The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after 200 years.

Answers

Answer 1
To solve this we are going to use the half life equation [tex]N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) } [/tex]
Where:
[tex]N_{0} [/tex] is the initial sample
[tex]t[/tex] is the time in years
[tex]t_{1/2} [/tex] is the half life of the substance
[tex]N(t)[/tex] is the remainder quantity after [tex]t[/tex] years 

From the problem we know that:
[tex]N_{0} =100[/tex]
[tex]t=200[/tex]
[tex]t_{1/2} =1600[/tex]

Lets replace those values in our equation to find [tex]N(t)[/tex]:
[tex]N(200) =100e^{( \frac{(-0.693)(200)}{1600}) } [/tex]
[tex]N(200)=100e^{( \frac{-138.6}{1600} )} [/tex]
[tex]N(200)=100e^{-0.086625} [/tex]
[tex]N(200)=91.7[/tex]

We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.


Related Questions

The total weight of 15 boxes is 45 pounds .how much would 40 boxes weigh

Answers

40 boxes would weigh would weigh 120 pounds
To answer this, we must first assume that each box weighs the same.  If this is true, you would make a rate of how many pounds in 15 boxes: 45 lbs/15 boxes.  From here determine the weight per box by dividing 45 by 15.  This means each box is 3 pounds.  Multiply this by the total number of boxes (3 x 40).  This gives you a total weight of 120 pounds for 40 boxes.

!!!!!30 POINTS!!! HELP ME ON THESE GEOMETRY QUESTIONS PLEASE! PLEASE SHOW WORK AND EXPLAIN

Answers

1. Corresponding angles are equal.
.. a) ∠H = ∠B
Corresponding sides have the same relationship.
.. b) GH/DJ = AB/DC

2. Segments of the same line are proportional, so
.. FG/(47 m) = (73.8 m)/(82 m)
.. FG = (47 m)*(73.8/82) = 42.3 m
The distance between the two campsites is 42.3 m.

3. Corresponding sides are proportional.
.. (x -3)/8 = 2.5/2
.. x -3 = 8*(2.5/2) = 10
.. x = 13

4. Expand the fractions and subtract 1.
.. (x +3)/3 = (y +2)/2
.. x/3 +3/3 = y/2 +2/2
.. x/3 = y/2

5. Solved elsewhere.
https://brainly.com/question/8861591

Clark and his brother Kent played floor hockey in their living room. Each goal was worth 2 points. Clark scored 6 points. Kent scored 8 points. How many points did they score all together?

Answers

28 is the answer because multiply 6 times 2 and multiply 8 times 2 you would get 12 and 16 which when u add them it equals 28

What type of transformation is demonstrated in the following figure?

Image by Phoebe Baker

A.
dilation
B.
reflection
C.
rotation
D.
translation

Answers

hello
the answer is d
have a nice day
Answer is d ma boii just copying her answer /
                                                                      /

ILL CHOOSE BRAINLIEST!!!Which region represents the solution to the given system of inequalities?

A
B
C
D

Answers

The answer is D, because that is the place where the lines intersect.

The solution of a set of inequalities is the place where the lines intersect.

Hope I helped!

Let me know if you need anything else!

~ Zoe

Answer :- D region represents the solution to the given system of inequalities.


Explanation:

In the graph we can see the two lines drawn from the given system are intersecting in the fourth quadrant.

⇒The solution of the system lie in the fourth quadrant.

∴region D represents the solution to the given system of inequalities.

The graph of the linear inequality is the graph of all solutions of the system where the solution of the system of inequalities is the intersection region of the solutions of the two inequalities.

What is the area of this figure?
Select from the drop-down menu to correctly complete the statement.

The area of the figure is ? cm2.

A. 102
B. 132
C. 168
D. 340

SOMEONE PLEASE HELP ASAP!!

Answers

First of all we can draw a parallel line to divide the figure into a triangle and a rectangle as shown in the figure. To find the area of our rectangle, remember that the area of a rectangle is length times width, so [tex]A_{r} =lw[/tex]. Since we know for our figure that the length and width of our rectangle are 13cm and 6cm respectively, lets replace those values in our formula to get its area:
[tex]A _{r} =(13cm)(6cm)[/tex]
[tex]A=78cm^{2} [/tex]
Similarly, the area of a triangle is one half times base times height, so [tex]At=( \frac{1}{2})bh [/tex]. Since we know that our base is 8cm and our height 6cm, lets replace those values in our equation to find the area of our triangle:
[tex]A_{t} =( \frac{1}{2})(8cm)(6cm) [/tex]
[tex]A_{t} =24cm^{2} [/tex]

Now the only thing left is add our areas:
 [tex]A_{total} =78cm^{2}+24cm^{2} =102cm^{2} [/tex]

We can conclude that the correct answer is A. 102

Have you ever thought about the number of times your heart beats in a life time? Consider the average life span of 75 years and the average heart beat of 1.2 heartbeats per second. Estimate, using scientific notation, the number of times your heart will beat in your lifetime.

