The amount of a radioactive substance remaining as it decays over time is A = A0(0.5)t/h ,where a represents the final amount
Ao represents the original amount, t represents the number of years, and h represents the half-life of the sibstance.
The half-life of the radioactive isotope carbon-14 is 5,730 years. Approximately how many years will it take a 50-gram mass of
carbon-14 to decay to 5 grams?
Answers
Ao represents the original amount, t represents the number of years, and h represents the half-life of the sibstance.
The half-life of the radioactive isotope carbon-14 is 5,730 years. Approximately how many years will it take a 50-gram mass of
carbon-14 to decay to 5 grams?
Carbon-14 will take 19,035 years to decay to 10 per cent.
What is the time of decay?
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:
[tex]N(t)=N_oe^{-\lambda t}[/tex]
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
[tex]\lambda[/tex] = The decay constant.
One important parameter related to radioactive decay is the half-life:
[tex]t_{1/2}=\dfrac{Ln(2)}{\lambda}[/tex]
If we know the value of the half-life, we can calculate the decay constant:
[tex]\lambda =\dfrac{ln(2)}{t_{1/2}}[/tex]
Carbon-14 has a half-life of 5,730 years, thus:
[tex]\lambda =\dfrac{ln(2)}{5730}[/tex]
[tex]\lambda[/tex] = 0.00012097
The equation of the remaining quantity of Carbon-14 is:
[tex]N(t)=N_oe^{-0.00012097t}[/tex]
We need to calculate the time required for the original amount to reach 10%, thus N(t)=0.10No
[tex]0.10N_o=-N_oe^{-0.00012097t}[/tex]
Simplifying:
[tex]0.10=e^{0.00012097t}[/tex]
Taking logarithms:
ln(0.10) = -0.00012097t
Solving for t:
[tex]t=\dfrac{Log0.10}{-0.00012097}[/tex]
t = 19035 years
Carbon-14 will take 19,035 years to decay to 10 per cent.
To know more about decay follow
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Related Questions
Which point satisfies the system of equations y=3x-2 and y=-2x+3?
Answers
Answer:
First line has y intercept -2 ( the blue line ) Second line has y intercept 3 ( the red line )The point where these two lines cross is "D"a village school starts at 8.30am and end at 3.45pm.how long is the school day
Answers
Answer:
7 hours and 15 minutes.
Step-by-step explanation:
Draw a timeline for this question.
8.30 + 7 hours = 3.30pm or 15 30
3.30 + 0.15 minutes = 3.45 or 15 45
7 hours + 0.15 minutes = 7 hours and 15 minutes.
The average price for a gallon of gasoline in Germany is $5.57 and in France it is $5.54. Assume these averages are population averages in two countries, and that the probability distributions are normally distributed with the standard deviation of $.35 in Germany and standard deviation of $.25 in France. What is the probability that a randomly selected gas station in France charges more than $5.30 per gallon?
Answers
Answer:
0.8315 = 83.15% probability that a randomly selected gas station in France charges more than $5.30 per gallon
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average price for a gallon of gasoline in France is $5.54. The standard deviation is $.25.
This means that [tex]\mu = 5.54, \sigma = 0.25[/tex]
What is the probability that a randomly selected gas station in France charges more than $5.30 per gallon?
This is 1 subtracted by the pvalue of Z when X = 5.30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.3 - 5.54}{0.25}[/tex]
[tex]Z = -0.96[/tex]
[tex]Z = -0.96[/tex] has a pvalue of 0.1685
1 - 0.1685 = 0.8315
0.8315 = 83.15% probability that a randomly selected gas station in France charges more than $5.30 per gallon
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Answer:
y=x+2
Step-by-step explanation:
Luella has a pond in her yard. She wants to surround it with 330 feet of fencing. Fencing is sold by the yard. How many yards should she buy?
Answers
Answer:
110 yards
330/ 3 ,=110
1yard =3 feet
Step-by-step explanation:
if you multiply 3 to 110=330
or 330 divided by 3=110 yards.
Jack had $25. He went to the grocery store and bought a few things. When he paid, he got $8 change.
How much money did he spend
Answers
Answer:
17$
Step-by-step explanation:
25-8=17
A cone has a radius of 10 meters and a height of 5 meters. What is the volume of the cone to the nearest cubic meter? Use 3.14 for
Answers
Answer:
523.3
Step-by-step explanation:
The volume of a cone is 1/3 hB where h is the height and B is the area of the base.
Step 1: Find the area of the base (B). The base of a cone is a circle so use the formula pi*r^2. Plug in numbers. 3.14*10^2. 3.14*100=314
Step 2: Plug into the formula. 1/3(5*314) --> 1/3(1570)=523.3
(Full answer is 523 1/3)
Help please due in 40 mins !!!!
