A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest tenth. Show your work.

please help

Answers

Answer 1

Answer:

The half-life of this radioactive substance is of 8.6 months.

Step-by-step explanation:

Exponential decay of an amount:

The equation that models an amount after t units of time, subject to exponential decay, is given by:

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

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

A radioactive substance decays to 30% of its original mass in 15 months.

This means that [tex]A(15) = 0.3A(0)[/tex]. We use this to find 1 - r.

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

[tex]0.3A(0) = A(0)(1-r)^{15}[/tex]

[tex](1-r)^{15} = 0.3[/tex]

[tex]\sqrt[15]{(1-r)^{15}} = \sqrt[15]{0.3}[/tex]

[tex]1 - r = (0.3)^{\frac{1}{15}}[/tex]

[tex]1 - r = 0.9229[/tex]

So

[tex]A(t) = A(0)(0.9229)^t[/tex]

Determine the half-life of this radioactive substance to the nearest tenth.

This is t for which A(t) = 0.5A(0). So

[tex]A(t) = A(0)(0.9229)^t[/tex]

[tex]0.5A(0) = A(0)(0.9229)^t[/tex]

[tex](0.9229)^t = 0.5[/tex]

[tex]\log{(0.9229)^t} = \log{0.5}[/tex]

[tex]t\log{0.9229} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.9229}}[/tex]

[tex]t = 8.6[/tex]

The half-life of this radioactive substance is of 8.6 months.


Related Questions

What is its equation in slope-intercept form ?

Answers

Answer:

Candice

Step-by-step explanation:

Solve the quadratic equation graphically using at least two different approaches. When necessary, give your solutions to the nearest hundredth.
x squared + 12 x + 11 = 0
a.
x = -11 or x = -1
c.
x = 10 or x = -3
b.
x = 1 or x = 6
d.
x =0 or x = -6



Please select the best answer from the choices provided


A
B
C
D

Answers

The answer is C i think

Answer:

answer a

a.

x = -11 or x = -1

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Answer:

A

Step-by-step explanation:

MArk me brainliest! pls :)

Can someone help me with this work ???

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Answer:

bottom left

Step-by-step explanation:

bottom left bc it says shade in 36% and the shaded squares give up a total of 36 squares

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Order
Translation
Reflection
Rotation

HELP ME PLEASE! 20 POINTS!

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Answer:

1 no answer=1/100

2 no answer=1/100

3 no answer=100

Step-by-step explanation:

1: 1/100
2: 1/100
3: 100

los trabajadores de una mina se encuentran a 20 metros bajo tierra .Si excavan 3 metros desde alli suben otros 8 metros para coger una caretilla a que altura estaba la carretilla

Answers

Answer:

carretilla

Step-by-step explanation:

la carretilla se encontraba a unos 18 metros de altura

If 3/4 of an inch on a map is equal to 45 miles , what does 1 inch represent?

Answers

Answer:

60 miles

Step-by-step explanation:

if 45 = 3/4

divide 45 by 3 = 15

15 * 4 = 60

Numerical expressions for add 12 to 8 then multiply by 5

Answers

Answer:

5(8+12)

Step-by-step explanation:

Tessellations

Determine whether the given figure tessellates the plane.

a. yes
b. no

Please select the best answer from the choices provided

Answers

Answer:

A. Yes

Step-by-step explanation:

I calculated it logically

Yes the given figure with triangular tessellates the plane.

All triangles tessellate.

The picture works because all three corners (A, B, and C) of the triangle come together to make a 180° angle - a straight line.

This property of triangles will be the foundation of our study of polygon tessellations, so we state it here: The sum of angles of any triangle is 180°.

Yes, the given figure tessellates the plane.

Hence, Yes the given figure tessellates the plane.

