Mathematics High School

The radioactive isotope 226Ra has a half-life of approximately 1599 years. There are 80g of 226Ra now.
(1) How much of it remains after 1,700 years? (Round your answer to three decimal places.)
(2) How much of it remains after 17,000 years? (Round your answer to three decimal places.)

Answers

Answer 1

1) 0.080 grams of 226Ra would remain after 17,000 years.

2) 44.000 grams of 226Ra would remain after 1,700 years.

To calculate the remaining amount of a radioactive isotope after a certain time, we can use the formula:

[tex]N(t) = N₀ * (1/2)^{(t / T_{ \frac{1}{2}} )}[/tex]

Where:

N(t) is the remaining amount of the isotope after time t.

N₀ is the initial amount of the isotope

[tex]T_{ \frac{1}{2} }[/tex] is the half-life of the isotope

Let's calculate the remaining amount of 226Ra for the given time periods:

(1) After 1,700 years:

[tex]N(t) = 80g * (1/2)^(1700 / 1599) \\ N(t) = 80g *(1/2)^(1.063165727329581) \\ N(t) ≈ 80g * 0.550 \\ N(t) ≈ 44.000g[/tex]

(rounded to three decimal places)

Therefore, approximately 44.000 grams of 226Ra would remain after 1,700 years.

(2) After 17,000 years:

[tex]N(t) = 80g * (1/2)^(17000 / 1599) \\ N(t) = 80g * (1/2)^(10.638857911194497) \\ N(t) ≈ 80g * 0.001 \\ N(t) ≈ 0.080g [/tex]

(rounded to three decimal places)

Therefore, approximately 0.080 grams of 226Ra would remain after 17,000 years.

Learn more about radioactive isotopes here,

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Related Questions

So is 0.147 a rational number?

Answers

Answer:

Yes because it is a terminating decimal.

Step-by-step explanation:

A can of soup has the shape of a cylinder.
The diameter of the base of the can is
3.4 inches, and the height of the can is
4.5 inches. What is the volume of the can
rounded to the nearest tenth of a cubic
inch?

Answers

Answer:

Step-by-step explanation:

Height h = 4.5 inches

Radius r = 3.4/2 = 1.7 inches

Area of base = πr² = 2.89π square inches

Volume of cylinder = πr²h = 2.89π4.5 = 13.0 cubic inches

Answer:

The answer is 40.8

Step-by-step explanation:

The volume of a cone equals the area of a circle multiplied by the height

[tex]v = \pi \times {r}^{2} \times h \\ = 3.14 \times 1.7 \times 1.7 \times 4.5 \\ = 40.8[/tex]

What is 73 x 4 + 13?

Answers

Answer:

73 x 4 + 13 is 305

Answer:

305

explaination:

73 x 4 = 292

292 + 13 = 305

30 people liked Brand X. This is 20% of the people in a survey.
a) How many people were there in the survey?
b) What percent of the people did not like Brand X?
c) How many people did not like Brand X?

Answers

a) 150 people
b) 80%
c) 120 people

The area of a rectangle is 2x^2-11x+15 square feet. The length of the rectangle
is 2x - 5 feet. What is the width of the rectangle?
A) W = x + 5
B) W = x-1
C) W = x-3
D) W = 2x-5

Answers

Answer:

A

Step-by-step explanation:

Determine a series of transformations that would map Figure G onto Figure H. I need help ASAPPP PLEASEEE

Answers

Answer:

A translation followed by a rotation would do it if they are congruent, which they should be.

Step-by-step explanation:

A transformation to move the corresponding points of each shape to the other, and a rotation to rotate the shape until the shapes map onto each other.

3/10 divided by 2/5?

Answers

Answer:

3/4 is your answer

Step-by-step explanation:

Can someone pls help me with this?? I’m in a rush it’s due at 11:59 pm..pls help! And show work pls and thx

Answers

Answer:

D. 4.5

Step-by-step explanation:

<3

Answer:the answer will be D)4.5

Step-by-step explanation:

five yellow m&m for every 3 green. How many green m&m if there are 95 yellow ?
PLEASE HELP

Answers

For this problem, you need to set up a proportion. For every three green there are five yellow, so your first fraction is 3/5. For the second fraction, plug 95 into the denominator. You should have an equation of 3/5 = x/95, x being the number of green. After cross multiplying (95(3)/5), you should get an answer of 57 green. Hopes this helps!

Given A=
What is the value of matrix B if A + B = C

Answers

Answer:

A

Step-by-step explanation:

We know that 8+3x= x

solve for x

8= -2x

-4 =x

The only answer that has -4 is A

A store pays $11 for a set of spoons and marks the price up by 30%. What is the amount of the markup?

Answers

Answer:

[tex]\$3.3[/tex]

Step-by-step explanation:

Given:

Amount paid by a store for a set of spoons = $11

Percentage increase in price = 30%

To find: amount of the mark up

Solution:

To find amount of the mark up, find 30% of (amount paid by a store for a set of spoons)

Amount of the mark up = [tex]\frac{30}{100} (11)=\$3.3[/tex]

Need help ASAP pls help

Answers

Answer: The correct answers are B, D, and F.

Step-by-step explanation: B is correct because 8 x 5 is 40, and 40-5 is less than or equal to 36. C is correct because if you plug in 41/8, the answer is 36. Anything higher than 41/8 is greater than 36.  F is correct because 5 is a solution and 5 is less than 41/8. Therefore, the correct answers are B, D, and F.

A computer at an electronics store costs $2,893 The tax is 6% how much money will you spend total?

Answers

Answer:

$3066.58

Step-by-step explanation:

$2893 x 1.06= $3066.58

Hope this helps!

