A sample of a radioactive isotope had an initial mass of 540 mg in
the year 2009 and decays exponentially over time. A measurement
in the year 2011 found that the sample's mass had decayed to 300
mg. What would be the expected mass of the sample in the year
2021, to the nearest whole number?

Answers

Answer 1

Answer:

16 mg

Step-by-step explanation:

[tex]N_0[/tex] = Initial mass of sample = 540 mg

t = Time taken = 2 years

[tex]t_{1/2}[/tex] = Half life of isotope

N = Final mass of sample = 300 mg

Radioactive decay is given by

[tex]N=N_0e^{-\dfrac{\ln 2}{t_{1/2}}t}\\\Rightarrow \ln\dfrac{N}{N_0}=-\dfrac{\ln 2}{t_{1/2}}t\\\Rightarrow t_{1/2}=-\dfrac{\ln2}{\ln\dfrac{N}{N_0}}t\\\Rightarrow t_{1/2}=-\dfrac{\ln2}{\ln\dfrac{300}{540}}2\\\Rightarrow t_{1/2}=2.358\ \text{years}[/tex]

In 2021 the number of years passed from 2009 would be 12 years

[tex]N=N_0e^{-\dfrac{\ln 2}{t_{1/2}}t}\\\Rightarrow N=540e^{-\dfrac{\ln 2}{2.358}12}\\\Rightarrow N=15.86\approx 16\ \text{mg}[/tex]

The expected mass of the sample in the year 2021 would be 16 mg.


Related Questions

2. Write the symbol that will make the statement true; -5__+3.
a. < b. > c. = d. /​

Answers

Answer:

a

Step-by-step explanation:

On the number line, negative numbers are less than zero. positive numbers are larger than zero.

the diagram shows a triangle drawn between a pair of parallel lines
Find value of x and y​

Answers

Answer:

x = 60

y = 80

Step-by-step explanation:

x° + 120° = 180° (interior angles on the same side of transversal)

x° = 180° - 120°

x° = 60°

x = 60

x° + y° = 140° (alternate angles)

60° + y° = 140°

y° = 140° - 60°

y° = 80°

y = 80

The measure of angle ∠x is 60° and ∠y is 80°.

What are Alternate Interior Angles?

Alternate Interior Angles is defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles. These angles are always equal.

Since angle ∠x and ∠120° are interior angles on the same side of transversal.

So, x° + 120° = 180°

x° = 180° - 120°

x° = 60°

x = 60

Since angle ∠x° and angle ∠y° are alternate angles

So, x° + y° = 140°

Substitute the value of x = 60 in above equation,

60° + y° = 140°

y° = 140° - 60°

y° = 80°

Hence, the measure of angle ∠x is 60° and ∠y is 80°.

Learn more about Alternate Interior Angles her:

https://brainly.com/question/2125016

#SPJ2

A new health drink has 150% of the recommended daily allowance (RDA) for a certain vitamin. The
RDA for this vitamin is 20 mg. How many milligrams of the vitamin are in the drink?
There are mg of the vitamin in the drink.

Answers

Convert 150% to a decimal by dividing by 100, = 1.5

Multiply 1.5 times the 20 mg = 30 mg in the drink.

150% is one and a half times a value.


Math problem I need help with

Answers

Answer:

31° is the answer thank you

31 degrees Hopefully that helps!

frecuencia del alcohol​

Answers

????
Dnbdusbsjeisbsbdbbd

In a '15% off sale, Freya bought a DVD player for £179.99. What was the original price of this

DVD player?

Answers

Answer:

211.75

Step-by-step explanation:

179.99/.85=211.75

Is my answer right? if not can you please tell me which won is right..

Answers

A = 4 is the correct answer!3 x ? = 1212 ÷ 3 = 4so1 x 4 = 4You're wrong. It is not six.By the way, it's "one" not "won".It was probably a mistake.:)Please let me know if I am wrong.

Order from greatest to least. 4. -4. 9. -7 *

Answers

Answer

9 4 -7 -4

Step-by-step explanation:

How do you write the equation in slope intercept form given (2,2) and (0,-2)?

