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

a savings account increases from $200 to $212. what is the percent increase of the savings account?

Answers

Answer:

6% increase

Step-by-step explanation:

To find the percent increase, divide the difference by the original:

12/200

= 0.06

Multiply this by 100:

0.06(100)

= 6

So, the percent increase was 6%

Madeline has a headache and takes 500
milligrams of a pain reliever. The brand
of pain reliever she takes has a half-life
of 2.5 hours. Which function could be
used to describe the amount of pain
reliever remaining in Madeline's system
at any given time?
lol

Answers

Answer:

f(x) = 500(1/2)^x

Did this end up in the wrong category lol

If a central angle measures 87°, then its arc will measure _____.

twice as much
the same
half as much

Answers

The same!

Hope This Helps! <3

Good Luck Studying ^-^

Find the value of the expression a--b* for a = 2 and b= 1

Answers

Answer:

3

Step-by-step explanation:

Given the expression a --b

Given that

a = 2

b = 1

Substitute into the expression

a--b

= 2 --1

= 2 - (-1)

= 2 + 1

= 3

Hence the required value is 3

6.833 + 3.594 + 1.369 nearest whole number

Answers

Answer:

12

Step-by-step explanation:

You add 6.833 + 3.594 + 1.369, which equals 11.796, and then you round up to 12.

Answer:

12

Step-by-step explanation:

1 1

6.833

3.594

+1.369

11.796

round the whole number to get 12

Simplify the expression: (-4x^10y^-8)^2

Answers

Answer:

(-8x)(20y)-16

Step-by-step explanation:

(-4x10y-8)2

distribute the two to all terms inside the parentheses

(-8x)(20y)-16

you cannot simplify this further

please help find the perimeter

Answers

Answer:

Perimeter of the given figure = 28 units

Step-by-step explanation:

Perimeter of the given figure = Length of AB + Length of BC + Length of CD + Length of DE + Length of EF + Length of FG + Length of GH + Length of AH

Length of AB = 4.5 units

Length of BC = 2 units

Length of CD = 2 units

Length of DE = 4 units

Length of EF = 5.5 units

Length of FG = 1.5 units

Length of HG = 1 units

Length of AH = 7.5 units

Perimeter of ABCDEFGH = 4.5 + 2 + 2 + 4 + 5.5 + 1.5 + 1 + 7.5

                                          = 28 units

How do I solve 1 1/3 × 2 2/4 is steps?​

Answers

Answer:

40/12 or 3 1/3

Step-by-step explanation:

To multiply mixed numbers, first change any mixed number to an improper fraction. Then multiply the numerators together and the denominators together

1 1/3 as an improper fraction is 4/3 and 2 2/4 as an improper fraction is 10/4.

4*10=40

3*4=12



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


Answers

Answer:

C

Step-by-step explanation:

Evolution is where organisms have developed over time from simple to complex. Therefore we can rule out D because older rock layers should have simple organisms and A because new rock layers should have more complex organisms. The previous organisms will be unlike those of today, therefore the correct answer is C.

Can someone help mee

Answers

Answer:

Check pdf

Step-by-step explanation:

HELP NEED NOW... Look at picture

Answers

Answer:

the answer is 2

Step-by-step explanation:

Which table of ordered pairs represents a proportional relationship? I’m a timer please hurry thank you so much
х
-3
-4
-5
у
3
2
1
x
-1
-3
-5
у
1
3
5
-2.
-4
-6
y
1-5
1-7
-9
х
--2
-3
-4
у
0
-1
1-2
I

Answers

Answer:

I'd say the second one. the others are all showing a linear relatiknship

Please help me! Thank you!

Leo wants to paint a mural that covers a wall with an area of 1,440 square feet. The height of the wall is 2/5 of its length. What is the length and the height of the wall?

Answers

Answer:

decide on your destiny

Step-by-step explanation:

i need you to decide on your own destiny  

Answer:

24 feet height, 60 feet length

PLZ HELP DUE IN 8 MINS PLZ HELP

Answers

Answer: for number 1 its negative 14

Step-by-step explanation:

A psychology professor assigns letter grades on a test according to the following scheme. A: Top 9% of scores B: Scores below the top 9% and above the bottom 56% C: Scores below the top 44% and above the bottom 20% D: Scores below the top 80% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 79.3 and a standard deviation of 8.4. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answers

Answer:

You get a D if you have a grade between 66 and 72.

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Scores on the test are normally distributed with a mean of 79.3 and a standard deviation of 8.4.

This means that [tex]\mu = 79.3, \sigma = 8.4[/tex]

D: Scores below the top 80% and above the bottom 6%

So between the 6th and the 20th percentile.