If you know the answer plz help

Answers

Answer:

I think that it will be (6)

Madison is starting her own sewing business. Madison has calculated that she needs to earn $840 per week to support her family. If she knows she will only be able to work 75 hours per week, what is the minimum amount of dollars per hour that she will need to charge her customers?

Answers

Answer:

$11.20 per hour

Explanation:

x = dollars per hour

75x = 840

x = 11.20

5 examples of theorems in math. :")

Answers

Theorem 1. Pythagoras Theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Theorem 2. Thales Theorem
If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio.

Theorem 3. Euclid’s Theorem
Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proved by Euclid in his work Elements.

Theorem 4. Fundamental Theorem of Arithmetic
The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes.

Theorem 5. Ceva’s Theorem
Ceva's theorem is a theorem of affine geometry, in the sense that it may be stated and proved without using the concepts of angles, areas, and lengths (except for the ratio of the lengths of two line segments that are collinear). It is therefore true for triangles in any affine plane over any field.

Please help ASAP I need this right now

Answers

Answer:

You have to look closely and you will find The letters D and C on the bottom of the triangle. D is kinda on the right and C is on the left. Hope this helps.

Step-by-step explanation:

what is the distance between-2 and -5 on the number line?

Answers

Answer:

3

Step-by-step explanation:

on a number line, we use the absolute values to find the difference.

the absolute value of -2 is 2

the absolute value of -5 is 5

5-2=3

so, the distance between -2 and -5 on a number line is 3

Me han descontado 10 euros en unos pantalones que estaban rebajados un 20 porciento .¿cuantos costaban los pantalones ?¿cuanto ha pagado por ellos ?

Answers

Answer:

los pantalones costaban 50 euros, y ha pagado 40 euros

The hotdog stand at a baseball game sells hotdogs for $3.50 each. The amount, D dollars, Mr. Moore paid for the hotdogs is directly proportional to the number of hotdogs, H, he buys. Identify the constant of proportionality and write a direc

Answers

Answer:

D α H

k = D/H

k = 3.50

Step-by-step explanation:

Amount paid, D is directly proportional to the number of hotdogs, H

D = $3.50 per hot dog

D = $3.50 is directly proportional to 1 hotdog

Hence,

D α H

D = kH

k = proportionality constant

H = 1

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k = 3.50

k = D/H

Proof that 1^√2 = 1 is true

Answers

Answer:

1^sqrt(2) = 1 is always true

Step-by-step explanation:

Step-by-step explanation:

it is always 1 because the teacher said.....lol

6*10^5 is how many times as large as 3*10^3

Answers

Answer: 200 times larger


Explanation (6*10^5)/(3*10^3)=2*10^2

2*100=200

The other answer was wrong because in order of operations (PEMDAS), exponents come before multiplication.

1. Does the system of linear equations shown below have a solution? Explain.

Answers

Answer:

hb      Step-by-step explanation:

You are going on an expedition to dig for dinosaur fossils. In digging you come across a small trunk left by another archeologist. In the trunk is a paper that lists how deep you need to dig to reach dinosaur fossils. Unfortunately, something spilled on part of the paper and it is damaged.
Using your knowledge of mathematics, find the missing numbers in the
chart. Write a generalization or rule to determine any number of feet you
must dig given the number of years.

If the Jurassic period was 200 million years ago, how deep would you need
to dig at this location to uncover fossils of that era? Explain why your
answer is or is not reasonable.

Answers

Answer:

200,000 feet to dig

Step-by-step explanation:

We use a ratio for this problem

30,000         200,000,000

-----------   =   ---------------------

30                        x

200,000,000 * 30

----------------------------  = 200,000 feet to dig

30,000

This answer is reasonable because 200,000,000 years ago was a long time ago so then the person must dig a reasonable amount of dirt. So then 200,000 feet is reasonable.

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Answers

Answer:

it should be D

Step-by-step explanation:

Because shes going back home.

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A. (7, 2)

B. (2, [tex]\frac{1}{2}[/tex])

C. (2, –1)

D. (2, –10)

Answers

for this problem the answer is B

Which side lengths represent the sides of a right triangle?
A)
1, 1, 2
B)
2, 3,5
C)
5, 12, 13
D)
7, 23, 25

Answers

Answer: the answer is C

Step-by-step explanation:

My friend is a math teacher

Hope this helps

A newsstand seller sold a total of 68 magazines and newspapers, which brought in a total of $199 on a certain day. Newspapers sell for $2 per copy and magazines sold for $5 per copy. How many magazines were sold on that day?

Answers

Answer:

21

Step-by-step explanation:

Using inequality to solve this question, we say

Let the total number of newspapers sold be x

Let the total number of magazines sold by y

x + y = 68

Suppose 1x = $2 and 1y = $5, then

2x + 5y = $199

Solving both as a simultaneous equation, we get that

2(68 - y) + 5y = $199

136 - 2y + 5y = $199

136 + 3y = $199

3y = 199 - 136

3y = 63

y = 63/3

y = 21

Then solving for x, we have

x + 21 = 68

x = 68 - 21

x = 47

Therefore, a total of 21 magazines were sold that day

The perimeter of a rectangular plot of land is 250 meters if the. Length of one side of the plot is 40 meters what is the area of the plot in square meters?

Answers

Answer:

3400 meters squared

Step-by-step explanation:

So if you know that one side 40 another has to be to. So those 2 sides add up to 80. 250-80= 170. Next, you divide 170 by 2 and get 85. Then you just multiply 40 by 85.

Hi I need help can someone simplify this?

Answers

The simplified expression is c^5

Answer:

c^5

Step-by-step explanation:

:)

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