(1 point) Carbon dating is often used to determine the age of a fossil. For example, a humanoid skull was found in a cave in South Africa along with the remains of a campfire. Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire. Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

Answers

Answer 1

Answer:

The estimated age of the skull is 39118 years.

Step-by-step explanation:

The amount of the substance after t years is given by:

[tex]A(t) = A(0)(1-r)^t[/tex]

In which A(0) is the initial amount, and r is the decay rate.

The half-life of carbon-14 is about 5600 years.

This means that [tex]A(5600) = 0.5A(0)[/tex]. We use this to find r, or 1 - r, to replace in the equation. So

[tex]A(t) = A(0)(1-r)^t[/tex]

[tex]0.5A(0) = A(0)(1-r)^{5600}[/tex]

[tex](1-r)^{5600} = 0.5[/tex]

[tex]\sqrt[5600]{(1-r)^{5600}} = \sqrt[5600]{0.5}[/tex]

[tex]1 - r = (0.5)^{\frac{1}{5600}}[/tex]

[tex]1 - r = 0.9999[/tex]

So

[tex]A(t) = A(0)(0.9999)^t[/tex]

Only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire.

This is t for which [tex]A(t) = 0.02A(0)[/tex]. So

[tex]A(t) = A(0)(0.9999)^t[/tex]

[tex]0.02A(0) = A(0)(0.9999)^t[/tex]

[tex](0.9999)^t = 0.02[/tex]

[tex]\log{(0.9999)^t} = \log{0.02}[/tex]

[tex]t\log{0.9999} = \log{0.02}[/tex]

[tex]t = \frac{\log{0.02}}{\log{0.9999}}[/tex]

[tex]t = 39118[/tex]

The estimated age of the skull is 39118 years.


Related Questions

Whoever can answer this will get brainlyest

Answers

Answer:

The proportion is [tex]\frac{35}{108}[/tex] = [tex]\frac{x}{84}[/tex], and the length of the unknown side is [tex]\frac{245}{9}[/tex] or 27.22 approximately rounded to the nearest hundredth.

Step-by-step explanation:

Since the triangles are similar, the proportion of corresponding sides are equal. The pairs of corresponding sides in these triangles which we'll use to solve it are LK, KE, MK, and KF. LK and KE are corresponding sides, and their proportion is [tex]\frac{35}{108}[/tex]. MK and KF are corresponding sides, and their proportion is [tex]\frac{x}{84}[/tex] in which x represents the missing side. The proportions are equal, so [tex]\frac{35}{108}[/tex] = [tex]\frac{x}{84}[/tex]. Multiply both sides by 84 to isolate the variable, and you'll get [tex]x = \frac{35*84}{108}[/tex], which is [tex]\frac{2940}{108}[/tex] or [tex]\frac{245}{9}[/tex].

Help it’s due today plz

Answers

I can help you with no.1 it is 40

Encryption Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take < space > = 0, A = 1, B = 2, and so on. Thus, for example, "ABORT MISSION" becomes [1 2 15 18 20 0 13 9 19 19 9 15 14]. To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the 2 × 2 matrix 3 4 1 2 . We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A. Encrypted Matrix = 3 4 1 2 1 15 20 13 19 9 14 2 18 0 9 19 15 0 = 11 117 60 75 133 87 42 5 51 20 31 57 39 14 , which we can also write as [11 5 117 51 60 20 75 31 133 57 87 39 42 14]. To decipher the encoded message, multiply the encrypted matrix by A−1. The following exercise uses the above matrix A for encoding and decoding. Use the matrix A to encode the phrase "GO TO PLAN B".

Answers

Answer:

ok

Step-by-step explanation:

(9, 19) (2, 16)
Write the coordinates as decimals or integers.

Answers

Answer:

In decimal 0.428571428

Step-by-step explanation:

The slope = (y2 - y1)/(x2 - x1) y2 = 16, y1 = 19x2=2 and x1=9

The slope = (16 - 19)/(2 -9)

The slope = (-3)/(-7)

The slope = 0.428571428

So in decimal form the coordinates are going to be written as 0.428571428

Slope is the steepness of a line, it is the difference between the y coordinates divided by the difference in x coordinates.

Can you answer this for me thank you

Answers

Make it into a simultaneous equation:

5p + 4e = 7.65
4p + 5e = 7.20

Use adding/subtracting formula

The cost of an eraser is $1.44

Please help. And show your work or your content answer will be removed and your points will be taken away from the one's you get from me.Thank you!

