the whole numbers from 1 to 50 is 1275.