Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-life of the substance? The half-life is:_______.
(A) Less than 600 years
(B) Between 600 and 700 years
(C) Between 700 and 800 years
(D) Between 800 and 900 years
(E) More than 900 years

Answers

Answer 1

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

[tex]A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years[/tex]

First, let us calculate the decay constant (k)

[tex]75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036[/tex]

Next, let us calculate the half-life as follows:

[tex]\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years[/tex]

Therefore the half-life is between 600 and 700 years


Related Questions

I need help with this one

Answers

Answer:

The first three

Step-by-step explanation:

A cashier worked an 8-hour day, and earned $58.00. The double number line shows the amount she earned for working different numbers of hours. For each question, explain your reasoning.



How much does the cashier earn per hour?

How much does the cashier earn if she works 3 hours? pls help me!!

Answers

Answer:

The cahier earns 7.25 an hour

and in three hours she will have 21.75

Answer:

Step-by-step explanation: IT Is The cashirs earns $7.25 each hour.She will have 21.7$

Suppose the manager of your local McDonalds tracks the

monthly sales of their new McBurger, Mini McBurger, and

Choco-Latte Shake. The data is listed below.

For January through December, the sales are as follows.

McBurger: 46, 63, 58, 77, 81, 102, 183, 197, 125, 111, 83, 218.

Mini McBurger: 23, 41, 35, 44, 62, 88, 95, 99, 108, 111, 98, 63.

Choco-Latte Shake: 88, 46, 39, 52, 67, 99, 189, 238, 188, 97,

51, 12

Create a matrix to display the data.

Answers

Answer:

Step-by-step explanation:

The question says "Create a matrix to display the data".

The are 3 products:

- McBurger   - Mini McBurger   - ChocoLatte Shake

The figures represent monthly sales for each product, in a given year. This means 12 figures for each product - represent the 12 months of the year.

These figures will appear on the matrix, with the horizontal arrangement representing each month of the year and the vertical arrangement representing each product's sales.

In that light, you'll have a 12 by 3 matrix.

[tex]\left[\begin{array}{ccc}46&23&88\\63&41&46\\58&35&39\\77&44&52\\81&62&67\\102&88&99\\183&95&189\\197&99&238\\125&108&188\\111&111&97\\83&98&51\\218&63&12\end{array}\right] 12 by 3 matrix[/tex]The first row represents sales in January, the second row represents sales in February, the third row represents sales in March, the fourth row represents sales in April, etcetera.

The first column represents sale of McBurger, the second column represents sale of Mini McBurger, the third column represents sale of Choco-Latte Shake.

the graph of linear function g is shown on the grid. What is the zero of g? (-8,3) (-3,-4.5)

Answers

Answer:

Zero of the function = (-6, 0)

Step-by-step explanation:

Let the equation of the function given in the graph is,

y = mx + b

where m = slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

b = y-intercept of the line

From the graph attached,

Slope of the line passing through (-8, 3) and (-3, 4.5) = [tex]\frac{-4.5-3}{-3+8}[/tex] = -1.5

y - intercept 'b' = -9

Therefore, equation of the line will be,

y = -1.5x - 9

Function representing this line will be,

g(x) = -1.5x - 9

Zeros of the given function will be,

g(x) = 0 Or x-intercept

-1.5x - 9 = 0

x = -6

Therefore, zero of the given function is (-6, 0).

A crew of highway workers paved1/4 mile in1//6 a hour. If they work at the same rate, how much will they pave in one hour?​

Answers

Answer:

1 1/2 mile

Step-by-step explanation:

In 1 hour they pave 6 times more what they paved in 1/6 of an hour.