Answers

Answer:

y = 2x - 2

Step-by-step explanation:

The slope-intercept form of the equation of a line is

y = mx + b

where m is the slope, and b is the y-intercept.

y = mx + b

First we find the slope, m.

slope = (difference in y)/(difference in x)

It does not make a difference which point is first and which point is second in finding the differences, but you must do the x- and y-differences in the same order.

slope = (-2 - 2)/(0 - 2) = -4/(-2) = 2

The slope is 2, so m = 2, and now we have:

y = 2x + b

We need to find the value of b, the y-intercept.

We use one of the given points. Let's use (2, 2). We plug in 2 for x and 2 for y and solve for b.

2 = 2(2) + b

2 = 4 + b

-2 = b

b = -2

Now that we know the y-intercept is -2, we substitute b with -2.

y = 2x + b

y = 2x - 2

Answer: y = 2x - 2

Evaluate 12s+3.5t when s=6 and t=7​

Answers

Step-by-step explanation:

(12 × 6) + ( 3.5 × 7)

72 + 24.5

= 96.5 #

Step-by-step explanation:

[tex] \underline{ \underline{ \large{ \tt{G \: I \: V \: E\: N}}}} : [/tex]

s = 6 & t = 7

[tex] \underline{ \underline{ \large{ \tt{T \: O\: \: F\: I \: N \: D}}}} : [/tex]

Value of the expression : 12s + 3.5t

[tex] \underline{ \underline{ \large{ \tt{S\: O \: L \: U \: T \: I\: O\: N}}}} : [/tex]

Plug the values of s and t as 6 and 7 respectively in the given expression :

⟷ [tex] \large{ \tt{12 \times 6 + 3.5 \times 7}}[/tex]

⟷ [tex] \large \tt{72 + 24.5}[/tex]

⟷ [tex] \large{ \tt{96.5}}[/tex]

[tex] \red{\boxed{ \bold{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{96.5}}}}}}}[/tex]

Hope I helped ! ツ

Have a wonderful day / night ! ♡

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

3 times a day Dylan mixes 2 oz of protein powder into a shake how many days can he make all 3 shakes from his 5 oz container of protein powder you #16 oz in a #

Answers

Answer:

13 days

Step-by-step explanation:

Protein powder in container = 16 oz

Number of containers = 5

Total ounces of protein powder = (16 * 5) = 80 oz

Oz of protein used per shake = 2 oz

Number of times shake is made per day = 3

Total oz used per day = 2 oz * 3 = 6 oz

Number of days hencan make all three shakes from container :

Total ounces / ounces per day

80 oz / 6 oz

= 13. 33 days

Krishna has $4.90 with a combined 34 nickels and quarters. How many of
each coin does she have?

Answers

Answer:

Step-by-step explanation:

-34 nickles is = 1.70

34 quarter is  = 8.50

1.70 plus 8.50 plus 4.90 = 15.1 i think

don't worry about the other writing I want to see it worked out step by step so I can work the rest out and learn how to do them. PLEASE DO NOT WRITE ON HERE UNLESS YOU ARE WORKING KT OUT STRP BY STEP AND I WILL GIVE BRAINLYIST ONCE CONFIRMED BY TUTOR.JUST NUMBER ONE.​

Answers

Answer:

see below

Step-by-step explanation:

6y = 12x + 26

15y = 45x + 60

First let's simplify these equations.

6y = 12x + 26

Divide each term by 6.

y = 2x + 26/6

Simplify the fraction.

26/6

= 13/3

Your simplified equation is:

y = 2x + 13/3

Let's simplify the other equation.

15y = 45x + 60

Divide each term by 15.

y = 3x + 4

These are your simplified equations.

y = 2x + 13/3

y = 3x + 4

We can see that the slope of the first equation is not equal to the slope of the second equation.

equation 1: slope is 2 shown from 2xequation 2: slope is 3 shown from 3x

The y-intercept of the first equation is not equal to the y-intercept of the second equation.

equation 1: y-intercept is 13/3 shown by + 13/3equation 2: y -intercept is 4 shown by + 4

Now we want to solve the equations.

