Question 4 (1 point) The half life of Cs-137 is 30.2 years. If the initial mass of the sample is 100kg, how much will remain after 151 years? Leave your answer as a decimal and do not round, Answer = kg Blank 1:​

Answers

Answer 1

Answer:

3.12 kg.

Step-by-step explanation:

Mass after t years:

The mass of the elements after t years is given by the following equation:

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

In which M(0) is the initial mass and r is the decay rate, as a decimal.

The half life of Cs-137 is 30.2 years.

This means that:

[tex]M(30.2) = 0.5M(0)[/tex]

We use this to find r.

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

[tex]0.5 = M(0)(1-r)^{30.2}[/tex]

[tex](1-r)^{30.2} = 0.5[/tex]

[tex]\sqrt[30.2]{(1-r)^{30.2}} = \sqrt[30.2]{0.5}[/tex]

[tex]1 - r = 0.5^{\frac{1}{30.2}}[/tex]

[tex]1 - r = 0.9773[/tex]

So

[tex]M(t) = M(0)(0.9773)^{t}[/tex]

If the initial mass of the sample is 100kg, how much will remain after 151 years?

This is M(151), with M(0) = 100. So

[tex]M(t) = 100(0.9773)^{t}[/tex]

[tex]M(151) = 100(0.9773)^{151} = 3.12[/tex]

The answer is 3.12 kg.


Related Questions

How many inches are equal to 16 feet

Answers

Step-by-step explanation:

16 feet is equal to 192 inches.

Hope it helps :)❤

Answer:

192 inches is equal to 16 feet.

(Hope this helps! Btw, I answered first. Brainliest please! :D)

Find the area of the parallelogram.



The area of the parallelogram is [a] in2. please help

Answers

Answer: 117in²

Step-by-step explanation:

area of a parallelogram= bh (base times height)

13 times 9 = 117in²

Which phrase best describes the relationship indicates by the scatter plotting?​

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Answer:B

Step-by-step explanation:

A + A =2,A + B =3,A + B × 2 =??..only for geniuses​

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Answer: 5

Step-by-step explanation:

Is 4(4f-8)+5= 16f+37

Answers

4(4f-8)+5= 16f-27
that’s the right answer

Need help ASAP!!!!!

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Answer:

cos 45 degree = A/H

cos 45 degree =  2 square root 2 / x

x = 2 square root 2 / cos 45 degree

x = 4

Sin 45 degree = O/H

Sin 45 degree = y/ 4

4 x Sin 45 degree = y

y = 2.83

or

we could use tan

tan 45 degree = O/A

tan 45 degree = y / 2 square root 2

2 square root 2 x tan 45 degree = y

y = 2.83

i hope this would elp a little bit.

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Answer:

5y + 8

and

8y +5 are the same solutions.

An angle measures 60 degree it is divided into 5 angles with equal measures. What is the measure of those angles

Answers

Answer:

Each part of the angle would measure 12 degrees

Step-by-step explanation:

What type of number is v5?

Choose all answers that apply:

1. Whole number
2. Integer
3. Rational
4. Irrational

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Answers

The square root 5 is irrational because a square root of a positive number is either an integer or irrational number. Therefore it is irrational.

A ship caption is mapping

Answers

I attached the answer and explanation below
Answer:
25 miles per hour

Explanation: In the 2nd column in the graph it says that in 1 hour (time) the ship captain can travel 25 miles (distance).

Glad to help!! :)

Somebody help me with this?

Answers

Answer:

2

Step-by-step explanation:

The solutions of a quadratic graph are the x-intercepts. As you can see from the graph, the only place that it intercepts the x axis is at 2, so the solution is 2.

2/5 g = 3/5 help I don't know what the answer is

Answers

Answer:

Step-by-step explanation:

2/5 g = 3/5

g = 3/5 - 2/5 = 1/5

Which scatterplot demonstrates the strongest relationship between two quantitative variables?

