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vovangra [49]
3 years ago
13

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass

. Starting with 220 grams of a radioactive isotope, how much will be left after 3 half-lives?
Mathematics
1 answer:
Sauron [17]3 years ago
6 0

Answer:

Quantity remaining= 27.5 grams

Step-by-step explanation:

If the initial quantity of the radioactive isotope= 220 grams

And for each half life it will reduce to half of its original quantity

For first half life

Quantity= 220/2

Quantity= 110 grams

Now for the second half life , the quantity to work with will be 110 grams

Second half life

Quantity= 110/2

Quantity= 55 grams

For the third half life , the quantity to work with is 55 grams

Third half life

Quantity= 55/2

Quantity= 27.5 grams

So after 3 half life's of this radioactive isotope, the amount remaining out of 220 = 27.5 grams.

Another simple way to do this

Since half life reduce the isotope by half of its original.

The third half life will reduce it by (1/2)^3= 1/8

So the quantity remaining= 1/8*220

Quantity remaining= 27.5 grams

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sladkih [1.3K]

Answer:

  18 terms

Step-by-step explanation:

The first given sequence has first term a1=2 and common difference d=5. Its explicit formula is ...

  an = 2 +5(n -1) = 5n -3

We want the n-th term of this sequence to be the same as the n-th term of the sequence defined by ...

  an = 4n +15

We can find n that makes this true by setting the 'an' values equal:

  an = an

  5n -3 = 4n +15

  n = 18 . . . . . . . . . . add 3-4n

The number of terms in each sequence is 18.

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<em>Additional comment</em>

The last term in each sequence is 87.

7 0
2 years ago
Dream borrowed $500 at an interest rate of 8%. At the end of the loan period, she had to pay back $530. How long was the loan fo
Aliun [14]

Answer:

The loan was for 9 months only

Step-by-step explanation:

In this question, we are concerned with calculating the time taken for a loan om an interest to be paid back

To calculate this, we use the simple interest formula

Mathematically;

I = PRT/100

where P is the principal which is the amount borrowed and that is $500 according to the question

R is the rate which is 8% according to the question

Interest can be calculated by subtracting the principal from the  amount paid back = 530-500 = 30$

We now plug these values into the equation

30 = (500 × 8× T)/100

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5 0
3 years ago
The system of equations is graphed on the coordinate plane.
ehidna [41]

Answer: The solution is (3, -2)

This means that x = 3 and y = -2 pair up together.

=====================================================

Explanation:

The solution is where the two lines cross. Note if we started at the origin (0,0) and moved to the right 3 units, and then down 2 units, we would arrive at the location (3, -2).

-----------------

As a way to check, we can plug x = 3 into each equation. We should get y = -2 as a result for each equation

y = (-5/3)x + 3

y = (-5/3)*3 + 3

y = -5+3

y = -2

The first equation is confirmed. Let's check the second equation

y = (1/3)x - 3

y = (1/3)*3 - 3

y = 1 - 3

y = -2

Both equations have the y value equal -2 when x = 3. Therefore, the overall solution is confirmed.

3 0
2 years ago
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Anna35 [415]

Answer:

4 3/4 yards

Step-by-step explanation:

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4 0
2 years ago
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Which graph shows the equation v=4+2t
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You need to give options for future reference
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