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,

https://brainly.com/question/18640165

#SPJ4

Related Questions

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.

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

Hi I need help can someone simplify this?

Answers

The simplified expression is c^5

Answer:

c^5

Step-by-step explanation:

:)

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

Need help ASAP I’m on an exam there is a timer

Thankss + BRAINLIST only for correct answer
(question in the picture )

Answers

Answer:

it should be D

Step-by-step explanation:

Because shes going back home.

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

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!

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

3/10 divided by 2/5?

Answers

Answer:

3/4 is your answer

Step-by-step explanation:

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 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!

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.

What is 73 x 4 + 13?

Answers

Answer:

73 x 4 + 13 is 305

Answer:

305

explaination:

73 x 4 = 292

292 + 13 = 305

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]

So is 0.147 a rational number?

Answers

Answer:

Yes because it is a terminating decimal.

Step-by-step explanation:

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.

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.

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

Answers

Answer:

hb      Step-by-step explanation:

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

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.

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]

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

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

Find the solution of y = –2x + 3 for x = 2.


A. (7, 2)

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

C. (2, –1)

D. (2, –10)

Answers

for this problem the answer is B

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.

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

3.50 = k

k = 3.50

k = D/H

If you know the answer plz help

Answers

Answer:

I think that it will be (6)

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:

Other Questions
The Jennings Group reacquired 4 million of its shares at $65 per share as treasury stock. Last year, for the first time, Jennings sold 2 million treasury shares at $66 per share.By what amount will Jennings' retained earnings decline if it now sells the remaining 2 million treasury shares at $62 per share? Create an abstract class called shape with pure virtual members called calcperimeter and calcarea. a stock is currently selling for $99.75 and is expected to sell for $105.71 in 1 year. if the company pays a dividend of $0.71 what is the stock's hpr? Microwaves (as used in microwave ovens, telephone transmission, etc.) are electromagnetic waves with wavelength of order 1 cm. Consider a microwave with wavelength of 1.25 cm. What is the energy of the microwave photon in eV? The so-called 3-K radiation from outer space consists of photons of energy k_BT, where T = 3K. What is the wavelength of this radiation? which of the folowing statements is not correct about a marekt in equilibrium Using only the periodic table arrange the following elements in order of increasing ionization energy:bismuth, polonium, radon, astatineLowest1234highest What is the equilibrium constant (Kp) at 45 C for the reaction below, given the thermodynamic values: AGf (O3(g)) = 163.4 kJ/mole and AGf (O2(g) = 0 kJ/mole 203(g) 3 029) 131.9 O 1.93 x 1057 O 4.80 x 1053 O 1.07 x 10-57 Read the article "The 17 February 2006 rock slide-debris avalanche at Guinsaugon,Philippines: a synthesis" by Guthrie et. Al. A copy of the article is attached in theend part of this module. Write notes describing the event and the conditions thathave led to its occurrence. Construct a reflection paper regarding the article. Yourpaper should include the following:1. Summarized version of your notes including details. 2. Explanation of your point of view regarding the article. 3. Relationship between the possible causes of the event In at least three complete paragraphs, fully explain two Eastern beliefs and practices that we do not have in the West and their importance. In the first two paragraphs, identify and explain the importance of two Eastern beliefs/practices, and clarify how they have helped shape Eastern culture. These beliefs/practices can be social or religious in nature. Support your analysis with at least two correctly cited quotes from two different texts in Unit 6.In the third paragraph, discuss whether these beliefs/practices can/should be integrated into Western culture. Explain how the West would be impacted by adopting these beliefs and practices. a thymectomy accomplished via a median sternotomy approach is performed in a client with a diagnosis of myasthenia gravis. the nurse creates a postoperative plan of care for the client that would include which intervention? Number these interactions in the order each first occurs in protein synthesis in bacteria. Hydrogen bonding between two RNA molecules to form three complementary base pairs. Interactions between a polypeptide and a consensus base sequence in DNA. Covalent bonding of an amino acid to an RNA molecule. 4 Covalent bonding of two amino acids by a ribozyme. Covalent bonding of two ribonucleotides. Hydrogen bonding between complementary bases in DNA and RNA. Research has shown that schizophrenia is influenced by biological factors. Specifically, brain imaging studies have shown that in people with schizophreniaa. the frontal and occipital lobes show a dramatic increase in activity.b. both the amygdala and the hippocampus are not very active.c. the brain's ventricles become smaller over time.d. the amount of overall brain tissue is reduced. Which of the following are the numbers of pins that can be found on DIMM modules used in desktop motherboards? (Choose two.)A. 168B. 180C. 184D. 200E. 204F. 232G. 240 give a geometric description of span v1 v2 for the vectors v1 = 15 9 -6 and v2 = 25 15 -10A. Span{vy. Vy) is the set of points on the line through v, B. Span {v,,v} is the plane in R that contains v., Vz, and 0. C. Span {v, V2) cannot be determined with the given information. D. Span {v, v} is RP money held for making everyday market purchases represents the: Enter the missing numbers in the boxes to complete the table of equivalent ratios. Select all of the key points that justify why oxidation of a fatty acid produces more ATP per carbon than glucose.C-C and C-H bonds are more reduced than C-O bondssimilar electronegativities of bonding atoms in C-C and C-H bonds means oxidation of these bonds is possiblethe process of glucose oxidation takes longer than fatty acid oxidationmore ATP is used in glucose oxidation as compared to fatty acid oxidationa fatty acid is mostly C-C and C-H bonds When a person exercises, muscle contractions produce lactic acid. Moderate increases in lactic acid can be handled by the blood buffers without decreasing the pHpH of blood. However, excessive amounts of lactic acid can overload the blood buffer system, resulting in a lowering of the blood pHpH. A condition called acidosis is diagnosed if the blood pHpH falls to 7.35 or lower. Assume the primary blood buffer system is the carbonate buffer system described in Exercise 81. Calculate what happens to the [H2CO3]/[HCO3][H 2 CO3 ]/[HCO 3 ]ratio in blood when the pHpH decreases from 7.40 to 7.35 . The profit margins of two different companies (a grocery store and a jewelry store) are as follows: Gross profit margin Profit margin Company. A 12.4% 5.8% Company B 65.8% 5.8% Which statement below is true? Company A generates net income of 12.4 cents on every dollar of sales. Company B is more profitable than Company A. For every dollar of sales, Company Bearns 65.8 cents in profit after covering the cost of its product Company A is likely the jewelry stor For a given set of rectangles, the length varies inversely with the width. In one set of these rectangles, the length is 76 inches, and the width is 2 in. For this set of rectangles, calculate the width of a rectangle whose length is 4 inches