A radioactive isotope has a half-life of 1,920 years. Let f(t)
be the amount of isotope, in milligrams, that is present after t years. If the sample originally contained 21 milligrams, write an equation modeling this situation.
F(t)=

Answers

Answer 1

The equation that models the given situation is: f(t) = 21e^(-0.000361)t

How to solve an exponential decay function?

We can model this situation with an exponential decay function.

f(t) = Pe^(rt)

Where:

f(t) = amount of isotope

P = starting amount

r = growth rate

t = time

Let's assume that there is 1 mg of our isotope. Thus,in 1920 years, we will have 1/2 mg. Thus:

(1/2) = (1)e^(1920r)

Take the natural log of both sides to bring the exponent down and to cancel out the e

ln(1/2) = ln(e^(r(1920))

ln(1/2) = r(1920)

ln(1/2)/1920 = r

r = -0000361

Thus, we have:

f(t) = Pe^(-0.000361)t

Plug in 21 for P to get:

f(t) = 21e^(-0.000361)t

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Related Questions

Gina and Marty are selling tickets for the school dance. On Monday, they sold 15 tickets, on Tuesday 23, on Wednesday 20, and on Thursday 32. What was their average daily income if each ticket cost $2.00?

Answers

Answer:

$45

Step-by-step explanation:

15×2=30

23×2=46

20×2=40

32×2=64

30+46+40+64=180

180÷4=45

Average=45

Answer:

Their average daily income would be 45 dollars a day.

Step-by-step explanation:

To solve this, add the 15 tickets, 23, 20, and 32 tickets from Monday to Thursday. This should get you a total of 90 tickets. Since each ticket cost 2 dollars, multiply the 90 by 2. This should get you 180. TO find the average, you must divide the total(180) by the amount of days(4) that passed. This should get you 45.

Answer:

45$

Bian wants to write the integers 1 to 9 in the nine boxes shown so that the integers in any three adjacent boxes add to a multiple of 3. In how many ways can she do this?​

Answers

Answer: To satisfy the given condition, we need to place the numbers in the boxes in a way that the sum of any three adjacent boxes is divisible by 3.

We can divide the boxes into three groups as follows:

Group 1: Boxes {1, 4, 7}

Group 2: Boxes {2, 5, 8}

Group 3: Boxes {3, 6, 9}

For any three boxes in a group, the sum of their contents must be divisible by 3. We can place any multiple of 3 in the middle box of each group, and the other two boxes will have to be filled accordingly.

Step-by-step explanation:

For Group 1:

If we place 3 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 1.

If we place 6 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 5}, {1, 8}, {4, 5}, {4, 8}, {7, 5}, {7, 8}. This gives us another 6 possible ways to fill the boxes in Group 1.

For Group 2:

If we place 3 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 2.

If we place 6 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 8}, {1, 5}, {4, 8}, {4, 5}, {7, 8}, {7, 5}. This gives us another 6 possible ways to fill the boxes in Group 2.

For Group 3:

If we place 3 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 9}, {2, 6}, {5, 9}, {5, 6}, {8, 9}, {8, 6}. This gives us 6 possible ways to fill the boxes in Group 3.

If we place 6 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 6}, {2, 3}, {5, 6}, {5, 3}, {8, 6}, {8, 3}. This gives us another 6 possible ways to fill the boxes in Group 3.

Therefore, the total number of ways to fill the boxes is:

6 x 6 x 6 x 6 = 1296.

Thus Bian can write the integers 1 to 9 in these ways.

hope it helps...

Q1 ? Help Robert is 7 ½ years old. How many months old is he? ​

Answers

Answer:

Step-by-step explanation:

If Robert is 7 1/2 months old you need to multiply 7 1/2 by 12 because there are 12 months in a year.  

7x12=84  

1/2x12=6

6+84=90

4x-5 2x+7 Find the value of x

answers should be from
27
37
47
57​

4x-5 2x+7 Find the value of xanswers should be from 27374757

Answers

To find the value of x that satisfies the given equations:

4x - 5 = 2x + 7

First, let's simplify the equation by combining like terms:

4x - 2x = 7 + 5

2x = 12

Next, divide both sides of the equation by 2 to solve for x:

x = 12 / 2

x = 6

Therefore, the value of x that satisfies the equation is 6. None of the provided answer options (27, 37, 47, 57) are equal to 6.

Regs.
Spinner A and Spinner B below are each to be spun once.
0 18
O 12
6
Spinner A
5
2
4
00
D
3
20 of 21
If the pointer cannot land on a line, how many different outcomes of a number and a color are possible?
v
Spinner B
Yellow
Brown
12 13
Red

Answers

Answer:

Step-by-step explanation:

Regs.

