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Grace [21]
3 years ago
5

Element X decays radioactively with a half life of 13 minutes. If there are 530 grams of Element X, how long, to the nearest ten

th of a minute, would it take the element to decay to 11 grams? y = a * (.5) ^ (1/7)
Mathematics
1 answer:
Leona [35]3 years ago
6 0

Answer:

t \approx 50.4\,min

Step-by-step explanation:

The time constant of the element X is:

\tau = \frac{13\,min}{\ln 2}

\tau = 18.755\,min

The decay function has the following form:

\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }

t = -\tau \cdot \ln \frac{m}{m_{o}}

t = -(13\,min)\cdot \ln \left(\frac{11\,g}{530\,g} \right)

t \approx 50.4\,min

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andrew-mc [135]
4n² - 15n + 14<span> is always the product of two numbers, for it to be prime number, one of these factors must be either 1 or -1.

Case n - 2 = 1
That would be n = 3
Then </span>4n² - 15n + 14<span> = 5 , which is prime.

Case n - 2 = -1
That would be n = 1
Then </span>4n<span>² - 15n + 14 = 3, which is also prime.

Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime

Case 4n-7 = -1
That would be n = 3/2 which is not integer, so </span>4n<span>² - 15n + 14 will not be interger.

For any other n values, </span>4n<span>² - 15n + 14 will be composite number since it is product of two factors.

Therefore we are left with n = 1 and n = 3; only two values of n.</span>
5 0
2 years ago
Solve for x.<br> Your answer must be simplified.<br><br> x+5≤−4
iren2701 [21]

Answer:

x ≤ -9

Step-by-step explanation:

to solve this equation you must subtract 5 from both sides

you get

x ≤ -9

that is your answer

4 0
2 years ago
Read 2 more answers
What is the leading coefficient in the quadratic below?<br> h(x)=-2x2+5x+10
Mars2501 [29]

Answer:

-2

Step-by-step explanation:

The leading coefficient in a polynomial is the coefficient that corresponds with the highest degree term. In this case, -2 is the leading coefficient since its term has x² as the highest degree of the quadratic.

5 0
2 years ago
Aaron has a triathlon. Sunday he bikes 12 5/8 miles and swims 5 2/3 miles. Monday, he runs 6 3/8 miles. How many total miles Aar
Alla [95]
Let’s put these into one fraction each:

Biking:
= (12*5)/8 miles
= 60/8 miles
This can be reduced to,
= 15/2 miles

Swimming:
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Running:
= (6*3)/8 miles
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This can be reduced to,
= 9/4

Now we add all the distances up:
= (15/2) + (10/3) + (9/4)

Now we just can add the numerators and the denominators. We must find the lowest common factor (LCF) for our 3 denominators (2,3,4). Our LCF turns out to be 12. *Remember what we do to the denominator we must do to the numerator. So:
= (15/2) + (10/3) + (9/4)
= [(15*6)/12] + [(10*4)/12] + [(9*3)/12]
= (90/12) + (40/12) + (27/12)
= (157/12)
Therefore Aaron Ran 157/12 miles or 13.08 miles.

Hope this helps!
4 0
3 years ago
How do you find the sum of 5 and 8
Solnce55 [7]

Answer:26

Step-by-step explanation:

8 0
3 years ago
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