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2 years ago

A 9-yard roll of white paper costs $1.98. What is the unit price?

Mathematics

1 answer:

lozanna [386]2 years ago

4 0

Answer:

$0.22

Step-by-step explanation:

divide $1.98 by 9 to get the unit price

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Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isot

Andrews [41]

Answer:

The approximate difference in the half-lives of the isotopes is 66 days.

Step-by-step explanation:

The decay of an isotope is represented by the following differential equation:

$\frac{dm}{dt} = -\frac{t}{\tau}$

Where:

$m$ - Current mass of the isotope, measured in kilograms.

$t$ - Time, measured in days.

$\tau$ - Time constant, measured in days.

The solution of the differential equation is:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$

Where $m_{o}$ is the initial mass of the isotope, measure in kilograms.

Now, the time constant is cleared:

$\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}$

$\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }$

The half-life of a isotope ( $t_{1/2}$ ) as a function of time constant is:

$t_{1/2} = \tau \cdot \ln2$

$t_{1/2} = -\left(\frac{t}{\ln\frac{m(t)}{m_{o}} }\right) \cdot \ln 2$

The half-life difference between isotope B and isotope A is:

$\Delta t_{1/2} = \left| -\left(\frac{t_{A}}{\ln \frac{m_{A}(t)}{m_{o,A}} } \right)\cdot \ln 2+\left(\frac{t_{B}}{\ln \frac{m_{B}(t)}{m_{o,B}} } \right)\cdot \ln 2\right|$

If $\frac{m_{A}(t)}{m_{o,A}} = \frac{m_{B}(t)}{m_{o,B}} = 0.9$ , $t_{A} = 33\,days$ and $t_{B} = 43\,days$ , the difference in the half-lives of the isotopes is:

$\Delta t_{1/2} = \left|-\left(\frac{33\,days}{\ln 0.90} \right)\cdot \ln 2 + \left(\frac{43\,days}{\ln 0.90} \right)\cdot \ln 2\right|$

$\Delta t_{1/2} \approx 65.788\,days$

The approximate difference in the half-lives of the isotopes is 66 days.

4 0

3 years ago

Read 2 more answers

It is 42 1/2 miles from Eaton to Baxter and 37 4/5 miles from Baxter to Wellington. How far is it from Eaton to Wellington if yo

mina [271]

All you need to do is add the miles from Eaton to Baxter and from Baxter to Wellington to get your answer...

42 + 37 = 79

Now we need to add the fractions

$\frac{1}{2} + \frac{4}{5} = ...
$

To add we need a common denominator.
2 and 5 can both go into 10, so that will be a our common denominator.
Now you have...
$\frac{5}{10} + \frac{8}{10} = \frac{14}{10}$
which is equal to $1 \frac{2}{5}$
add that to the 79 we got earlier ...

The toal and final answer is $80 \frac{2}{5}$ miles !
Hope I helped and remember to vote this as the brainliest answer ! :)

5 0

3 years ago

What is the perimeter of the square?

kolezko [41]

Answer:

D.68ft

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Which of the given expressions results in 0 when evaluated at x = 5? A. 5x(x − 7) B. (x − 8)(x − 5) C. (x + 7)(x − 2) D. (x + 5)

SSSSS [86.1K]

Answer:

B. (x - 8)(x - 5)

Step-by-step explanation:

If you plugged in x = 5 into the 2nd equation, you would see that you would be multiplying by 0, which would turn everything zero.

3 0

3 years ago

Read 2 more answers

What is a equivalent rational number to 1.28 repeating?

goblinko [34]

<span>the line over the 28 means the 28 repeats forever. 1.282828.... and so on let x be the rational number 1.28... we can use this trick: 100*1.282828....= 128.282828... (the decimal 28 part repeats) 100x = 128.28... next: 100x - x = 128.282828... - 1.282828... the .282828... part will be subtracted away 99x = 127 divide both sides by 99 to get x= 127/99</span>

3 0

2 years ago