Spinner A and Spinner B below are each to be spun once.

0 18

O 12

6

Spinner A

5

2

4

00

1) (b + a) = 4; use a = 1 and b = 3

2) c(b + b); use b = 1 and c = 5

3) 4+ pm; use m = 4 and p =3

4) 5+ pm; use m = 4 and p = 2

5) m(p + 2); use m = 5 and p = 2

6) h+j²; use h = 1 and j = 4

7) y-(x - 5); use x = 5 and y = 6

8) 4xy; use x = 5 and y = 2

9) n(p + 3); use n = 2 and p = 2

10) y +x+x; use x = 3 and y=5

11) 6+ a-b; use a = 4 and b = 4

Answers

The equations will be solved by putting the values of the variables in the bracket.

How to calculate the values?

1. (b + a) = 4; use a = 1 and b = 3

( 1 + 3) = 4

2) c(b + b); use b = 1 and c = 5

5(1 + 1)

= 5 × 2 = 10

3) 4+ pm; use m = 4 and p =3

= 4 + (4 × 3)

= 4 + 12

= 16

4) 5+ pm; use m = 4 and p = 2

= 5 + (2 × 4)

= 5 + 8

= 13

5) m(p + 2); use m = 5 and p = 2

= 5(2 + 2)

= 5 × 4

= 20

6) h+j²; use h = 1 and j = 4

= 1 + 4²

= 17

7) y-(x - 5); use x = 5 and y = 6

= 6 - (5 - 5)

= 6 - 0

= 6

8) 4xy; use x = 5 and y = 2

= 4 × 5 × 2

= 40

9) n(p + 3); use n = 2 and p = 2

= 2(2 + 3)

= 10

10) y +x+x; use x = 3 and y=5

= 5 + 3 + 3

= 11

11) 6+ a-b; use a = 4 and b = 4

= 6 + 4 - 4

= 6

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PLZ ANSWER ASAP PLZ

factor the polynomial -2x^3-4x^2-6x​

Answers

Answer:

-2x(x^2+2x+3)

Step-by-step explanation:

-2x^3-4x^2-6x

=-2x(x^2+2x+3)

Find the missing probability.


P(B)=1/4P(AandB)=3/25P(A|B)=?

Answers

The missing probability is P(A|B) is 12/25 if P(B) is 1/4P and (A and B) is 3/25P.

P(B) = 1/4

P(A and B) = 3/25

The conditional probability is used to find the P(A|B):

P(A|B) = P(A and B) / P(B)

Conditional probability is defined as the number of possible outcomes from a given event based on the previous outcomes of the events.

By substituting the given values in the given probability, we get:

P(A|B) = (3/25) / (1/4)

Divide the fraction and multiply it with its reciprocal:

P(A|B) = (3/25) * (4/1)

P(A|B) = 12/25

Therefore, we can conclude that the missing probability is P(A|B) is 12/25.

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The complete question is:

Find the missing probability.

P(B)=1/4P

(AandB)=3/25P

P(A|B)=?

You are running a fuel economy study. One of the cars you find is blue. It can travel 28 1/2 miles on 1 1/4 gallons of gasoline. Another car is red. It can travel 28 4/5 on 4/5 gallons of gasoline. What is the unit rate for miles per gallon for each​ car? Which car could travel the greater distance on 1 gallon of​ gasoline?

Answers

If you are running a fuel economy study. the unit rate for miles per gallon for each​ car is 22.8 miles and 23.04 miles and the fastest car is Red car.

How to find the unit rate?

Units rate = Distance /Time

Blue car

Unit rate = 28 1/2 miles ÷ 1 1/4 gallons of gasoline

Unit rate = 28.5miles ÷ 1.25 gallons of gasoline

Unit rate = 22.8 miles

Red car

Unit rate = 28 4/5 miles ÷  4/5 gallons of gasoline

Unit rate = 28.8miles ÷ 0.8 gallons of gasoline

Unit rate = 23.04 miles (Fastest)

Therefore the unit rate for each​ car is 22.8 miles and 23.04 miles and the fastest car is Red car.

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Determine the length of DE.

Determine the length of DE.