6th percentile:

X when Z has a pvalue of 0.06. So X when Z = -1.555.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.555 = \frac{X - 79.3}{8.4}[/tex]

[tex]X - 79.3 = -1.555*8.4[/tex]

[tex]X = 66.2[/tex]

Rounds to 66

20th percentile:

X when Z has a pvalue of 0.2. So X when Z = -0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.84 = \frac{X - 79.3}{8.4}[/tex]

[tex]X - 79.3 = -0.84*8.4[/tex]

[tex]X = 72.2[/tex]

Rounds to 72

You get a D if you have a grade between 66 and 72.

find the missing lengths of the sides

Answers

Answer:

a=9, c=19

Step-by-step explanation:

Aight so basically in 30, 60, 90 triangles there is a formula for the sides

the hypotenuse(the longest side)=2a

The tiny side (the smallest side)=a

and the middle child =[tex]a\sqrt{3}[/tex]

Based on that we see that a is 9

and since c=2a then it's 18

A=9 C=19
Explanation: I took this test and got it right

Which choice shows 1/4 of 8

Answers

Answer:

there is no picture so I dont know what i have to do..

Circle A has a radius of 5 units. Circle B has a radius of 3 inches. Which best represents the area of the figure below?

Answers

A 107.

Since the formula is (5x5)3.14+(3x3)3.14≈107

200 students attend Ridgewood Junior High School. 25% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?

Answers

sorry est un site Web Internet spécialement conçue 4

50 students.

25% of 100 is 25 and 200 is twice as much as 100. So then double the 25 to 50.

You can also set up a proportion of 25%/100% = ?/200 and cross multiply and divide.

Another way is to manipulate the numbers. Instead of 25% of 200 you can say 200% of 25. 200% is the same as saying twice as much as the number so what is twice the number 25? 50!

In ΔJKL, j = 520 inches, k = 730 inches and l=640 inches. Find the measure of ∠K to the nearest degree.

Answers

Answer:

It’s 56.7

Step-by-step explanation:

Fudisks

What is a angle called when two angles share a common side and a common vertex

Answers

They are called “Adjacent Angles”

Answer:

Adjacent Angles

Step-by-step explanation:

Adjacent angles are two angles that have a common vertex and a common side but do not overlap. They share the same vertex and the same common side.

Use calculus to evaluate (lhopitals rule)
lim x>infinity x^2 - ln(2/x)/3x^2 + 2x

Answers

Answer:

1/3

Step-by-step explanation:

[tex][x^2 - ln(2/x)]/[3x^2 + 2x]\\[/tex]

∞/∞

[tex]\frac{d}{dx}[x^2-ln(2/x)] =2x+\frac{1}{x}\\ \frac{d}{dx}[3x^2+2x]=6x+2\\\frac{2x+\frac{1}{x}}{6x+2}[/tex]

Also ∞/∞

[tex]\frac{d}{dx}[2x+\frac{1}{x}]=2-1/x^2\\\frac{d}{dx}[6x+2]=6\\\\[/tex]

[tex]\lim_{x \to \infty} \frac{2-\frac{1}{x^2} }{6}\\=\frac{2}{6} \\=\frac{1}{3}[/tex]

Which is a perfect square?
61
62
63
65

Answers

Answer:

None of them really,

A perfect square is a number that can be expressed as the product of two equal integers...which is not seen here.

Th closest perfect square that could be possible would be 64, but thats not an option, so go with none.

Helpppp!!! Pleaseeee

Answers

Answer:I’m pretty sure it’s 90

Step-by-step explanation:

Answer:

tan 60=√3/t

t=√3/√3=1 is your answer

when given a choice of a favorite pet, 32% of children choose a dog and 24% of children choose a cat. if 175 kids were asked what their favorite pet was, how many would choose a cat?

Answers

Answer:

42

Step-by-step explanation:

24% of 175 = 0.24 * 175 = 42

Answer:

175 x .24= 42 kids

...............

A $7.00 item is marked down by 10%.
What is the new cost of the item?
Round to two decimals if needed.
$

Answers

Answer:

6.3

Step-by-step explanation:

Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)

Answers

Better quality would help, have a good day/night

What is the area of the triangle?
6
2
3

Answers

Answer:

6

Step-by-step explanation:

Find the area of both triangles inside the bigger triangle and add them together.

Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:

a² + b² = c²

2² + b² = 3²

4 + b² = 9

5 = b²

2.2 ≈ b

Calculate the area of the smaller triangle:

1/2(bxh)

1/2(2 x 2.2)

1/2(4.4)

2.2

Calculate the area of the bigger triangle:

We know that the longer leg is 3.8 units because we were able to subtract the length of the smaller triangle's leg from 6.

1/2(bxh)

1/2(2 x 3.8)

1/2(7.6)

3.8

Add both areas to find the area of the largest triangle:

3.8 + 2.2 = 6

Suppose that the water level of a river is 34 feet and that it is receding at a rate of
0.5 foot per day. Write an equation for the water level, L, after d days. In how many
days will the water level be 26 feet? -3x+4y=y

Answers

The answer is C I just took the test

Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)

Answers

Answer:

28

Step-by-step explanation:

(a+b)h/2  

(6+8)4 / 2

14 x 4 / 2

= 28

I hope im right!!

Answer=28cm^2

6+8=14
14/2=7
7x4=28

Area of trapezium= ( a+b/2 )xh
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