Answers

Final answer:

The average human heart beats approximately 108,000 times in one day, 39 million times in one year, and nearly 3 billion times during a 75-year lifespan. In a lifetime, your heart will beat an estimated 2.925 x 10^9 times.

Explanation:

The average human heart beats approximately 108,000 times in one day, 39 million times in one year, and nearly 3 billion times during a 75-year lifespan. To estimate the number of times your heart will beat in your lifetime, we can multiply the number of heartbeats in one year by the average life span:



39 million heartbeats/year x 75 years = 2.925 billion heartbeats in a lifetime



In scientific notation, this can be expressed as 2.925 x 10^9 heartbeats.

Final answer:

The average heart beats approximately 3 billion times during a 75-year lifespan.

Explanation:

The average heart beats approximately 108,000 times in one day, more than 39 million times in one year, and nearly 3 billion times during a 75-year lifespan. To estimate the number of times your heart will beat in your lifetime, you multiply the average heartbeats per year by the number of years in your lifespan.

For example, if we assume an average lifespan of 75 years, we can estimate the number of heartbeats in a lifetime:

39,000,000 heartbeats/year x 75 years = 2,925,000,000 heartbeats in a lifetime (2.9 x 10^9)

A piece of wood is 1.75 meter long A carpenter saws off 0.8 meter from it. Then he saws the remaining piece into 2 pieces of equal length. How long is each of the equal pieces?

Answers

1.75-0.8= 0.95m
0.95/2. to get equal halves would be 0.475m just under half a meter

what's the area of a square picture with 16 inch sides

Answers

To find the area of a square picture with 16 inch sides, we must use the formula for the area of a square: A=s^2, where s represents the value of the side length of the square.  

To solve, we must plug in the given side length of 16 inches into the formula.

A = (16 inches)^2
A= 256 inches^2

Therefore, your answer is 256 inches^2.  

Hope this helps!

Answer:

256

Step-by-step explanation:

dividing fractions (pt. 2)

Answers

A) 2/3 / 1/4 = 2/3 x 4/1 = 8/3 = 2 and 2/3

b) 7 / 2/3 = 7/1 x 3/2 = 21/2 = 10 and 1/2
1. 0.167
2. 1.16666666667

10 more points need it fast

Answers

As given in the question above, the formula for the area of a rectangle is Length x Width.
We have our width, 3.75, and our length, 2.33. Multiply these two values.

2.33 x 3.75 = 8.7375. Convert this to a mixed fraction;
8 73/100 is your mixed fraction in simplest form.

I hope this helps.

Which property can be used to expand the expression -2(3/4x + 7)?

Answers

distributive property
-2(3/4 x + 7)
-3/2 x - 14 <<<<<------- answer.

Warning. don't go any further.

Answer:

C

Step-by-step explanation:

Right in edge2020

Alexa's friends got her a skydiving lesson for her birthday. Her helicopter took off from the skydiving center, ascending in an angle of 20^\circ20

20, degree, and traveled a distance of 3.43.43, point, 4 kilometers before she fell in a straight line perpendicular to the ground.
How far from the skydiving center did Alexa land?

Answers

Answer:

3.19495491 rounded to the nearest hundredth is 3.19

Step-by-step explanation:

The distance from the skydiving center did Alexa land will be 3.19 km. The formula of trigonometry is used in the given problem.

What is trigonometry?

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

From ΔABC it is obtained that;

[tex]\rm Cos A = \frac{AC}{AB} \\\\ COS 20^0 = \frac{AC}{3.4} \\\\ AC= 0.9694 \times 3.4 \\\\ AC = 3.19 \ km[/tex]

Hence the distance from the skydiving center did Alexa land will be 3.19 km.

To learn more about the trigonometry refer to the link;

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Factor the expression 8x3y − 8x2y − 30xy.

Answers

Answer:  Our factorized term will be

2xy(2x+5)(2x-3)

Explanation:

Since we have given that

[tex]8x^3y-8x^2y-30xy[/tex]

All we need to do is to factorise this expression.

Here are the steps given below:

[tex]2xy(4x^2-4x-15)[/tex]

By manipulating the terms, we get:

[tex]2xy[(2x)^2-4x+1-16]\\\\2xy[(2x-1)^2-16]\\\\2xy[(2x-1)^2-(4)^2]\\\\2xy[(2x-1-4)(2x-1+4)]\\\\2xy[(2x-5)(2x+3)][/tex]

Alternatively,

By using splitting the middle terms,

[tex]2xy(4x^2-4x-15)\\\\2xy(4x^2-10x+6x-15)\\\\2xy[2x(2x-5)+3(2x-5)]\\\\2xy(2x-3)(2x+5)[/tex]

Hence, our factorized term will be

2xy(2x+5)(2x-3)

identity the pair of numbers that does not belong with the other three. explain.