Both equations are equal to y, so you can set them equal to each other.

2x + 13/3 = 3x + 4

Combine like terms.

1/3 = x

Plug x = 1/3 into both of the equations separately..

y = 2(1/3) + 13/3

y = 2/3 + 13/3

y = 15/3

y = 5

y = 3(1/3) + 4

y = 3/3 + 4

y = 1 + 4

y = 5

Your solution is (1/3, 5)

The system of equations has one solution.

Hope this helps!

−3(5x + 8) − 7(5x + 3)

Answers

Answer:

-50x-45

Step-by-step explanation:

-3(5x+8)-7(5x+3)

-15x-24-35x-21

-50x-45

i need some help pls

Answers

Answer:

C would be your answer

Step-by-step explanation:

The answer for this question is c probably

$26,000 is invested at 8% p.a. If interest is compounded annually, find the balance after 35 years.​

Answers

Answer:

At the end of 35 years, your savings will have grown to $384,418.

You will have earned in $358,418 in interest.

How long does it take an account with a principal of $400 to earn $48 in interest at a simple annual interest rate of 2%?

Answers

Answer:

it'll take 6 years

Step-by-step explanation:

I =put

48= 400(.02) t

48= 8t

t= 6 years

write the equation of the line passing through the points (-4 -1) and (2 8)

Answers

Answer:

y=3/2x+5

Step-by-step explanation:

PLEASE HELP
Simplify the expression by combining like terms.



4 x + 3 − 2x + 5 − 2y

Answers

Answer:

2x+8-2y

Step-by-step explanation:

4x-2x+5+3-2y

2x+8-2y

Answer:

There you go!!

Step-by-step explanation:

4x - 2x - 2y + 3 + 5

What does |(-18)+(-2)/(7)+(-2) equal?

Answers

Answer:

-4

Step-by-step explanation:

(-18)+(-2)/(7)+(-2)

Add -18 and -2 to get -20.

-20/(7)+(-2)

Add 7 and -2 to get 5.

-20/5

-4

Hope this helps.

How do you know (2, 1) is a solution to 4x+y=9?
Select all that apply.

1.[] The coordinate lies on the line
2.[] When substituting x=2 and y=1 into the equation, you get a true statement .
3.[] (2,1) is a positive and so is all the numbers in the equation
4.[] 9-4=5 and 2(2)+1=5​

Answers

Answer:

2. When substituting x=2 and y=1 into the equation, you get a true statement.

Hope this helps you.

solve (x - 4)^2 = 5 ​

Answers

Answer

If you are solving for X, take the root from both sides.

Exact Form:

x

=

5

+

4

,

5

+

4

Decimal Form:

x

=

6.23606797

,

1.76393202

Answer:

Step-by-step explanation:

[tex](x-4)^2=5\\ \\ x-4=\pm \sqrt{5}\\ \\ x=4\pm \sqrt{5}\\ \\ x=4-\sqrt{5},\ 4+\sqrt{5} [/tex]

I NEED THE SLOPE INTERCEPT FORM, ITS DUE BY 12

Answers

Answer:

really what is the answer

Step-by-step explanation:

Answer:

y=x+2

Step-by-step explanation:

i cant see clearly if line is on the x axis or not, so im going to guess that it starts on a 2, cause its really close to 2.

hope this helps.

The eighth term of an arithmetic sequence is double the value of the third term. The fifth term is equal to 14. Determine the first term and the common difference of the sequence.