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Answer:
In this option B is correct
let f:A=B such that f(x)=y and g:B=C such that g(y)=z.name the function defined from A to C.
Answers
Answer:
since g:B→C is onto
suppose z∈C,there exists a pre-image in B
Let the pre-image be y
Hence y∈B such that g(y)=z
similarly f:A→B is onto
suppose y∈B,there exists a pre-image in A
Let the pre-image be x
Hence x∈A such that f(x)=y
Now gof(x)=g(f(x))=g(y)=z
So for every x in A,there is an image z in C
5/8 plus 1/16 simplified
Answers
So 5/8 will become 10/16
now we can add both fractions easily
10/16 + 1/16 = 11/16
which of the following doesn't describe a point?
Answers
Answer:
It has infinite length, but no width and no thickness (It describes a Line )
Hope it helps...
Have a great day :P
Find 22% of 48
Help please- i need this answer i’m stuck on it
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What is 25 x 65 / 73?
Answers
25x65=1625
1625/73=22.26
Bethany is a biologist who has been measuring and recording the rabbit population at a park over the last several years. She has noticed that a trigonometric function can model the population, which reaches a maximum population, m, each summer and a minimum population, n, each winter. If she uses to represent the rabbit population t years from the start of her study, what is the domain of function p?
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Answer:
[0,∞)
Step-by-step explanation:
Answer:
[0,∞)
Step-by-step explanation:
Correct on Plato!
What are some tips for the SAT math section?
Answers
Answer:
You should study hard and look through the test first to answer the ones you do know and then go back to the ones you don't know. Also if you use any methods or anything related to help with math try to use those through. Therefore try your best and just prepare for it, and always have supplies.
7) Find 18th term of the arithmetic sequence:
{13, 8, 3, -2, -7, ...}
Tysm
Answers
13-8=5
8-5=3
3-5=-2
-2-5=-7
etc.
Just keep subtracting 5 until you have the 18th term
---
hope it helps
Answer:
-77
Step-by-step explanation:
Reasoning:
Every step is decreasing by 5, therefor you will do 13-5 18 times. this will get you -77
y = 2x + 7
y = -3x - 33
Solve using the Substitution Method
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Answer:
-8
Step-by-step explanation:
A Hertz Rent-a Car is a car agency charges $40 for one day plus $0.10 per mile to rent a full size car. Enterprise Rent-A-Car charges $18 for one day plus $0.20 cents per mile to rent the same car. How many miles could you drive in one day that would result in the final bill to be the same from both companies?
Answers
Answer: 220 miles
Step-by-step explanation:
Let's write the equations for each case:
A Hertz Rent-a Car:
Charges a fixed amount of $40, plus a $0.10 per mile.
Then if you drive x miles, we get a total cost of:
C(x) = $40 + $0.10*x
Enterprise Rent-A-Car:
Chares a fixed amount of $18 plus $0.20 per mile, so if you drive x miles, the cost is:
K(x) = $18 + $0.20*x
Now, we want to find how many miles you can drive such that you would pay the same in both companies.
Then we need to find x such that:
C(x) = K(x)
$40 + $0.10*x = $18 + $0.20*x
Let's solve this for x.
$40 - $18 = $0.20*x - $0.10*x
$22 = ($0.20 - $0.10)*x
$22 = $0.10*x
$22/$0.10 = x
220 = x
So if you drive exactly 220 miles, you would pay the same in both companies.
The perimeter of a rectangle is 62cm.if the length of the rectangle is 24cm,what is tge width of the rectangle
Answers
Answer:
b= 7
Step-by-step explanation:
here's your solution
=> perimeter of rectangle = 62 cm
=> length = 24 cm
=> let width be (b)
=> perimeter of rectangle = 2(l + b)
=> 2(l + b ) = 62
=> 2(24 + b) = 62
=> 48 +2b = 62
=> 2b = 62 - 48
=> 2b = 14
=> b = 14/2
=> b = 7
hope it helps
In a bag filled with 200 M&M's, 80 are yellow. What percent is yellow?
