The half-life of cesium-137 is 30 years. Suppose we have a 20 mg sample.

a. Find the mass (in mg) that remains after t years.
b. How much of the sample (in mg) remains after 20 years?
c. After how long will only 1 mg remain?

Answers

Answer 1

Answer:

(a) A = (20mg)/(2^(t/30))

(b) 12.6mg

(c) 129.6years

Step-by-step explanation:

To calculate the amount remaining after a number of half-lives, n, we can make use of:

[tex]A = \frac{B}{2^n}[/tex]

Where A = amount remaining

B = initial amount

[tex]n = \frac{t}{t_{0.5}}[/tex]

(a) A = (20mg)/(2^(t/30))

(b) Mass after 20years

A = (20mg)/(2^(20/30)) ≈ 12.6mg

(c) After how long will only 1mg remain:

1mg = (20mg)/(2^(t/30))

[tex]20mg = {2^{\frac{t}{30}}[/tex]

Taking log of both sides we have:

Log(20) = (t/30)log(2)

t/30 = (log(20))/(log(2)) ≈ 4.3

t/30 = 4.3

t = 30 x 4.3 ≈ 129.6years.


Related Questions

An account manager for a local software agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected:
Sales person Number of Contacts Sales (in millions)
1 14 24
2 12 14
3 20 28
What most likely is the direction of the correlation between the two variables?
a. positive
b. negative
c. zero
d. can not tell

Answers

Answer:

b is the correct answer

Step-by-step explanation:

hopefully think that it helps you

Answer:

B

Step-by-step explanation

(sorry if this is wrong)

What is the prime factorization of 504

Answers

Answer: 23 x 32 x 71

Step-by-step explanation: The orange divisor(s) above are the prime factors of the number 504. If we put all of it together we have the factors 2 x 2 x 2 x 3 x 3 x 7 = 504. It can also be written in exponential form as 23 x 32 x 71.

The orange divisor(s) above are the prime factors of the number 504. If we put all of it together we have the factors 2 x 2 x 2 x 3 x 3 x 7 = 504. It can also be written in exponential form as 23 x 32 x 71.

Equation A
Х
Y
-2
6
2
1
0
2
-2
-9
Equation B
х
Y
-2
-1
-6
0
-3
1
0
What is the solution to this system of equations?
0 (-1,-5)
0 (0,2)
O (-2, 6)
O (1,0)

Answers

its c

Step-by-step explanation:

Using only the values given in the table for the function, f(x) = x3 – 3x – 2, what is the interval of x-values over which the function is decreasing?

(–4, 1)
(–4, –1)
(–1,1)
(–1, 2)

Answers

Answer:(-1.1)

Step-by-step explanation:

Answer: The answer is (-1,1)

Step-by-step explanation:

I just did it and I hope this helps you❤️

which value completes the table?​

Answers

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Plug in -3 to t^2-3

-3^2-3

9-3

6

A is the only answer that has 6. So your answer would be A

The carter family budgets a total of 2,700 for a ski vacation in Colorado if they plan to go spend 275$ per day and 1,000 on meals about how many days n can the carter family go on vacation ?

Answers

Answer:

275n + 1000 = 2700

They will go 6 days on vacation.

Step-by-step explanation:

Given that the Carter family wants to go on vacation with a budget of $ 2700, of which $ 1000 will be used exclusively for food, and for each day of stay $ 275 will be spent, the formula to obtain the number of days they can spend on vacation is following:

1000 + 275n = 2700

275n = 2700 - 1000

n = 1700/275

n = 6.18

Therefore, with this amount, the Carters will be able to spend 6 days on vacation, and they will have money left over.

A line is drawn so that it passes through the points (-5,-3) and (-7,-5). What is the slope of the line?

Answers

Answer:

1

Step-by-step explanation:

The required slope of the line is 1 which passes through the points (-5, -3) and (-7, -5).

What is the slope of the line?

The slope of a line is defined as the change in the y-coordinate (the "rise") divided by the change in the x-coordinate (the "run").

To determine the slope of the line that passes through the points (-5, -3) and (-7, -5), we can use the formula:

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Let

x₁ = -5, y₁ = -3

x₂ = -7, y₂ = -5

∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )

Plugging in the coordinates of the two points, we get:

slope = (-5 - (-3)) / (-7 - (-5))

Simplifying this expression gives us:

slope = -2 / -2

Which simplifies to:

slope = 1

Therefore, the slope of the line that passes through the points (-5, -3) and (-7, -5) is 1.

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a square has an area of 49 square meters

Answers

Answer:

7x7

Step-by-step explanation:

its base (length) and width is 7.

Answer is 7 sq m
Because formula of square is S*S and 7 square is 49 7*7 = 49

HELP PLZ WILL GIVE BRAINLYEST

Answers

Answer:

Light blue

Step-by-step explanation:

Answer:

x ≥ -5

Step-by-step explanation:

Let tk be the number of ways to choose k beads from a drawer that contains 10 red beads, 8 blue beads, and 11 green beads. Find the generating function for the sequence {tk} 29 k = 0. Do not find a formula for tk.

