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3 years ago

5

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for

carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.

1 answer:

Rudik [331]3 years ago

8 0

A(t) = Ao*e^(-rt)

-rt = ln [ A(t)/ Ao]

t = - ln [ A(t)/ Ao] / r

r= 0.0124% = 0.0124/100 = 0.000124

A(t)/A0 = 10% = 10/100 = 0.1

Now substitute

t = - ln [0.1] / 0.000124 = 2.3025851 / 0.000124 = 18,569 years

Your result will depend on how you round ln(0.1).

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marta [7]

You can cross multiply
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3 years ago

What is <br><br> 3x+2y=-13<br> 3x+4y=1

Zepler [3.9K]

Answer:

The values are

x = -25/9 = -2 7/9

y = 7/3 = 2 1/3

Step-by-step explanation:

3x + 2y = -13 --------eqn 1

3x + 4y = 1-------------eqn2

Using eqn 2 to get the value of y

3x + 4y = 1

4y = 1 - 3x

Dividing both sides by 4,to get y

4y/4 =( 1 -3x) / 4

y = (1 - 3x) / 4

Since we've gotten the value for y, substitute the value into eqn 1

3x + 2y = -13

3x + 2(3x - 1)/4 = -13

Opening the bracket

3x + (6x - 2)/4 = -13

LCM = 4

(12x + 6x - 2) / 4 = -13

18x - 2 / 4 = -13

Then we cross multiply

18x - 2 = -13 * 4

18x - 2 = - 52

18x = -52 + 2

18x = -50

Divide both sides by 18, to get the value of x

18x/18 = -50/18

x = -25/9

or x = -2 7/9

The value of x is now known, so let's go back to eqn 2

Substitute x = - 25/9

3x + 4y = 1

3(-25/9) + 4y = 1

Open the bracket

-75/9 + 4y = 1

Make y the subject of the formula

4y = 1 + 75/9

LCM = 9

4y = (9 + 75)/ 9

4y = 84/9

To get y, divide both sides by 4

4y/4 = 84/9 / 4/1

y =

Note : when division changes to multiplication, it always be in its reciprocal form

y = 84/9 / 1/4

y = 84 * 1 / 9 *4

y = 84/ 36

y = 7/3

Or

y = 2 1/3

4 0

3 years ago

Write an equation of a ine in slope-intercept form that passes through a point (4,-6) and has a slope of -3.

Sindrei [870]

Answer:

y= -3x +6

Step-by-step explanation:

<u>slope-intercept form</u><u>:</u>

y=mx +c, where m is the slope and c is the y-intercept.

Given that the slope is -3, m= -3.

Susbt. m= -3 into the equation:

y= -3x +c

Since the line passes the point (4, -6),

(4, -6) lies on the line and must therefore satisfy the equation. Thus, susbt. (4, -6) into the equation to find the value of c.

y= -3x +c

when x=4, y= -6,

-6= -3(4) +c

-6= -12 +c

c= 12 -6

c= 6

Hence, the equation of the line is y= -3x +6.

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3 years ago

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of

iris [78.8K]

Answer:

The probability that the mean battery life would be greater than 533.2 minutes (in a sample of 75 batteries) is $\\ P(z>0.48) = P(x>533.2) = 0.3156$

Step-by-step explanation:

The main thing we have to take into account in this question is that we are about to find the probability of a <em>sample mean</em>. The distribution for <em>sample means</em> follows a <em>normal distribution</em> with mean $\\ \mu$ and standard deviation $\\ \frac{\sigma}{\sqrt{n}}$ . Mathematically

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

For values of the sample $\\ n \ge 30$ , no matter the distribution the data come from.

And the variable <em>z</em> follows a <em>standard normal distribution</em>, and, as we can remember, this distribution has a mean = 0 and a standard deviation = 1. Mathematically

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

That is

$\\ z \sim N(0, 1)$

We have a variance of 3364. That is, a <em>standard deviation</em> of

$\\ \sigma^2 = 3364; \sigma = \sqrt{3364} = 58$

The population mean is

$\\ \mu = 530$

The sample size is $\\ n = 75$

The sample mean is $\\ \overline{x} = 533.2$

With all this information, we can solve the question

The probability that the mean battery life would be greater than 533.2 minutes

Using equation [1]

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{533.2 - 530}{\frac{58}{\sqrt{75}}}$

$\\ z = \frac{3.2}{\frac{58}{8.66025}}$

$\\ z = \frac{3.2}{6.69726}$

$\\ z = 0.47780$

With this value of z we can consult a <em>cumulative standard normal table</em> (or use some statistic program) to find the cumulative probability for <em>z</em> (and remember that this variable follows a standard normal distribution).

Most standard normal tables have values for z for only two decimals, so we can round the previous value for z as z = 0.48.

Then

$\\ P(z$

However, in the question we are asked for $\\ P(z>0.48) = P(x>533.2)$ . As well as all normal distributions, the standard normal distribution is symmetrical around the mean, and we have

$\\ P(z>0.48) = 1 - P(z$

Thus

$\\ P(z>0.48) = 1 - 0.68439$

$\\ P(z>0.48) = 0.31561$

Rounding to four decimal places, we have

$\\ P(z>0.48) = 0.3156$

So, the probability that the mean battery life would be greater than 533.2 minutes is (in a sample of 75 batteries) $\\ P(z>0.48) = P(x>533.2) = 0.3156$ .

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3 years ago

X/-5+3=-2 <br> What is it step by step

son4ous [18]

Answer:

Step-by-step explanation:

X/-5+3=-2

Collecting like terms

x/-5 = -2 - 3

x/-5 = -5

Multiply each term by -5

-5(x/-5) = -5(-5)

x = 25

7 0

3 years ago