Answers

3/5 and 5

In the first pair, the only numbers are 9 and 6. Converting 4 into a fraction leaves us with 4/1 - the only numbers in that pair are 1 and 4. In the final one, the only numbers are 2 and 7.
However, converting 5 gives 5/1. What this means is that the top and bottom numbers are not flipped in this pair, making it the odd one out. 

Hope I helped!
3/5 and 5 is the pair that doesn't belong
The other pairs are made of reciprocal numbers .
9/6*6/9=1
4*1/4=4/1*1/4=1
2/7*7/2=1

but 3/5*5/1=3, not 1.

Complete the statements below that show y = 8x2 + 32x + 17 being converted to vertex form. Factor out the leading coefficient. y = 8(x2 + 4x) + 17 Write in vertex form.

Answers

y=8(x+2)^2+-15

This answer showed as correct  
for the assignment 

Answer:

4, -32

2, -15

Step-by-step explanation:

Trust me bro.

Dana wants to make two types of dog treats. She has 10 cups of peanut butter and 12 cups of flour. Her dog bone treat recipe uses 3 cups of peanut butter and 2 cups of flour to make one tray. A tray of her oatmeal dog treat recipe uses 1 cup of peanut butter and 4 cups of flour. She plans to sell trays of dog treats at the town festival and charge $6 for a tray of dog bone treats and $7 for a tray of oatmeal treats. Dana wants to maximize her income from selling the dog treats.
When writing constraints for the problem, what is the most reasonable definition for the variables x and y?

A) Let x represent the number of cups of peanut butter used and y represent the number of cups of flour used.

B) Let x represent the number of cups of peanut butter used and y represent the number of trays of dog bone treats made.

C) Let x represent the number of dog bone treats made and y represents the number of cups of flour used.

D) Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Answers

D. Let x represent the number of trays of dog bone treats made and y represent number of trays of oatmeal dog treats made.

Answer with explanation:

Number of cups of peanut that Dana has =10 cups

Number of cups of flour that Dana has =12 cups

Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Constraints

⇒x>0, y>0

⇒3 x+y ≤10

⇒2 x+4 y ≤ 12

Maximize(Objective Function):

Z=6 x +7 y

⇒⇒ The most reasonable definition for the variables x and y as Dana wants to maximize her income from selling the dog treats

Option D: Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

What is the answer. Do not need to explain.

Answers

Add 5% of what the balance is every year for four years.

5% of $1200 is $60.
5% of $1260 is $63.
5% of $1323 is $66.15.
5% of $1389.15 is $69.45. So the final balance is $1458.45.
1200(.20)=240
1200+240=1440

3c-d=t solve for d

I'm confused on this

Answers

d= 3c-t

Hope this helps ;)
To solve for d simplify both sides of the equation then isolate the variable
d=3c-t

You have two summer jobs. At the Burger Palace you earn $8 per hour. At the community center you teach soccer clinics for $10 per hour. You want to earn at least $200 a week. If x is the number of hours you work at Burger Palace and y is the number of hours you work at the community center, which graph shows all the ways you can earn at least $200 a week? A. 2003-09-04-00-00_files/i0160000.jpg B. 2003-09-04-00-00_files/i0160001.jpg C. 2003-09-04-00-00_files/i0160002.jpg D. 2003-09-04-00-00_files/i0160003.jpg Please select the best answer from the choices provided A B C D Mark this and return

Answers

the complete question in the attached figure
 we have that
x-------------> number of hours works at Burger Palace -----> $8
y-------------> number of hours works at community center -----> $10

8x+10y>=200

using a graph tool
see the attached figure

the answer is the option B

the surface area of a pyramid is 533 square meters. what is the slant height? (base=13m) (width=13m)

Answers

To answer this question you will set up an equation that represents how to find the surface area of the net of the pyramid. You would represent it as four times the base of the triangle times the height of the triangle (this is the slant height) divided by two for each triangle plus the area of the square base. I have attached a picture of all the steps you would take to solve for the slant height.

Find (19 x 10*5) -(5 x 10 *4)

Answers

(19 x10*5) is 950
(5 x 10*4) is 200
soo 950 - 200 = 750

Answer:d


Step-by-step explanation:


The dining room table in Logan’s dollhouse is a replica of the dining room table in the actual house . The replica is 4 7/8 in. Long how long is the table in the actual house

Answers

To find the length of the actual table, multiply the replica's length by the scale factor:
4 7/8 x 1/16 = ___ ↓
39/8 x 1/16 = 39/128.

Hope this helps,
A.W.E.S.W.A.N.

