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steposvetlana [31]
3 years ago
13

What’s the domain and range for (2,4) (5,3) (-1,-4) (0,9) (-3,1)

Mathematics
1 answer:
Citrus2011 [14]3 years ago
3 0

Step-by-step explanation: In this problem, we're asked to state the domain and range for the following relation.

First of all, a relation is just a set of ordered pairs like you see in this problem. The domain is the set of all x-coordinates for those ordered pairs. So in this case the domain or D is {2, 5, -1, 0, -3}.

The range is the set of all y-coordinates for those ordered pairs. So in this case our range or R is {4, 3, -4, 9, 1}.

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25% of data is in quartile 1
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Using the following image, find GH given HI = 1 and GI =<br> = 9.
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8

Step-by-step explanation:

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Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li
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Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years

First, let us calculate the decay constant (k)

75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036

Next, let us calculate the half-life as follows:

\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2}  \approx 669\ years

Therefore the half-life is between 600 and 700 years

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Hey how are you, also can you please give me brainlest. I only need 2 more to level up.
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