If 12 gallons cost $36. How much would 8 gallons cost?

Mathematics

2 answers:

Alex17521 [72]2 years ago

7 0

Answer:

$24

Step-by-step explanation:

12 x 3 = 36

8 x 3 = 24

Taya2010 [7]2 years ago

3 0

Use proportional math. 12 is to $36 as 8 is to ___. Or 12/36 is to 8/X.
36 x 8 = 288 divided by 8 = 24

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Solve 4x^2 - 36x + 32 = 0<br><br>Sorry! It's suppose to be + 32.<br>Please show all work.

mylen [45]

Answer:

x=1, x=8

Step-by-step explanation:

4x2−36x+32=0

Step 1: Factor left side of equation.

4(x−1)(x−8)=0

Step 2: Set factors equal to 0.

x−1=0 or x−8=0

(+1) (+8)

x=1 or x=8

6 0

3 years ago

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:

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