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2 years ago

Question 5/Multiple Choice Worth 4 points)

Mathematics

1 answer:

Nonamiya [84]2 years ago

7 0

Answer:

690

Step-by-step explanation:

12 boxes, each of them have 36 so you multiply 12 by 36. There's another 258 cookies so you add those on as well and you should get 690.

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Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14

PilotLPTM [1.2K]

Answer:

<em>Carbon-14 will take 19,035 years to decay to 10 percent.</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

$N(t)=N_{0}e^{-\lambda t}$

Where:

No = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

$\lambda$ = The decay constant.

One important parameter related to radioactive decay is the half-life:

$\displaystyle t_{1/2}=\frac {\ln(2)}{\lambda }$

If we know the value of the half-life, we can calculate the decay constant:

$\displaystyle \lambda=\frac {\ln(2)}{ t_{1/2}}$

Carbon-14 has a half-life of 5,730 years, thus:

$\displaystyle \lambda=\frac {\ln(2)}{ 5,730}$

$\lambda=0.00012097$

The equation of the remaining quantity of Carbon-14 is:

$N(t)=N_{0}e^{-0.00012097\cdot t}$

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

$0.10N_o=N_{0}e^{-0.00012097\cdot t}$

Simplifying:

$0.10=e^{-0.00012097\cdot t}$

Taking logarithms:

$ln 0.10=-0.00012097\cdot t$

Solving for t:

$\displaystyle t=\frac{log 0.10}{-0.00012097}$

$t\approx 19,035\ years$

Carbon-14 will take 19,035 years to decay to 10 percent.

6 0

3 years ago

Read 2 more answers

What's a rational number between 7.7 and 7.9?

svet-max [94.6K]

A rational number is a number that can be expressed as the relationship between two integers. Fractions and decimals will either repeat or end. An example is 5. Maybe 7. 53573 is an example as well. So is 5/1, because 5 and 1 are both integers. so is 7.5, because 7 and 5 are both integers, and it ends (the numbers after the decimal doesn't keep going). Your answer is 7.8, because it ends.

6 0

3 years ago

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Im not sure how to do this or what function to use SIN, COS, or TAN but if you could walk me through it that would be so so so a

Elanso [62]

Answer: 3.8

Step-by-step explanation:first, you need to figure out what side you’re looking for. Side AC is opposite of the angle you’re given. They also give you length of side AB which is 4. That is the hypotenuse (side directly across from right angle). So, you have the hypotenuse, and need the find the opposite side measure. Which option uses opposite and hypotenuse? That’s Sin. So, you would do: sin70 = ? / 4.

sin (of given angle)= opposite / hypotenuse.

Sin (70 degrees) = ? / 4

Then you solve for “?”

Type sin70 into your calculator, then multiply both sides by 4 to get “?” by itself. You should get 3.758770483, which rounds to 3.8

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3 years ago

Matt have 2 cookies, while christine have 2 more than matt how many cookies will they have if the add them altogethe?.

mojhsa [17]

Answer:

6 cookies

____________________

Christine has 2 MORE than Matt.

2 + 2 = 4(Christine)

4 + 2 = 6(total)

5 0

3 years ago

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A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the

Andre45 [30]

Answer:

Option: B

There are three times as many participants in the 40-59 age group than in the 0-19 age group.

Step-by-step explanation:

From the histogram we have following observations:

Number of people in the age group 0-19= 20

Number of people in the age group 20-39=40

Number of people in the age group 40-59=60

Number of people in the age group 60-79=50

Hence, from the data we could say that there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).

Hence, option B is correct.

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4 years ago

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