Answer:

6ft 6 in

Step-by-step explanation:

Write a proportion that uses the scale factor 1/16. The numerator corresponds to the dollhouse, and the denominator corresponds to the actual house. So 4 7/8 goes in the numerator, and the variable goes in the denominator.

1/16=478xx=16⋅478x=78

There are 12 in. in a foot, so 78 in. equals 6 ft 6 in.

If 5^3 b-1=5^b-3, what is the value of b?

Answers

Answer:

wht the girl ontop said

Step-by-step explanation:

fcxccccccccccccxxxxxxxx

B= [2 8 .6 3 ] A= 3 0 2 -1]
what is BA ?

Answers

The product of matrices[tex]\(B\) and \(A\) is \([12 \, 24 \, 4 \, -2]\).[/tex]

To find the product (BA), we multiply each row of (B) by each column of (A) and sum the products.

Let's calculate the elements of the resulting matrix (BA):

  a. First row, first column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  b. First row, second column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  c. First row, third column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  d. First row, fourth column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

Therefore, the first row of [tex]\(BA\) is \([4.2 \, 4.2 \, 4.2 \, 4.2]\).[/tex]

Similarly, for the second row of (BA):

  a. Second row, first column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  b. Second row, second column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  c. Second row, third column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  d. Second row, fourth column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

Therefore, the second row of [tex]\(BA\) is \([4.2 \, 4.2 \, 4.2 \, 4.2]\).[/tex]

Hence, the product [tex]\(BA\) is \([12 \, 24 \, 4 \, -2]\).[/tex]

Find the (real-valued) general solution to the differential equation. z″+8z′=0 z(t)=

Answers

Try this option (see the attached picture).
Final answer:

The general solution to the differential equation z″+8z′=0 is z(t) = Ae^(-8t) + B, where A and B are arbitrary constants.

Explanation:

The differential equation z″+8z′=0 can be solved by separating variables and integrating.

Let v = z′ be the derivative of z.

Then the equation becomes v′+8v=0.

This is a first-order linear homogeneous differential equation, which can be solved by multiplying both sides of the equation by the integrating factor e^(∫8 dt) = e^(8t).

After solving for v, we can integrate it again to find z(t) by substituting back the expression for v in terms of z.

The general solution to the differential equation is z(t) = Ae^(-8t) + Be^(0t) = Ae^(-8t) + B, where A and B are arbitrary constants.

Learn more about Differential equation here:

https://brainly.com/question/33433874

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With two dice, each numbered 1-6, there are two possible ways to roll a 3: thus, for the outcome of 3 (a particular macrostate) there are 2 microstates. how many possible ways are there to roll a 4?

Answers

Microstates for a sum of 3 :  (1,2) and (2,1)
Microstates for a sum of 4:  (1,3),(2,2),(3,1)  so three possible microstates.

a baker used 4 cups of flour to make 5 batches of brownie. How many cups of flour does the baker need to make 1 batch of brownies

heeelp
please I will mark the brainliest, please help and show your work

Answers

hello

the asnwer is 6.4 ounces of flour per batch U have to add the batches and brownies then divide

Have  a nice day
6.4 ounces. you have to divide the batches of brownies by the cups of flour

-6x+5-4(x-1)=-4x-(5x-3)+4

Answers

Hello there!

-6x + 5 - 4(x - 1) = -4x - (5x - 3) + 4

We need to use the distributive form

-6x + 5 + (-4)(x) + (-4)(-1) = -4x - 5x + 3 + 4

-6x + 5 - 4x + 4 = -4x - 5x + 3 + 4

-10x + 9 = -9x + 7

Now we can subtract 9 from both sides

-10x + 9 - 9 = -9x + 7 - 9

-10x = -9x - 2

Add 9x to both sides

-10x + 9x = -9x + 9x - 2

-x = -2

We cannot leave it with a negative sign, divide both sides by -1

-x/-1 = -2/-1

x = 2

I hope the steps are clear to understand. If you have any misunderstanding feel free to let me know.

As always, I am here to help!

Ally bought a mattress and 4 pillows. The mattress cost $769
more than the 4 pillows. She gave the cashier $1300 and
received $51 change.
How much did each pillow cost?

Answers

each pillow costs $120

Answer:

Cost of each pillow is $120.

Step-by-step explanation:

Let P denotes cost of each pillow and M denotes cost of mattress.

Then, given cost of mattress is $769

also, Ally gave the cashier $1300 and received $51 change.

Total amount Ally paid = total amount she gave - total amount she receives back.

                                     = $( 1300 - 51 )

                                     = $1249

Since, Ally brought one mattress and 4 pillow . Thus, Total cost is given as,

⇒ M + 4 P = 1249

⇒ 769 + 4 P = 1249

⇒ 4 P = 1249 - 769

⇒ 4 P = 480

⇒ P = 120

Thus, cost of each pillow is $120.




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