Answers

Answer: first term = 6

Common difference = 2

Step-by-step explanation:

Eight term =a +(n-1)d = a +(8-1)d = a + 7d

Third term = a+(n-1)d = a + (3-1)d =a + 2d

a + 7d = 2(a + 2d)

a + 7d = 2a + 4d

7d - 4d = 2a - a

a = 3d

The fifth term is equal to 14. This is:

a + 4d = 14

Put the value of a into the equation here

3d + 4d = 14

7d = 14

d = 14/7

d = 2

Recall that a + 4d = 14

a + 4(2) = 14

a + 8 = 14

a = 14 - 8

a = 6

what is the rate of change of the line through (2, -7) and (3, 12)

Answers

Answer:

Hi! Your answer is m = 19

Step-by-step explanation:

~use the slope formula to find the average rate of change~

y’all plz- help this is so hard
giving brainlest ;)

Answers

Answer:

B

Step-by-step explanation:

Answer:

Answer: B.

Step-by-step explanation:

Quadrants in the Coordinate Plane

The coordinate plane is divided into 4 quadrants named I, II, III, and IV as shown in the image attached below.

The first quadrant (I) has the x positive and the y positive

The second quadrant (II) has the x negative and the y positive

The third quadrant (III) has the x negative and the y negative

The fourth quadrant (IV) has the x positive and the y negative.

A point located in quadrant III must have both coordinates negative. This only corresponds to choice B where both components are negative.

Answer: B.

A pink paint mixture uses 4 cups of white paint for every 3 cups of red paint
The table shows different quantities of red and white paint for the same shade of pink complete the table

Answers

Answer:

See attached.

Step-by-step explanation:

The table is as shown

White paints {cups}   Red paints{cups}

4                                       3

2                                       1

1                                       0

5                                      4

5                                      4

The white paint mixes with the red paint is the ratio of 4 is to 3 in that every 4 cups of white paints is mixed with 3 cups of red paints.

What is the answers to this? I am not sure if the ones I already have are correct. Please help!

Answers

That is incorrect because 2+2143=1233627 wich is not ur answer therefore meaning it’s wrong

find 2 numbers whose sum is 36 and diffrence is 10​

Answers

Answer:

23 and 13

Step-by-step explanation:

can you help me with my latest answer too??i'm on a time limit rn

Answer:

13 and 23

Step-by-step explanation:

let 2 number be x and y

x + y = 36 ---- equation ( 1 )

x - y = 10 -----equation ( 2 )

from ( 1 ) and ( 2 )

2y = 26

y = 13

putting value of Y in equation ( 1 )

x + y = 36

x + 13 = 36

x = 36 - 13

x = 23

MARK ME AS BRAINLIST

cyclops frogggggggiiiiiiieeeeeeeee

Answers

Answer:

It is a little creepy....

Step-by-step explanation:

