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salantis [7]
3 years ago
7

Donnie's dad is 3 times older than Donnie, and the sum of their ages is no less than 56. What is the youngest that Donnie can be

?
Mathematics
1 answer:
Gala2k [10]3 years ago
4 0

Answer:

14

Step-by-step explanation:

If Donnie is 3 times younger than Donnie's dad, that adds up to four parts. In other words, Donnie is 1/4 his dads age. So, divide 56 by four and you have Donnie's age. The rest is Donnie's dad age.

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he radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost
elena-s [515]

Answer:

The bones were 12,485 years old at the time they were​ discovered.

Step-by-step explanation:

Amount of the element:

The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:

A(t) = A(0)e^{-kt}

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The radioactive element​ carbon-14 has a​ half-life of 5750 years.

This means that A(5750) = 0.5A(0), and we use this to find k. So

A(t) = A(0)e^{-kt}

0.5A(0) = A(0)e^{-5750k}

e^{-5750k} = 0.5

\ln{e^{-5750k}} = \ln{0.5}

-5750k = \ln{0.5}

k = -\frac{\ln{0.5}}{5750}

k = 0.00012054733

So

A(t) = A(0)e^{-0.00012054733t}

A scientist determined that the bones from a mastodon had lost 77.8 ​% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Had 100 - 77.8 = 22.2% remaining, so this is t for which:

A(t) = 0.222A(0)

Then

0.222A(0) = A(0)e^{-0.00012054733t}

e^{-0.00012054733t} = 0.222

\ln{e^{-0.00012054733t}} = \ln{0.222}

-0.00012054733t = \ln{0.222}

t = -\frac{\ln{0.222}}{0.00012054733}

t = 12485

The bones were 12,485 years old at the time they were​ discovered.

8 0
3 years ago
HELP ASAP ALL THREE PLEASE 1. if a cyclic alkene has 12 carbon atoms, how many hydrogen atoms does it have 2.if a cyclic alkene
Marina CMI [18]

Answer:

1. 24

2. 6

3. No

Step-by-step explanation:

The formula for cyclic alkene is C^{n} H^{2n}, so if it has 12 carbon atoms, it will have double the amount of hydrogen atoms, therefore, 24 hydrogen atoms.

The same works in reverse. If we have 12 hydrogen atoms in this, then there will be half the amount of carbon atoms, therefore 6.

Since the relationship between Carbon and Hydrogen here is double and half, odd numbers can't be divided by 2 and end up with a whole number, so an odd number of hydrogen atoms is not possible.

Hope this helped!

5 0
3 years ago
Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x =
lord [1]
Using washers, the volume is given by

\displaystyle\pi\int_{x=1}^{x=e}((1+3)^2-(\ln x+3)^2)\,\mathrm dx
=\displaystyle\pi\int_{x=1}^{x=e}(7-6\ln x-(\ln x)^2)\,\mathrm dx
5 0
3 years ago
A pipe is leaking and 1.5 cups per day about how many gallons per week is the pipe leaking
MatroZZZ [7]
The question asks per week. So 1.5 cups times 7 days is 10.5 cups. 

<span>The pipe leaks </span>10.5 cups<span> every week.</span>
7 0
3 years ago
Read 2 more answers
Which equation matches the graph?
DIA [1.3K]

Answer:

y=3x-2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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