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Answer:
Below are explanations!
Step-by-step explanation:
6) 5^4/5^2 means the ^4 and ^2 needs to subtract from the 5s. This results in 5^2, which equals 25.
7) The 9 as the denominator will cross with the first nine above. This leaves as follows: 9^3 x 9^2 x 9^6 (I don't know if it is a 6 or 0). You may solve from there. Just add all the exponents up.
8)^-6 will be multiplied by ^6, which is ^-36. Therefore, the answer is 5^-36.
The other questions, please, remember to read carefully.
The value that remains under the radical is 2
<h3>How to determine the value under the radical?</h3>
The correct expression in the question is:
1250^4
This can be rewritten as:
![\sqrt[4]{1250}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B1250%7D)
Express 1250 as product
![\sqrt[4]{(2 * 5^4)}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%282%20%2A%205%5E4%29%7D)
Expand the expression
![\sqrt[4]{2} * \sqrt[4]{5^4}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%7D%20%2A%20%5Csqrt%5B4%5D%7B5%5E4%7D)
Simplify
![\sqrt[4]{2} * 5](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%7D%20%2A%205)
Evaluate the product
![5\sqrt[4]{2}](https://tex.z-dn.net/?f=5%5Csqrt%5B4%5D%7B2%7D)
Hence, the value that remains under the radical is 2
Read more about radical expressions at:
brainly.com/question/3008670
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Answer:
$98,048.77
Step-by-step explanation:
First you want to find out how much he has put in without interest so you would do 237.95*12 to figure out how much he puts in per year then times that number by 30 to figure out how much he has put in in total, after this you subtract this total from the 183,710.77 to get the total amount of interest
Answer:
There are at least two runners whose times are less than 9 seconds apart.
Step-by-step explanation:
Let's assume that Tₙ is the time of the n-th runner, we know that:
6 min < Tₙ < 7 min
knowing that:
1 min = 60 s
We can rewrite this as:
6*60 s < Tₙ < 7*60 s
360 s < Tₙ < 420 s
We know that there are 7 runners, and we want to see if we can conclude that there are two runners whose times are less than nine seconds.
So, the smallest time allowed in seconds is 361 seconds (the first value larger than 360 seg) while the largest time allowed is 419 seconds (the largest time allowed smallest than 420 seconds).
Now, let's assume that the first runner has the smallest time:
then:
T₁ = 361 s
Now let's add 9 seconds to the time of each runner (here we want to check that we can have all the runners with exactly 9 seconds apart in their times, so we will prove that the statement is false), then:
T₂ = 361s + 9s = 370s
T₃ = 370s + 9s = 379s
T₄ = 379s + 9s = 388s
T₄ = 388s + 9s = 397s
T₅ = 397s + 9s = 406s
T₆ = 406s + 9s = 415s
T₇ = 415s + 9s = 424s
But 424s > 420s
So this is not allowed (as the maximum time allowed was 419 s), so at least two of the runners must have times that are less than 9 seconds apart.
Then; Can you conclude that there are two runners whose times are less than nine seconds apart? Yes.