lol that totally looks like one

Other Questions
PLS HELP ME!!!!!!!!!!! Satish's register shows a deposit on February 4 in the amount of $150.00, an atm withdrawal on February 5 in the amount of $180, and another deposit on February 7 in the amount of $225.56. What should Satish's balance in his register be? A. $610.82, B.$792.91, C.$910.82, or D.$947.14 cual es el resuido de 72938 Choose the best answer. _____________ never became part of the League.JapanThe United StatesItalyGermanySpain Please please help me I NEED THIS FAST PLZ HELP!!!!!Read the paragraph from a writer's argument essay in support library funding. "Unfortunately, we will no longer have the resources to maintain our Makerspace program," said Library Director Sarah Tomlinson. "This will be a terrible blow to many local artists and small businesses who use our equipment to produce beautiful and innovative creations."The paragraph provides support for the claim that library funding should not be cut because it provides important services to the community. Which statement could the writer add to the paragraph to provide additional logical and relevant support for the claim?A. Community groups that use library spaces for meetings, presentations, fundraisers, and outreach programs would also be affected by library budget cuts.B. Some people question whether libraries should bear the burden of paying for spaces that are used by outside individuals and businesses. C. Libraries should partner with local businesses willing to give a percentage of their sales to public libraries.D. Libraries provide spaces where artists can display their work for the community to admire. solve the simultaneous equations To start a great night of doing physics homework, you sit down to pour yourself a good cup of coffee. Your coffee mug has a mass 137 g and a specific heat of 1089 J/kg K. The mug starts out at room temperature (23.8 o C). Your coffee has an initial temperature of 79.8 oC and has the same specific heat as water (4186 J/kg K). 1) Let's say you pour enough coffee into the mug so that the mass of coffee is equal to the mass of the mug. If we assume that no heat is lost to the outside room, once the mug and coffee reach the same temperature, will that temperature be closer to the initial temperature of the coffee or the initial temperature of the mug? (Notice that the mass of the coffee and the mass of the mug are the same.)2) What is the final temperature of coffee and mug once they come to thermal equilibrium?Tfinal = ____________ degrees c 3) Now lets assume that instead of the 137 g of coffee, you pour in 225 g of coffee. What is the final temperature of the coffee and mug? (Again, assume that you loose no heat to the outside.)Tfinal = ____________ degrees c 4) Now lets say that along with the 225 g of coffee, you pour in 11.7 g of cream in your mug. The cream has an initial temperature of 5.2 oC and also has the same specific heat as water. What is the final temperature of the coffee, cream and mug? (Again, assume that you loose no heat to the outside.)Tfinal = _____________ degrees c If the sum of the measures of H and J is 76 , what is the measure of I ? FREE BRAINLIEST IF YOU ANSWER CORRECTLY!! (50pts) 2/3 X 12 for simplest form 2. With sufficient detail, Discuss how materiality and risk are related and integrated into the auditprocess.Can anyone solve this fast. Geometry Help!Please only answer if you know the answer. Look at the image below to answer the question. Be sure to show all of your work and explain your thinking.I posted 3 of these, so if you understand it, please go and check them out.If you do not know the answer use the comment section, don't answer my question with a comment. Thanks, Good Luck! The table shows the coordinates of trapezoid ABCD and trapezoid A'B'C'D' after a transformation.What are the coordinates of point C? On a trip to Washington, D.C., you and your friend are standing next to the Washington Monument. Your friend wants to buy a guide book to find out how tall the Washington Monument is, but will use the money to buy a snack to share instead if you can figure it out. If you know your own height, what two additional measurements must you know to solve the problem?(1 point)the length of the shadow cast by the Washington Monument and the length of the shadow cast by the Lincoln Memorialthe length of your shadow and the length of your friends shadowthe length of your shadow and the length of the shadow cast by the Washington Monumentthe length of your friends shadow and the length of the shadow cast by the Washington MonumentIf a 30-foot tree casts an 18-foot shadow, find the length of the shadow cast by a 24-foot tree. (1 point)14.4 feet432 feet22.5 feet40 feetIn ABC, mA=42, mB=50, AB=4, and AC=3. In XYZ, mX=42, mZ=88, XY=14, and YZ=9.5. Find the measures of BC and XZ. Round to one decimal place.(1 point)BC=2, XZ=7.1BC=2, XZ=10.5BC=2.7, XZ=7.1BC=2.7, XZ=10.5 Liz ran 4/5km on Monday and 5/6 km on Tuesday. Select the true statement about the distance Liz ran.Choose 1 answerA:Both fractions are almost 1 whole.B:One fraction is about 1/2 and the other is less than 1/2Select the best estimate for the combined distance Liz ran Monday and Tuesday.Choose 1 answer:1/2 km1 km2 km Bud has shown persistence throughout the novel. What was the major obstacle Bud needed to overcome to meet his father? Why was that obstacle so important to overcome? (Bud not Buddy book. Just give me a general idea, please!) Which word is a synonym for the word desolate found in the line: "how desolate the landscape can be"?a. impoverished b. starkc. fruitfuld. disrespect Help! Which statement correctly tells why the Internet became easily accessible?AInternet news was trustworthy and accurate.B.Personal computers made it easy to access the Internet.C.Radio programs were not available and became less popularTV technology was not advancing with people's needs.D.Resetkt (C) Describe ONE way in which population growth affected thedevelopment of technology in the period c. 1750-c. 1900. Determine whether each equation is true or false.TrueFalse32 = 2 x 2 x 253 = 1581 = 71If answer i will make brainliest