At a track meet, Jacob and Daniel compete in 220 m hurdles.
Daniels finishes in of the a min.
Jacob finishes with of a min remaining.
Question:
Who ran the race in faster time?
The Process:
Let us see the denominators. The least common multiple (LCM) of 4 and 12 is 12.
Let us draw the diagram that represents a minute.
12 units represent in one minute.
Daniels finishes in of the a min.
or 9 of 12 units.
Jacob finishes with of a min remaining, or 5 of 12 units. This means Jacob finishes in or 7 of 12 units, that is
And now we conclude who ran the race in a faster time.
Daniels:
Jacobs:
Because Jacob took the race in a shorter time, he was who ran the race in a faster time.
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Quick Steps
Daniels: in of the a min.
Jacob: in of the a min.
Jacob's time is shorter, so he's the fastest.
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Calculate the speed
Recall
Daniels:
Jacob:
Thus, Jacob's speed proved greater than Daniels's speed.
Answer:
43/13 or 1.0769 = 1
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
1/4 ÷ 2
~Turn 2 into a fraction
1/4 ÷ 2/1
~Copy dot flip
1/4 * 1/2
~Multiply
1/8
Best of Luck!
Answer:
We want to find two irrational numbers between 0.8275496 and 0.84218972
The easier way to solve this is to remember that the product between an irrational number and a rational number (different than zero) is irrational. Then:
Now, remember that the square root of a prime number is always irrational, so we can start working with that.
√5 = 2.236......
As our two rational numbers are 0.8275496 and 0.84218972, any irrational number such that the first two digits after the decimal point are 0.83 will be between these, then we can do the calculations with rational numbers:
2.236 and 0.83
2.236*A = 0.83....
Where A is a rational number:
A = 0.83/2.236 = 0.371
Now we know that 0.371 is a rational number, then:
0.371*√5 will be an irrational number, and:
0.371*√5 = 0.82958....
then 0.371*√5 is an irrational number between 0.8275496 and 0.84218972
Now let's find other, this time using √2.
√2 = 1.414....
1.414*A = 0.83
A = 0.83/1.414 = 0.587
Then:
0.587*√2 will be an irrational number, and:
0.587*√2 = 0.830143...
So 0.587*√2 is an irrational number between 0.8275496 and 0.84218972