Answers

Answer:

[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]

Step-by-step explanation:

From the given information;

The total number of beads  = 10 + 8 + 11 = 29

To choose k beads out 29 beads, let assume that [tex]t_k[/tex] be the no. such that:

[tex]t_k = ( ^{29}_{k}) \ \ \ where; k =0,1,2,3,....,29[/tex]

The sequence [tex]\{ t_k\}^{29}_{k=0} = (^{29}_{k})[/tex]

The generating function for [tex]\{ a_k \}^n_{k=0}[/tex] is:

[tex]G(x) = a_o +a_1x +a_2x^2 +...+a_nx^n[/tex]

[tex]G(x) = \sum \limits ^{n}_{k=0} \ a_k x^k[/tex]

For the sequence above;

[tex]G(x) = \sum \limits ^{29}_{k =0 } (^{29}_{k}) x^k[/tex]

By applying binomial series [tex](1+x)^n = \sum \limits ^n_{k=0} ( ^n_k) x^k[/tex]

Thus:

[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]

PLZ HELP, WILL GIVE BRAINLIEST!!!
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets.

What is the price each of one senior citizen ticket and one child ticket?

Answers

Answer: $4 senior, $7 child

Step-by-step explanation:

(3s + 9c = 75)

8s + 5c = 67

please help me asap and​

Answers

Answer:

you have it right! 3x - 4= 23

Answer: 3x-4 = 23

Step-by-step explanation:

Cos ik

The definition of similarity in terms of similarity transformations states that two figures are
similar if and only if there is a compositon of rigid motion and dilation that maps one figure to
the other. Suppose triangle ABC~triangle DEF. Explain how this definiton ensures:
1. The equality of all corresponding pairs of angles.
2. The proportionality of all corresponding pairs of sides.
PLEASE HELP

Answers

2 she is not smart so i think it’s 2

a drum full of rice weighs 241/6 kg. If the empty drum weighs 55/4 kg, find the weight of rice in the drum

Answers

Answer:

I believe the answer would be 186

Step-by-step explanation:

241-55=186

Solve the system using substitution.
3x - 4y = 11
y + 3x = 1

Answers

Answer:

x= 1

y= -2

Step-by-step explanation:

1. y+3x=1 subtract 3x from both side to get y= 1-3x

2. Put the new found y value in the equation

3x-4(1-3x)=11

3. Distribute the 4

3x-4+12x=11

4. Add 4 to both sides

3x+12x=15

5. Add the x's

15x=15

6. Solve for x

x=1

7. Plug in the x in the y equation y= 1-3x

y=1-3(1)

8. Solve for y

y= -2

The solution to the system of equations is x = 1 and y = -2.

To solve the system of equations using substitution, we need to solve one of the equations for one variable in terms of the other variable and then substitute that expression into the other equation. Let's solve the second equation for y and then substitute it into the first equation:

Given system of equations:

3x - 4y = 11

y + 3x = 1

Step 1: Solve the second equation for y:

y = 1 - 3x

Step 2: Substitute the value of y from equation (2) into equation (1):

3x - 4(1 - 3x) = 11

Now, let's solve for x:

3x - 4 + 12x = 11

Combine like terms:

15x - 4 = 11

Step 3: Solve for x:

15x = 11 + 4

15x = 15

x = 15 / 15

x = 1

Step 4: Now that we have the value of x, we can find y using equation (2):

y = 1 - 3(1)

y = 1 - 3

y = -2

So, the solution to the system of equations is x = 1 and y = -2.

To know more about equations

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For y=4x-3, find the
domain value when
the range is 17.
I NEED IT ASAP WILL GIVE BRIANIEST

Answers

Answer:

X=5

Step-by-step explanation:

HELP I NEEED ANSWER ASAP 95.11 = (100.50 + 78.35 + x)/3

Answers

Answer:

Here u go hoped it at least helped u !!!

Step-by-step explanation:

Answer:

106.480

I hope this helps!

whats the slope of a perpendicular line that passes through the lines (29,24) and (3,4)

Answers

I believe the answer is 1.3
explanation: to find slope you do x’s over y’s so you would have

29-3
———
24-4

which gets you

26
——
20

and simplified its 1.3. Sorry if it is wrong :/.

Your uncle purchases a $25,000 car this year. The car depreciates in value by 20% per year.

a) Write an exponential equation for the value of the car.

b) Use your equation to find the value of the car in 10 years.

c) When will the car be worth $10,000? Solve an equation with logarithms and show your work.

Answers

Answer:

b

Step-by-step explanation:

Edmundo wrote the expression 4²-5•2³. What is the value of this expression

Answers

let’s use PEMDAS

P: there are no parenthesis
E: the exponents need to be solved
4^2-5x2^3
16-5x8
M: we need to multiply 5 and 8
16-40
now we just need to do the rest
16-40=-24

-24 is your answer

The value of the expression is -24.