To learn more on triangles click:

https://brainly.com/question/2773823

#SPJ7

Randy wants to save $21 to buy a basketball he saved $7 each week which array represents the number of weeks randy needs to save $21

Answers

Answer:

he will have to save $7 for 3 weeks to get $21

Step-by-step explanation:

The probability of tails of a weighted coin is 0.58. The number of tails is noted each of the 25 times the coin is tossed. If this procedure is repeated 150 times, what type of distribution is simulated

Answers

Answer:

It is a  sampling distribution of the sample proportion for which n = 150 and p = 0.58

Step-by-step explanation:

Given -

Probability of tails of a weighted coin = 0.58

Number of tail is noted each 25 times

Repetition of procedure = 150 times

mean =  p = 0.58

SD = Sqrt {p(1-p)/n}

Substituting the given values, we get -

SD = Sqrt {0.58(1 – 0.58)/150}

=  0.04029

It is a  sampling distribution of the sample proportion for which n = 150 and p = 0.58

Answer:

The options are not given so these are the options:

- A binomial distribution with n = 25 and p = 0.58

- A binomial distribution with n = 2 and p = 0.58

- A sampling distribution of the sample proportion with n = 25 and p = 0.58  

- A sampling distribution of the sample proportion with n = 150 and p = 0.58

- There is not enough information to determine the distribution.

Step-by-step explanation:

The answer is - A binomial distribution with n = 25 and p = 0.58.

I got it right on my test.

Good luck!

a) Work out (8 x 10*) * (2 x 10-)
Give your answer in standard form.
b) Work out (6 x 10?) + (3 x 10°)
Give your answer in standard form.

Answers

Answer:

A. 16 × 10¯⁷

B. 2 × 10⁷

Step-by-step explanation:

A. 8×10¯³ × 2×10¯⁴

Recall:

Mᵃ × Mᵇ = Mᵃ⁺ᵇ

Thus,

(8×10¯³) × (2×10¯⁴) = (8×2) × 10¯³ ⁺ ¯⁴

= 16 × 10¯³¯⁴

= 16 × 10¯⁷

Therefore,

(8×10¯³) × (2×10¯⁴) = 16 × 10¯⁷

B. (6×10²) ÷ (3×10¯⁵)

Recall:

Mᵃ ÷ Mᵇ = Mᵃ¯ᵇ

Thus,

(6×10²) ÷ (3×10¯⁵) = (6/3) × 10² ¯ ¯⁵

= 2 × 10²⁺⁵

= 2 × 10⁷

Therefore,

(6×10²) ÷ (3×10¯⁵) = 2 × 10⁷

the parabola y=-x^2+12x-11 has an axis of symmetry of x=6. which of the following represents its range?
1) y>-11
2)y<25
3)y<6
4)y>10

(all of the ">/<" are underlined ones)

Answers

Answer: 1) y>-11

Step-by-step explanation:

Estimate the solution to the following system of equations by graphing. 3x + 5y = 14
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Answers

Step-by-step explanation:

hope helps u

have a nice day

Write the length of the radius if the diameter is 6 centimeters

Answers

Answer:

3 centimeters

Step-by-step explanation:

The diameter is 2 times the radius, meaning 6/2 is 3.

Answer:

3cm (This is because diameter is double the radius)

A bag contains seven red marbles and three blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. Find the probability that both the first and second marbles are red.

Answers

Answer:

Step-by-step explanation:

A bag contains 8 red marbles, 3 blue marbles and 7 green marbles.

Total = 18 marbles.

Probability of drawing three red marbles = probability of drawing one red without replacement + probab of drawing another without reeplacement + probab of drawing a third without replacement.

Probability of drawing three red marbles = 8/18 + 7/17 + 6/16 = 0.4444 + 0.4118 + 0.3750 = 1.2312.

Borrows 15,200 for 10 months at an annual rate of 4.55%. What is the interest owed after 10 months

Answers

the answer in the photo check it

A is 150m 2 miles long Directional signs are posted along the trail every 1/3 mile. How many signs are posted along the trail?

Answers

Cjdjjsjvjrksowowkakfjdjkakskek

The length of a rectangle is 10 more than the width. If the
area is 24 square inches, what are the dimensions?

