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3 years ago

I NEED HELP WITH BOTH THESE QUESTIONS ASAP

Mathematics

1 answer:

GenaCL600 [577]3 years ago

3 0

None of the above:

Mean
10+29+15+29+35+2 = 120
120/6 = 20 is the mean

120+27 = 147
147/7 = 21 is the new mean

So mean increases by 1

Median
2 10 15 29 29 35
Write the numbers in order and find the middle number, there is no middle number

2 10 15 27 29 29 35
27 is the middle number

Mode
2 10 15 29 29 35
The repeated numbers are 29

2 10 15 27 29 29 35
The repeated number, your mode is 29

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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

For the following exercises, determine whether each of the following relations is a function.

irina1246 [14]

Answer:

The relation y=2x+8 is a function because the two different output values of the function have the one unique input value.

Step-by-step explanation:

The given relation is y=2x+8.

It is required to determine the relation is a function.

This solution can be obtained by using the concept of function. First write the given relation y=2x+8 and determine whether the given relation is a function.

Step 1 of 1

The given relation is y=2x+8.

This relation shows that the two different output values of the function have one unique input value and this relation is a linear function.

Hence, the relation is a function.

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2 years ago

Matt has 20 marbles in a bag. 15 are red, 2 are blue, and 3 are green. What is the probability that Matt will pick a red marble

aliina [53]

Answer:

75%

Step-by-step explanation:

there is a 75% chance of getting a red marble as there is 15/20 marbles that are red