Calculation of the value of the expression:

Since the equation is [tex]4^2-5\times 2^3[/tex]

So, the value should be

[tex]= 4^2-5\times 2^3\\\\[/tex]

= 16 - 5(8)

= 16 -40

= -24

Here we use PEDMAS

P denotes for parenthesis

E denotes for exponents

D means divide

M means multiply

A means addition

S means subtraction

Therefore, we can conclude that The value of the expression is -24.

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(6p+ 15) + (10p-9)
O A. 16p- 6
OB. 16p+ 24
O C. 16p+ 6
O D. 6p+ 6

Answers

16p+6

Add 10p and 6p to get 16p
And add 15+-9 to get 6
(Adding a negative and positive number is like subtracting like in this example it is like saying 15-9)

Answer:

B

Step-by-step explanation:

sjfudshfuhfuhdufhshfsudhfusdfl

Answers

qjqjqjqkqkqkqjqkqkqkkqqoqoqooq

Answer:

I love cookies too.

answers
|x-3|
-|x+3|
-|x-3|
|x|+3

Answers

-|x+3|

its a positive 3 because you move it the opposite way im pretty sure
and it’s negative because it’s pointed down

Answer:

B) -|x+3|

Step-by-step explanation:

Use the equation y=a|x-h|+k

a=-1 since the graph opens downwards with no stretch or shrink

h=-3 since the horizontal shift is 3 units right

k=0 since there's no vertical shift

Therefore, our equation is y=-|x+3| making B the correct answer

distance from -3 to 0​

Answers

The space from -3 to 0 is 3 units. The answer is positive 3, not negative.

Factor the expression.
-28.2 - 14

Answers

-42.2
i hope this helps!

Given vectors u = ⟨–2, 1⟩ and v = ⟨4, –2⟩, which statement is true concerning u and v? The vectors form an obtuse angle of approximately 93°. The vectors form an obtuse angle of approximately 96°. The vectors form an obtuse angle of approximately 127°. The vectors point in opposite directions.

Answers

Answer:

D) The vectors point in opposite directions.

Step-by-step explanation:

got it right on edge :)

see graph below

Given vectors u = (-2,1) and v =( 4, -2) represents the vectors point in opposite directions.

What is vectors?

"Vectors is a quantity which gives us both magnitude and direction of the given quantity."

According to the question,

Given vectors u(-2,1) and v(4,-2) represented on the graph.

From the graph we conclude that given vectors u and v

Does not form obtuse angle of approximately 93° , 96° or 127°.

The vector 'u(-2,1)' is in second quadrant and v(4,-2) is in fourth quadrant.

Second quadrant and fourth quadrant are in opposite direction.

Hence, we conclude the vectors point in opposite directions.

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A certain computer can perform a maximum number of operations per second. If this computer is running at 23% of the maximum and is performing 105 operations per second, what is the maximum number of operation the computer can perform per second

Answers

Answer:

I believe 457 operations

The radius of the sphere is 9 inches. Which equation can be used to find the surface area of the sphere?

Answers

Answer:

Option (2)

Step-by-step explanation:

Formula to get the surface area of a sphere is,

Surface area = 4πr²

Here 'r' = Radius of the sphere

We have to calculate the surface area of a sphere with radius r = 9 inches.

By substituting the value of r in the formula,

S = 4π(9)²

Therefore, Option (2) will be the correct option.

Answer:

B.    S = 4 pi r squared = 4 pi (9) squared

Kyle uses a school gym to run a weekly yoga class. He must pay the school a fee for the use of the gym. Each person who comes pays x dollars. The amount of profit Kyle makes can be represented by the expression:

nx−d
What does the term nx represent?

A
the fee for the use of the school gym

B
the number of people in the yoga class

C
the cost of the yoga class for each person attending the class

D
the total money Kyle collects from people attending the class

Answers

Answer:

I believe it is D

Step-by-step explanation:

The entire equation y=nx-d means that d is the fee Kyle pays the school. SO that means that nx is the amount of money he earns from the people attending a yoga class.

Term nx represents the total money Kyle collects from people attending the class.

What is linear equation in one variable?

" Linear equation in one variable represents straight line and it is a equation in one variable in which degree of the given variable is equals to one. General form is written as ax + b =0."

According to the question,

x represents fees paid by each person for yoga class.

Condition is Kyle has to pay a fee for the use of gym.

It mean gym fees would be deducted from her earned fees from yoga class.

Therefore , d represents gym fee.

n represents number of people comes for yoga class.

From the given condition it is a linear equation in one variable,

Therefore, nx represents amount Kyle collects from people attending the class.

Hence, Option (D) is the correct answer.

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i finished the other question but i need help with this one!!!! I will give brainleist

Answers

Answer:

1.22 meters aprx.

Step-by-step explanation:

This is talking about meters right. If it is 1.22 would be your answer.

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