6 * 1/4 mile = 6/4 mile = 3/2 mile = 1 1/2 mile

Help me with this question pleasee

Answers

Answer:

√23 = a

Step-by-step explanation:

/ab/²= /ac/²+/bc/² (Pythagoras theorem)

12² = a² +11²

144 = a² + 121

144 - 121 = a²

23 = a²

√23 = a

Sharon went bowling with her friends. She paid $3 to rent
her shoes and then $3.75 for each game (x) of bowling. She
spent a total of $18. How many games did she bowl?
WRITE YOUR EQUATION:
SOLVE:
SOLUTION:

Answers

Answer:

3 + 3.75x=18

subtract 3 from both sides

3.75x=15

divide by 3.75 on both sides

x=4

Step-by-step explanation:

The scatterplot and trend line show a positive correlation between advertising costs and sales.
Which two points can be used to find the slope of the trend line?

Point 1: ?
Point 2: ?

Answers

Answer:

Point 1: (6.4, 117)

Point 2: (6.6, 120)

Step-by-step explanation:

Answer:

Point 1: (6.4, 117)

Point 2: (6.6, 120)

Step-by-step explanation:

Sharee and her two sisters ate 3 5 of a pizza. How much of the pizza did each girl have? A) 1 3 B) 1 5 C) 2 15 D) 3 10

Answers

Sharee and her two sisters ate 3 /5 of a pizza. How much of the pizza did each girl have? A) 1 /3 B) 1/ 5 C) 2 /15 D) 3 /10

Answer:

B) 1/ 5

Step-by-step explanation:

Number of persons = Sharee and her two sisters = 3 persons

Quantity of pizza eaten = 3/5

Each person ate:

3 persons = 3/5 pizza

1 person = x pizza

Cross Multiply

3 × x = 3/5 × 1

x = 3/5 × 1/3

x = 3/5 ÷ 3

x = 3/5 × 1/3

x = 1/5

Hence, each person ate 1/5 pizza.

Whatbis the slope of a line that is perpendicular to the line y= 2x-6? A. -2
B. 2 C. 1/6 D. -1/2

Answers

Answer:

D. -1/2

Step-by-step explanation:

When a line is perpendicular to another line the slope will be the exact opposite. For example line A = y = 3x + 5 the line perpendicular to it will be -1/3x.

So -1/2 is the slope of your perpendicular line.

Use the number line to answer the question. Each tick represents 1 unit.







Which of the following points are neither negative nor positive? Select all that apply.


H
M
L
J
P
K
N
Please help

Answers

Answer:

M is niether Negitive or positive

Step-by-step explanation:

Because it is on the zero

mark me brainliest plz

Answer:

Answer:

M is niether Negitive or positive

Step-by-step explanation:

Because it is on the zero

Step-by-step explanation:

-6(x+4) what this answer simplified.

Answers

Answer:

-6x-24

Step-by-step explanation:

all you have to do is multiply, so -6*x and -6*4 and since -24 is a negative the equation is going to be subtracting

Answer:

Step-by-step explanation:

PLEASE HELP!!! Chloe is working two summer jobs, landscaping and clearing tables. She must work no less than 12 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours landscaping, l and the number of hours clearing tables, c, that Chloe can work in a given week.

Answers

Answer:

got u homie

Step-by-step explanation:

Answer:

l +c _> 12

Step-by-step explanation:

A marathon runner travels 9/2 miles in 1/2 hour what is the unit rate

Answers

Answer:

9/2:1/2

Step-by-step explanation:Here's the answer

The Tigers’ first play when they had possession of the ball went for -3 yards. Did the Tigers gain or lose yards on that play? How many yards did they gain or lose?

Answers

Hi I’m Abbi, pls brainiest me! The answer is loose yards and -3 hope this helps :)

Answer:

вы молодец и увас всё получилось

What is |-24| + |13| =?

Answers

Answer:

37

Step-by-step explanation:

just add the two numbers like they are not negative.