A graph has x on the x-axis, and y on the y-axis. Points are scattered throughout the graph.
A graph has x on the x-axis, and y on the y-axis. Points curve up and then down in a line.
A graph has x on the x-axis, and y on the y-axis. Points increase loosely together.
A graph has x on the x-axis, and y on the y-axis. Points decrease loosely together.

Answers

Last one because they decrease together

The scatterplot demonstrates the strongest relationship is, a graph has x on the x-axis, and y on the y-axis. Points increase loosely together.

What is Correlation coefficient of scatterplot?

The correlation coefficient of scatterplot is used to demonstrate the relationship between variables.

When two variables increases together, they are said to have positive correlation.

When one is increasing and another is decreasing, they are said to have negative correlation.

When most of  data points form a straight line or lies close to the straight line, it indicates strong linear correlation.

From the given options;

Option A, zero correlation

Option B, less than 1

Option C, 1 or greater than 1

Option D, -1 or less than 1

Thus, the scatterplot demonstrates the strongest relationship between two quantitative variables is option C, "a graph has x on the x-axis, and y on the y-axis. Points increase loosely together".

Learn more about scatterplot here: brainly.com/question/6592115

#SPJ2

Answer this correctly I’ll give u brainalist + 10 points

Answers

Answer:

c

Step-by-step explanation:

Answer:

C. II and III

Step-by-step explanation:

Vertical angles are all start across from each other.

So:

∠3 and ∠6 are across from each other

∠2 and ∠5 are across from each other

∠1 and ∠4 are across from each other

The only option with at least two of the true statements above is C.

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
time after launch, x in seconds, by the given equation. Using this equation, find the
maximum height reached by the rocket, to the nearest tenth of a foot.
y = -16x2 + 136x + 57

Answers

Answer:

Maximum height = 346 feet

Step-by-step explanation:

Given that,

The height of the rocket, y in feet, is related to the  time after launch, x in seconds, by the given equation as follows :

[tex]y = -16x^2 + 136x + 57[/tex] .....(1)

We need to find the maximum height reached by the rocket. For maximum height,

Put dy/dt = 0

So,

[tex]\dfrac{d}{dt}( -16x^2 + 136x + 57)=0\\\\-32x+136=0\\\\x=\dfrac{136}{32}\\\\x=4.25[/tex]

No, put x = 4.25 in equation (1).

[tex]y = -16(4.25)^2 + 136(4.25)+ 57\\\\y=346\ feet[/tex]

So, the maximum height reached by the rocket is equal to 346 feet.

4. What is the circumference of a circle whose area is 81π cm squared?

Answers

Area = pi*r^2
Circumference = 2pi*r

Step 1: find the radius from area
81pi=pi*r^2
81=r^2
9=r

Step 2: plug in radius to the circumference equation

Circumference = 2pi*r

18pi is the answer, otherwise know as 56.52 as well.

Step-by-step explanation:

Let us assume R be the radius of circle We know that, area of circle = πR2 81πr2 = πR2 R = √81 r R = 9r Circumference = 2 πr = 2 π (9r) = 18πr

Please please help help

Answers

the answer is 17 because that’s how many players ran over 1 score

Answer:

17 players

Step-by-step explanation:

6 people scored 2

8 people scored 3

3 people scored 4

Show how you found the slope and y-intercept

Answers

Answer:

Slope: [tex]\frac{5}{2}[/tex]

y-intercept: 0

Step-by-step explanation:

First, find the slope. Use two points given to you. In this case, I will use the following:

(x₁ , y₁) = (2 , 5)

(x₂ , y₂) = (4 , 10)

Use the following equation:

slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the corresponding numbers to the corresponding variables:

slope (m) = [tex]\frac{10 - 5}{4 - 2}[/tex] = [tex]\frac{5}{2}[/tex]

Note the slope intercept form:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

Plug in the slope into m for the equation:

[tex]y = \frac{5}{2} x + b[/tex]

Choose a point to use to find b. In this case, I will use (2 , 5). Plug in 2 for x, and 5 for y:

[tex]5 = \frac{5}{2}(2) + b[/tex]

Simplify. Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other:

[tex]5 = \frac{5}{2}(2) + b\\5 = 5 + b\\5 (-5) = 5 (-5) + b\\b = 5 - 5\\b = 0[/tex]

Y-intercept: 0

Are the ratios 3:6 and 1:2 equivalent?