Answers

Answer:

“It’s not hard to steal points”.........................................so thx for points....................................bye

Step-by-step explanation:

HELP ME QUICKLY AND PLS EXPLAIN HOW YOU GOT YOUR ANSWER! ILL EVEN GIVE BRAINLIEST<3
Laura wants to cut the board into equal pieces so that each piece is 5/8 foot long. How many pieces will she have? (The board is 12ft)

Answers

Answer:

Step-by-step explanation:

This is a straight forward division problem.

12/(5/8).

The rule for division of fractions is: invert the denominator and multiply.

For this problem: 12/(5/8) = 12 * 8/5 = 96/5.

whats 8 x 2 40 points

Answers

Answer:

Error hehehheheheh

Step-by-step explanation:

crown me please hehehhhe hahahahahh hohohoohoho points more more more more points

Help me please!!
15 points!

Answers

Answer:

Hi Hi really sorry may i get some points i need them to give it to other people cuz some people want points, ik its not the answer u wanted sorry but hope u get the answer soon!

Step-by-step explanation:

What do all Quadrilaterals have in common?

Answers

they have parallel lines and edges, both your answers are correct that you put

Answer:

The number of edges

Step-by-step explanation:

quad means 4 so all quadrilaterls have 4 sides.

Consider a force F = 〈–1, 3〉 applied to an object that is moving from the point (3, –9) to the origin.
Find the displacement vector of the object.
d = 〈 _,_ 〉
Find the work done in moving the object.
W = ___ Joules

Answers

Answer:

-3,9

30

Step-by-step explanation:

Edge 2021

The displacement is (-3, 9)

Work done= 30 Joules

What is vector?

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction.

Given:

F= (-1, 3)

point (3, -9)

So, displacement from origin to (3, -9)

d=  (0-3, 0-(-9))

d= ( -3, 9)

Work done = F. d

= 3 + 27

= 30 joules.

Learn more about vector here:

https://brainly.com/question/24256726

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The cost of a new 19-inch television would be around
a) $40.
b) $400.
c) $4,000.

Answers

Answer:

A

Step-by-step explanation:

They are typically around $100 or less. closest would be 40

Help

Don’t use for points and also be clear or I will take the points back

Answers

Answer:

x=47°

Step-by-step explanation:

..,........................

Answer:

I believe it is 47.  

Step-by-step explanation:  The reason why is because for a right angle it must be 90 degrees So, the way I solved this was getting 90-43 I got the 43 from BCD.  then subtracted it and applied it to the other side,  keep in mind I am only a freshman and it might be wrong super tiny chance but it might.  

What is the common factor in 14xy – 25yz?

1. z
2. x
3. xyz
4. y

Answers

Answer:

it would be y since both are common there

Types of operating system

Answers

Answer:

unary and binary

Step-by-step explanation:

Unary operations involve only one value, such as negation and trigonometric functions. Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation.

Answer:

multiprocessing operating system

batch operating system

realtime operating system

multi tasking operating system

mobile operating system

network operating system

8.
Tom works 1 3/4 hours a day at a café. He is paid $8 an hour. How much
money is he paid in 10 days?

Answers

Answer:

1 3/4 x 8 = 14. In 10 days, he will be paid the amount of one day x 10. 14 x 10 = 140. Tom will be paid $140 in 10 days

Step-by-step explanation:

tom will be paid $140 in 10 days

How many fourths are in 3 fourths?​

Answers

Answer:

12 one fourths

Step-by-step explanation:

Answer:

12 one fourths

Step-by-step explanation:

There 3 × 1 1/4 = 3 × 4 = 12 one fourths in 3

Jeff had 20 $ he spent 1/8 on his money on lunch and 2/5 of his money at the movies. How much money does Jeff have left

Answers

Answer:

9.50$

Step-by-step explanation:

First, multiply 20 by the given fractions

20*1/8=2.5

20*2/5=8

Add the two together to get the total amount of money Jeff spent, 10.5, then subtract 10.5 from 20 to get the total amount he has left, 9.5

Answer:

$9.50

I did a test with this question and the correct answer was 9.50

a punch recipe calls for 3 liters ginger ale, 1.5 liters tropical fruit juice. and 500 milliliters pineapple juice. how much punch will the recipe make?

Answers

Answer

189

Step-by-step explanation:

just is

Translate the expression: Four-fifths of the sum of 4 and y (pls hurry it's timed)​

Answers

[tex]\frac{4}{5}(4+y)[/tex]

A state began an effort to increase the deer population. In year 2 of the effort, the deer population in a state forest was 3,000. In year 4, the population was 4,320.