Read 3 integer numbers from the user; these numbers represent the lengths of 3 straight lines. From the 3 lengths, determine whether a triangle can be formed with the corresponding lines. If it is possible to form a triangle, determine whether the triangle is a right triangle or not. The rules to be used are: 1. To form a triangle where all lines’ ends meet (form vertices), the sum of the lengths of two sides must be greater than the length of the third side. This short video illustrates this concept: How to determine if the three sides make up a triangle. 2. Per the Pythagorean theorem: in a straight triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. 3. The user can enter the lengths of each line in any order, i.e.: you may not assume that the first length is the longest or the smallest or the middle value.

Answers

Answer:

Written in Python

print("Enter three sides of a triangle: ")

length = []

for i in range(0,3):

    inp = int(input(""))

    length.append(inp)    

length.sort()

if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:

    print("Triangle")

    if length[2]**2 == length[0]**2 + length[1] **2:

         print("Right Angled")

    else:

         print("Not Right Angled")

else:

    print("Not Triangle")

Step-by-step explanation:

This line prompts user for sides of triangle

print("Enter three sides of a triangle: ")

This line declares an empty list

length = []

The following iteration gets user input

for i in range(0,3):

    inp = int(input(""))

    length.append(inp)    

This line sorts user input

length.sort()

The following if condition checks if user input is triangle

if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:

The following is executed is the if condition is true

    print("Triangle")

The following if condition checks if user input forms a right angled triangle

    if length[2]**2 == length[0]**2 + length[1] **2:

         print("Right Angled")

    else:

         print("Not Right Angled")

This is executed if user input is not a triangle

else:

    print("Not Triangle")

A square is removed from the right hand corner

Answers

Answer:

C im pretty sure

Step-by-step explanation:

Because the square taken out has a 4x4 area which is 16 and the area of the whole square used to be 14x14 which is 196 and if u subtract 16 from that you get 180

I need help please and thank you in advance

Answers

im pretty sure it’s g(x) = x^2 - 3

2+2=4 because 2 fingers and then another 2 fingers

Answers

Answer:

yes

Step-by-step explanation:

Answer:

yes? That's right. ummmm lol

In ΔFGH, the measure of ∠H=90°, the measure of ∠F=18°, and GH = 9.4 feet. Find the length of HF to the nearest tenth of a foot.

Answers

Answer:

28.9

Step-by-step explanation:

tan (18) = 9.4/x times x

x times tan(18) = 9.4 / tan(18)

            tan(18)

        crosses out.

On a calculator do 9.4/

                             tan(18).

x = 28.9

         

what is the Quotient: 3/4divided1/4

Answers

Answer:

3

Step-by-step explanation:

The living room of Ann's house is a square with an area of 121 square feet. What is the length of each side of the foyer

Answers

Answer:

30.25

Step-by-step explanation:

121 divided by 4 is 30.25

Which statement describes how to geometrically divide a complex number, z, by a second complex number, w?
O Scale z by the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the modulus of w, then rotate counterclockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate counterclockwise by the argument of w.

Answers

Answer: C

Step-by-step explanation:

I just took the quiz and I got it right

Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

What is Complex number?

In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit

What is Modulus of a complex number?

Modulus of the complex number is the distance of the point on the argand plane representing the complex number z from the origin

Given,

Complex number z divides by a second complex number w

To divide a complex number a complex number then multiply the conjugate with the numerator and the denominator of the complex fraction

From the given statements Scale of z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w

Hence, Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

Learn more about Complex number and Modulus of a complex number here

https://brainly.com/question/19554199

#SPJ2

Help ill give brainliest
Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below.

4(x – 1) – x = 3(x + 5) – 11
4x – 4 – x = 3x + 15 – 11
3x – 4 = 3x + 4
How can her partial solution be interpreted?

A. The equation has one solution: x = 0.
B. The equation has one solution: x = 8.
C. The equation has no solution.
D. The equation has infinite solutions.

Answers

The equation has B. no solution

Answer:

C. no solution

Step-by-step explanation:

3x – 4 = 3x + 4

3x-3x=4+4

0=8

which is not possible.