Answers

Answer:

yes these are equivalent bcz

3/6=1/2

Step-by-step explanation:

PlZ make me brainliest

Answer:

Yes

Step-by-step explanation:

3/6= 0.5

1/2= 0.5

Does this graph represent a function? Why or why not?
-10 -884
O A. Yes, because it passes the vertical line test.
O B. Yes, because it passes the horizontal line test.
C. No, because it is not a straight line.
D. No, because it fails the vertical line test.

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I think the correct answer is A

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-5.25 is shown inside the points
all the other answers are outside of the points, hope this helps !

12cm and 8 cm find the ratio and reduce them in term of lowest term​

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Answer:

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Step-by-step explanation:

at a clothing store, levi's jeans are on sale for 40% off. sales tax is 7%. which expression will calculate the total cost of levi jeans with an original price of x?​

Answers

Given:

Discount = 40%

Sales tax = 7%

To find:

The total cost of levi jeans with an original price of x.

Solution:

Let x be the original price of the jeans. Then the price after 40% discount is

[tex]Price=x-40\%\text{ of }x[/tex]

[tex]Price=x-\dfrac{40}{100}x[/tex]

[tex]Price=x-0.4x[/tex]

[tex]Price=0.6x[/tex]

The price after 7% of sales tax.

[tex]Price=0.6x+7\%\text{ of }0.6x[/tex]

[tex]Price=0.6x+\dfrac{7}{100}\times 0.6x[/tex]

[tex]Price=0.6x+0.042x[/tex]

[tex]Price=0.642x[/tex]

Therefore, the total cost  of the levi jeans with an original price of x is represented by the expression 0.642x.

A car dealer sells four model types: A,B,C,D. On a given week, this dealer sold 10 cars of model A, 5 of model B, 8 of model C and 3 of model D. The selling prices of each automobile are respectively $12,500, $11,800, $15,900 and $25,300. Represent the data using matrices and use matrix multiplication to find the total revenue.

Answers

me Q i did not know somebody Help My frann

If y = 0.5x + 1 and x = 2, what Is y?

Answers

Answer: 2

Explanation:
y = 0.5x + 1
y = 0.5(2) + 1
y = 1 + 1
y = 2

PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((

Answers

Answer:

Yes

Step-by-step explanation:

(3, 2) is a solution to the given system of linear equations.

x - 8y = 3 - 8*2 = 3 - 16 = - 13

16x - 16y = 16(x - y) = 16( 3 - 2) = 16*1 = 16

Answer this correctly with an explanation I’ll give u brainalist + 10 points

Answers

Answer:

option D

Step-by-step explanation:

Angle ADF and Angle FDE

ADF+ FDE

Answer:

D

Step-by-step explanation:

John was having a party he knows his bowl can hold 2/3 of a bag of Doritos.if he has 4 bags or Doritos how many bowls does he need

Answers

Step-by-step explanation:

2•4 =8

8/3 =2 2/3

answer : 3

Write the slope of a line that is parallel to the following line:

Answers

Answer:

y = 1/5x + 3

Step-by-step explanation:

To have a parralel line to another line, have the slopes of the lines be the same, just change the y- intecept. HOPE THIS HELPS!

13 The Lozano's chartered a boat over the holiday
weekend. The cost for the day was $350 plus the
6.5% sales tax. They also decided to tip their
guide 25% of the original cost of the boat rental.
What is the total amount they paid?

Answers

Answer:

$460.25

Step-by-step explanation:

350 + .065(350) + .25(350)

= 350 + 22.75 + 87.5

$460.25

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