Answers

Answer:

Dimensions : L = 12 inches, Width = 2 inches

Step-by-step explanation:

Let width be w

Let length be w + 10

Area = length x width

24 = w x (w + 10)

[tex]24 = w^2 + 10w\\\\w^2 + 10w - 24 = 0\\\\w^2 +12w -2w -24 = 0\\\\w(w+12) -2(w+12) = 0\\(w-2)(w+12)=0 \\w = 2 , -12[/tex]

Since width is a side of a rectangle , it cannot be negative. so w = 2 inches .

Therefore , length = w + 10 = 12inches

Which answer choice below best describes the number (22 + 6)

Answers

Answer:

You FAILED to include any choices.

Step-by-step explanation:

can you add a picture?

Marcus bought a booklet of tickets to use at the amusement park. He used 50% of the tickets on rides, 1/3 of the tickets on video games, and the rest of the tickets in the batting cage. Marcus says he used 10% of the tickets in the batting cage. Do you agree? Explain.

Answers

Answer:

No, i dont agree as 1/3 in percentage is 33%

33+50=88

100-88=12

Meaning that he used 12% of the tickets in the batting cage.

Which expressions are equivalent to -3(t - 7 + 5t + 8)?

Answers

Answer: It's B, C, F Hope it helps!

Step-by-step explanation: -3(t-7+5t+8) collect like terms -3(6t+1)

which would give you -18t-3

It C to because 1. expand by distributing terms -(18t+9)+6

2. Remove parentheses -18t-9+6

3. Collect like terms -18t+(-9+6) simplify and it would give you -18t+3  it also F because I collect like terms (-3t-15t)+(21-24) and you simplify and that would give you -18t-3 as well can you make me brainliest bye!

Use the picture to answer the questions.

What is the value of x in the figure?

Answers

Answer: b

Step-by-step explanation:

10 + 50=60

60+30=90

You are correct the answer is B

Answer : C


60+30=90

30 degrees was already taken up so if it went up 60 degrees more then it would be 90 degrees.

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Answers

Answer:

Step-by-step explanation:

1.  (a) 24 X 3/4= 18 multiplication

you have to multiply to get a smaller answer since you are using a fraction.

2. (a) 24 / (-3/4)= -32 division

you have to divide to get a bigger number than started since you are using a fraction

3. (A) 12-15= -3 subtraction

when you subtract a bigger number than the first number you end up normally with a negative number

4. (a) 12 -(-15) subtraction

when you subtract with a negative number you distribute so the two negatives cancel out and it become an addition sign. (if you look at it the two negatives and the parenthesis looks like an addition sign (+)

5. (A) -18 / (-3/4) =24 division

when you divide two negative values you will always get a positive answer. And again dividing a fraction will get you a bigger answer.

helppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

character

Step-by-step explanation:

I think Character because character is basically position and who you're playing as

Which problem can be solved using the equation below?

Answers

Answer:

Mr. peter puts 24 students into groups of 8. How many groups are there?

Step-by-step explanation:

Whenever the word "groups" is used, it typically means to divide. Because we see the word "groups", it would be reasonable to assume that you will be dividing something.

HELP HELPP PLEASEEEE!

Answers

the length is b 12 !

Answer:

Step-by-step explanation:

volume of pyramid with square base=a^2(h/3)

84=a^2*7/3

84*3/7=a^2

252/7=a^2

36=a^2

[tex]\sqrt{36[/tex]=a

6=a

therefore length=6

Can Some One Help Me. Plz

Answers

Answer:

$16,000

Step-by-step explanation:

This is because 5 is the thousand place and the hundredth place is more than 5 so, it rounds up (to 16000)

Feel free to mark this as brainliest :D

Answer:

16,000

Step-by-step explanation:

15,827

8 is greater than 4 so you round up

5 turns to 6 and everything to the right turns to 0

So the answer is 16,000

Find the
area of the parallelogram.

Answers

The area of this parallelogram is:

10 unit²

Answer:

10 units

Step-by-step explanation:

2x5

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