So, it has no solutions.

he production of pipes has a mean diameter of 3.25 inches and a standard deviation of .15 inches. The shape of the distribution is approximated by a normal distribution since approximately an equal number of parts are above or below average, and most parts are very close to the mean value. A part will be discarded is it has a diameter of greater than 3.5 inches or less than 3 inches. What proportion of parts are discarded from the production line

Answers

Answer:

The probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525

Step-by-step explanation:

[tex]Mean = \mu = 3.25 inches[/tex]

Standard deviation = [tex]\sigma = 0.15 inches[/tex]

We are supposed to determine the probability that a randomly chosen part has diameter of 3.5 inches or more

[tex]P(Z \geq 3.5)=1-P(z<\frac{x-\mu}{\sigma})\\P(Z \geq 3.5)=1-P(z<\frac{3.25-3.5}{0.15})\\P(Z \geq 3.5)=1-P(z<-1.67)[/tex]

Refer the z table for p value

[tex]P(Z \geq 3.5)=1-0.0475\\P(Z \geq 3.5)=0.9525[/tex]

Hence  the probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525

What is the value of y?
B
60°
12
12
ro
60°
А
12 to 60

Answers

answer 60°

solve:180°-(60°+60°)

180°-120°

60°##

write an equation in standard form for the line that is parellel to the graph of -8x=5-4y and has a y-intercept -0.5

A x+.05=0.25

B 10x-5y=2

C 4x-2y=1

D 2x-y=1

Answers

9514 1404 393

Answer:

  C  4x -2y = 1

Step-by-step explanation:

The y-intercept of the offered choices can be found by dividing the constant by the y-coefficient.

  A: not in standard form (coefficients are not integers)

  B: 2/-5 = -2/5 . . . not -1/2

  C: 1/-2 = -1/2 . . . a good candidate

  D: 1/-1 = -1 . . . not -1/2

w(t) = 3t – 1; t = 5

Answers

I’m not sure if your asking for the solution, but Hope this helps!

You are given $893 in one, five, and ten dollar bills. There are 165 bills. There are twice as many five dollar bills as there are ones and tens combined. How many bills of each type are there?

Answers

Given:

You are given $893 in one, five, and ten dollar bills.

There are 165 bills.

There are twice as many five dollar bills as there are ones and tens combined.

To find:

How many bills of each type are there?

Solution:

Consider the number of bills of one dollars, five dollars and ten dollars are x, y and z respectively.

According to the question,

Number of bills : [tex]x+y+z=165[/tex]         ...(1)

Total amount : [tex]1x+5y+10z=893[/tex]         ...(2)

Condition : [tex]y=2(x+z)[/tex]     ...(3)

Equation (3) can be written as

[tex]\dfrac{y}{2}=x+z[/tex]       ...(4)

Substituting [tex]x+z=\dfrac{y}{2}[/tex] in (1), we get

[tex]\dfrac{y}{2}+y=165[/tex]

[tex]\dfrac{3y}{2}=165[/tex]

[tex]3y=330[/tex]

[tex]y=110[/tex]

Substituting y=110 in (4), we get

[tex]x+z=\dfrac{165}{2}[/tex]

[tex]x+z=55[/tex]

[tex]x=55-z[/tex]       ...(5)

Substituting y=110 and x=55-z in (2), we get

[tex](55-z)+5(110)+10z=893[/tex]

[tex]55-z+550+10z=893[/tex]

[tex]9z+605=893[/tex]

[tex]9z=893-605[/tex]

[tex]9z=288[/tex]

Dividing both sides by 9, we get

[tex]z=32[/tex]

Substituting z=32 in (5), we get

[tex]x=55-32[/tex]

[tex]x=23[/tex]

Therefore,

One dollar bills = 23

Five dollars bills= 110

Ten dollars bills = 32

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