Answers
Answer:
40% i think
Step-by-step explanation:
Answer: 40%
Step-by-step explanation:
Divide 80 by 200 and you get 0.4
Multipy 0.4 by 100 and u get 40 which is your answer
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Answers
Answer:
(0, 4 ) and (2, - 4 )
Step-by-step explanation:
(2)
3x + 4y = 16 → (1)
- 3x + 2y = 8 → (2)
Adding (1) and (2) term by term will eliminate the x- term
0 + 6y = 24
6y = 24 ( divide both sides by 6 )
y = 4
Substitute y = 4 into either of the 2 equations and solve for x
Substituting into (1)
3x + 4(4) = 16
3x + 16 = 16 ( subtract 16 from both sides )
3x = 0 , then
x = 0
solution is (0, 4 )
(3)
2x - 4y = 20 → (1)
5x + 4y = - 6 → (2)
Adding (1) and (2) term by term will eliminate the y- term
7x + 0 = 14
7x = 14 ( divide both sides by 7 )
x = 2
Substitute x = 2 into either of the 2 equations and solve for y
Substituting into (2)
5(2) + 4y = - 6
10 + 4y = - 6 ( subtract 10 from both sides )
4y = - 16 ( divide both sides by 4 )
y = - 4
solution is (2, - 4 )
Infinity cost $100,000. The sale is 60% off, then additional 40% off. How much would it cost after all sales applied?
Answers
An automobile dealer can sell 12 cars per day at a price of $17,000. He estimates that for each $300 price reduction he can
sell two more cars per day. If each car costs him $14,000, and fixed costs are $1000, what price should he charge to
maximize his profit? [Hint: Let x = the number of $300 price reductions.]
How many cars will he sell at this price?
Answers
Answer:
$ 1100
Step-by-step explanation:
Let p(x) be the price he charges for a car after x price reductions.
Since car costs him $10,000, and fixed costs are $1000
p(x) = 13000-10000-1000-300x = 2000 - 300x
Let q(x) = 12 + 2x the quantity of cars sold after x price reductions.
and the profit he can make are given by:
Profit = R(x) = (12+2x)(13,000 - 10,000 - 1,000 - 300x) dollars.
As you can see, maximizing profit , we have to check where P'(x) = 0
And P''(x)<0.
So we get x = 3.
Replacing the value we get we get 2000 - 300 X 3 = 2000 - 900
= $ 1100
]
i need help right now!!!!
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Answer:
look at the picture i sent...........
The question that is asked...
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Answer:
ps is perpendicular to line ur.
angle pvr is 90°
12x+3x=90°
15x=90°
x=90°/15
x=6
by putting value of x
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Help mmmmmmmmmmemmmemeeeee
Answers
Answer:
P-E-M-D-A-S
Step-by-step explanation:
Ok, so start with what i call "P-E-M-D-A-S"
P: parentheses | Also known as these: ( )
E: exponents | Its a small number by another number, like the 3 on your screen
M: Multiply | Also Known as x or a dot
D: Divide | i forgot how to make it
A: Add | also known as +
S: Subtract | also known as -
now go in order to solve it, it makes it much more easy!
Answer:
49 is your answer
Step-by-step explanation:
let's do b-pemdas
brackets
parentheses
e(I forgot the name for it but it's basically a small number next to the big number)
Multiply
Divide
Add
Subtract
you do the equation in that order
so
2+8•7-(3^2)
we focus on (3^2)
that's 3•3 which equals to 9
so now the equation is
2+8•7-9
Now we focus on 8•7 which equals to 56
the equation now looks like
2+56-9
you then add 56 to 2 which equals to 58 and then subtract 9 from it so it should look like this
2+56=58
58-9= 49
and 49 is your answer
hope this help!!!
if you would give me brainliest that would help a lot!!
x^2 + y^2 + 8x - 6y-15=0
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Answer:
use ither apps to solve for x or y desmos also is a good app for plotting thjs function0
AB =
Round your answer to the nearest hundredth.
A
50°
B
2
с
Answers
Answer:
50.04
Step-by-step explanation:
Answer: 3.11
Step-by-step explanation:
khan academy hint.
4 1/3 inches by 5 1/3 inches. Find the area of a rectangular
Answers
Answer:
23 1/9 sq. inches
Step-by-step explanation:
Start by making 4 1/3 into 13/3 and 5 1/3 into 16/3. You can find area by multiplying one side by another, so we multiply 13/3 and 16/3. We can multiply the numerators (Top) of the fractions and put them over the denominators (Bottom) of the fractions multiplied for our result. 13 * 16 is 208 and 3 * 3 is equal to 9. The simplified form is 23 1/9.
Chandler can mow 2 lawns per hour. Use an equation to determine the number of hours it will take him to mow 7 lawns.
14 hours
3 1/2 hours
2 1/2 hours
7 1/2 hours
Answers
Answer:
3 1/2
Step-by-step explanation:
2x2x2 is 6 and 1/2 of 2 is 1 which means 6+1 is 7 so it's 3 and half
Answer:
3 1/2
Step-by-step explanation:
I didn't copy i had to use my finger five times