30 POINTS why are 3/4 and 6/8 equivalent

1 answer:

3 0

Step-by-step explanation: In order to decide whether the given fractions are equivalent, first write each fraction in lowest terms. Remember, a fraction is written in lowest terms if the greatest common factor of the numerator and the denominator is 1.

For our first fraction which is 3/4, the greatest common factor of 3 and 4 is 1, the fraction is already in lowest terms.

For our second fraction however, since the greatest common factor of 6 and 8 is 2, we must divide both the numerator and denominator by 2 which gives us 3/4.

3/4 = 3/4 which means these fractions are equivalent.

3/4 and 6/8 are equivalent because if you reduce 6/8 in lowest terms, you end up with the fraction 3/4.

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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

krok68 [10]

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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2 years ago

Mr. Rodriguez has only $62.50 to spend at a clothing store. He wants to buy a shirt that costs $35, including tax and some brace

BARSIC [14]

Answer:

5 bracelets

Step-by-step explanation:

Part A

35 + 5.50x = 62.50

Part B

5.50x = 62.50 - 35
5.50x = 27.50
x = 27.50/5.50
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Step-by-step explanation: i love your pfp

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2 years ago

Solve for k <br> 7k+2m = kr + 4m + 3

professor190 [17]

Answer:

$\large\boxed{k=\dfrac{2m+3}{7-r}\ \text{for}\ r\neq7}$

Step-by-step explanation:

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