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Evgen [1.6K]
2 years ago
7

The radioactive isotope 14C has a half-life of approximately 5715 years. A piece of ancient charcoal contains only 81% as much o

f the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal
Mathematics
1 answer:
NikAS [45]2 years ago
5 0

Answer:

1758 years

Step-by-step explanation:

0.693/t1/2 = 2.303/t log No/N

t1/2 = half life of the C-14

t= time taken

No= amount of radioactive material originally present

N= amount of isotope after time t.

But N= 0.81 No

0.693/5715= 2.303/t log No/0.81No

0.00012 = 0.211/t

t =0.211 /0.00012

t= 1758 years

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How many integers between 10 and 60, inclusive, can be evenly divided by neither 2 nor 3?
erastovalidia [21]
Find total number of integers.

a_1=10,a_n=60,d=1 \\a_n=a_1+(n-1)d \\60=10+(n-1)1 \\n-1=50 \\n=51

Find how many integers is divisible by 2.

a_1=10,a_n=60,d=2
\\a_n=a_1+(n-1)d
\\60=10+(n-1)2
\\2(n-1)=50
\\n-1=25
\\n=26

Eliminate even numbers.

11, 13, 15,..., 57, 59

This array contains 51 - 26 = 25 numbers.

Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.

15, 17, 19,..., 55, 57

This array contains 25 - 3 = 22 numbers.

Now we should eliminate numbers divisible by 3: 15, 21, 27...

a_1=15,a_n=57,d=6,n=?
\\a_n=a_1+(n-1)d
\\57=15+(n-1)6
\\6(n-1)=42
\\n-1=7
\\n=8

There are 8 such numbers.

Therefore, there are 25 - 8 = 17 numbers that <span>can be evenly divided by neither 2 nor 3</span>

6 0
3 years ago
James has just sold his motorbike for £1,890. He bought the motorbike for £2,700. What was his percentage loss? %
Usimov [2.4K]
£2.700 - £1890 = £810

<span>£ (money) -------------- percentage (%)
</span>2.700 -------------------- 100
810 ----------------------- x

2700*x = 810*100
2700x = 81000
x =  \frac{81000}{2700}
\boxed{x = 30}

Answer: 
Percentage loss = 30%
6 0
3 years ago
What is 3 x 10,000 + 4 x 1,000 + 6 x 100 + 8 x 10 + 8 written in standard form?
Talja [164]

Answer:

thirty four thousand six hundred and eighty eight

Step-by-step explanation:

4 0
3 years ago
An operational definition is used to ____ a hypothetical construct.
Alona [7]
An operational definition can both define and measure the hypothetical construct. The hypothetical construct is also called psychological construct is an explanatory variable which cannot be directly observed. It is also a tool to understand someone’s behavior. For example measuring you friend happiness.
8 0
3 years ago
Read 2 more answers
What is the value of x? Please show step by step.
3241004551 [841]
Start by using trig to find the length of the line LJ

The triangle KJL (big right angled triangle) has been given the following dimensions

Hypotenuse = 8 \sqrt{2}
The adjacent angle is 30 degrees

Since we have the hypotenuse and the  angle we must use the equation 
opposite = Sin(angle) x Hypotenuse

Opposite= sin30 x 8 \sqrt{2}

Opposite= 4 \sqrt{2}

Therefore line LJ is 4 \sqrt{2}


Now look at the smaller right angled triangle (LMJ) 

Hypotenuse is the line LJ which is 4 \sqrt{2}

The adjacent angle is 45

Since we have hypotenuse and angle we must use the equation opposite = sin(angle) * h

therefore 
x= 4 \sqrt{2} * sin45= 4


3 0
3 years ago
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