The explicit rule for the geometric sequence is aₙ =

Answers

Step-by-step explanation:

i guess math is the hardest subject

Answer:

The answer is aₙ = 2,500 (6/5)^n-1

Hope i helped, have a wonderful day! :D

I need help on this question please

Answers

What question I don’t see no question

Answer:

dont mind me im just getting my points back

Step-by-step explanation:

how do I find b of the traingal​

Answers

Answer:

Pythagorean Theorum:

16ft

Step-by-step explanation:

pythagorean theorum states a^2+b^2=c^2

it only works for right triangles, c is the hypotenuse, a and b are the legs

so to find b we plug in the info we have!

7.8^2+b^2=17.8^2

next we simplify:

60.84+b^2= 316.84

subtract 60.84 from both sides to isolate the variable:

b^2=256

square root both sides

b=16

16ft is the answer

I hope this helps!

50 de 100 ün en sade halı acil​

Answers

Answer:

srry buddy I don't understand your language

I am from India

can ask it in English

then I could help you

I'm having struggles with this, it would be much appreciated for assistance (:

Answers

I would be happy to help, but there is no problem

Step-by-step explanation:

Write the exponent for 3 x 3 x 3 x 3 x 3 (shift 6 to make the ^ sign). *

Answers

Answer:

3^5

Step-by-step explanation:

The exponent is just the amount of times you multiply a number by itself. So if you're multiplying three five times, the power would be 5.

Why is California at higher risk for earthquakes than North Dakota

( Also i know this isnt math but people answer faster when its in math )

Answers

California is at higher risks for earthquakes, because it near the Pacific Ocean

What is the sum of the matrices shown below?

Answers

Answer:

[tex] \red{ \bold{\begin{bmatrix} - 4 & 26 & - 5 \\ \\6 & 17& - 8\end{bmatrix} }}[/tex]

Step-by-step explanation:

[tex] \begin{bmatrix} 4 & 19 & - 5\\ \\ 7 & 0 & - 14\end{bmatrix} + \begin{bmatrix} -8 & 7 & 0\\ \\ - 1 & 17 & 6\end{bmatrix} \\ \\ = \begin{bmatrix} 4 + ( - 8) & 19 + 7 & - 5 + 0\\ \\ 7 + ( - 1) & 0 + 17& - 14 + 6\end{bmatrix} \\ \\ = \begin{bmatrix} 4 - 8 & 19 + 7 & - 5 + 0\\ \\ 7 - 1 & 0 + 17& - 14 + 6\end{bmatrix} \\ \\ \purple{ \bold{ = \begin{bmatrix} - 4 & 26 & - 5 \\ \\6 & 17& - 8\end{bmatrix} }}[/tex]

[tex]\left[\begin{array}{ccc}-4&26 &-5 \\6&17&-8\\\end{array}\right][/tex] is the sum of the given matrices.

What is matrices?

There are columns and rows in a matrix. The dimensions or size of a matrix are determined by these rows and columns. There are many different kinds of matrices, including row, column, null, square, diagonal, upper triangular, lower triangular, symmetric, and antisymmetric matrices.

Given two matrices,

[tex]\left[\begin{array}{ccc}4&19&-5\\7&0&-14\\\end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}-8&7&-0\\-1&17&6\\\end{array}\right][/tex]

We need to find the sum of this given matrices

The only matrices that may be added together are ones of the same size. As a result, you can only add matrices if they are both  m × n. For example, you can add two or more 3 × 3, 1 × 2, or 5 × 4 matrices. You cannot add a 2 × 3 and a 3 × 2 matrix, a 4 × 4 and a 3 × 3, etc. The number of rows and columns of all the matrices being added must exactly match.

thus,

Sum of matrices = [tex]\left[\begin{array}{ccc}4 -8&19 +7 &-5 + 0\\7 -1&0 + 17&-14 +6\\\end{array}\right][/tex]

Sum of matrices = [tex]\left[\begin{array}{ccc}-4&26 &-5 \\6&17&-8\\\end{array}\right][/tex]

Therefore, option D is correct.

Learn more about matrices here:

https://brainly.com/question/11367104

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Yesterday, 72 students from Red Rock Middle School went on a trip to the zoo. There are a total of 80 students in the school.
What percent of the students in the school went to the zoo2
O A 72%
OB. 80%
Oc88%
OD. 90%
OE 92%


pls sorry ty

Answers

Answer : option D 90%

Explanation : 72/80 as a percentage is 90%.

Good luck !!

3 1/8 - 7/12


NEED HELP ASAP!!! Plz

Answers

Step-by-step explanation:

hope this right.but if its not,im so sorry

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