Answers

It is 5 ! :) because since the triangle ABC = DEF The measurements will be the same. The formula for finding the DC (hypothenuse) is a squared + b squared = c squared


Plug it in-
3*3=9
4*4=16
9 + 16 =25
Find the square root of 25 which brings the answer to 5 :)

What is the result of 5 divided by one-fifth? 5 fraction bars. Each bar is labeled 1 with 5 boxes labeled one-fifth underneath. StartFraction 1 Over 25 EndFraction One-fifth 1 25

Answers

Answer:

25

Step-by-step explanation:

Answer:

it is 25

Step-by-step explanation:


Sasha Cohen does a triple toe loop (rotating 1080 degrees) in 1.5 s. What is her average angular speed during this jump
360°/s
3.0 rad/s
12.6 rad/s
720 rad/s

Answers

9514 1404 393

Answer:

  12.6 rad/s

Step-by-step explanation:

1080 degrees in 1.5 seconds is an angular rate of ...

  (1080°)/(1.5 s) = 720 °/s

There are π radians in each 180°, so this angular speed is ...

  720 °/s = 4×180 °/s = 4×π rad/s ≈ 12.6 rad/s

Sasha's average angular speed is 12.6 rad/s.

What is the average rate of change of g over the interval [-1 4]

What is the average rate of change of g over the interval [-1 4]

Answers

Answer:

your answer will be -1.2

Step-by-step explanation:

hope it helps you

have a great day

Need help with the provided questions

Need help with the provided questions
Need help with the provided questions

Answers

The graph is in the right slot

Can Someone help with this​

Can Someone help with this

Answers

Answer:

x        y

-2      5

-1 .      1

3 .       1

-1        -2

Step-by-step explanation:

in 1 just put in

x        y

-2      5

-1 .      1

3 .       1

-1        -2

Kyle buys a bag of cookies that contains 4 chocolate chip cookies, 9 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies. What is the probability that Kyle randomly selects a sugar cookie from the bag, eats it, then randomly selects a peanut butter cookie

Answers

Multiply all them then stubbtrac to number

The function f(x)=−3x+2 is defined over the domain −1

Answers

The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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WWW DoNow Simplifying Exponential Expressions Simplify 1. 7ab2ab 2, - Byg

WWW DoNow Simplifying Exponential Expressions Simplify 1. 7ab2ab 2, - Byg

Answers

Simplify the radical expression.

\(\begin{gathered} 7a^5b^{-4}2a^6b=14a^{5+6}b^{1-4} \\ =14a^{11}b^{-3} \end{gathered}\)

So answer is 14a^(11)b^(-3).

solve x^2-12x+36=44 by factoring!!
please help asap with work shown :)

Answers

x^2 - 12x + 36 is a perfect square trinomial and can be written as (x-6)(x-6).

(x - 6)^2 = 44.

Take the square root of both sides to get...

x - 6 = ±√44 (Always make the square root + or - when you square root)

Add 6 to both sides...

x = √44 + 6

x = -√44 + 6

These are the 2 values of x.

You can also write it to be -0.633 and 12.633. (Once you round.)

Given m∥n, find the value of x

Given mn, find the value of x

Answers

Answer:

x=55

Step-by-step explanation:

2x+6+x+9=180

3x=165

x=55

:]

√3 + (4 + √x + 3)² / 6 = 3

3 + (4 + x + 3) / 6 = 3

Answers

Answer: x = 1

Step-by-step explanation:

Discussion Topic
Explain 2 different ways we use rates outside of class. Explain 2 ways we use
percentages outside of class. Be specific and explain why understanding rates and
percentags is important.

Discussion TopicExplain 2 different ways we use rates outside of class. Explain 2 ways we usepercentages

Answers

Two ways we use rate out of class

interest ratesexchange rates

Two ways we use percentages outside of class

Discounts and salestax rates

Two different ways we use rates outside of class are:

Interest rates: Interest rates are used in financial transactions such as loans, mortgages, and investments. Understanding interest rates is important to make informed decisions about borrowing money or investing in stocks and bonds.

Exchange rates: Exchange rates are used when converting one currency into another. They affect international trade, travel, and investment. Understanding exchange rates is important for businesses and individuals who deal with international transactions.

Two ways we use percentages outside of class are:

Discounts and sales: Percentages are commonly used in advertising to promote discounts and sales. Understanding percentages is important to evaluate whether a discount or sale is a good deal or not.

Tax rates: Tax rates are expressed as a percentage of income or value of goods and services. Understanding tax rates is important for individuals and businesses to calculate their tax obligations and make informed financial decisions.

Understanding rates and percentages is important because they are used in many real-world situations. Knowing how to calculate and interpret rates and percentages can help individuals make informed decisions related to personal finance, investments, and business transactions. It also helps individuals understand and evaluate advertisements and government policies that involve rates and percentages.

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hi so im really bad at math im just wondering how do u become good at math​

Answers

Answer:

Break Down Complex Problems.

Master The Basic Math Skills.

Understand The Topic Before Moving On To Another.

Know The Importance Of Number Sense.

Have A Regular And Consistent Practice.

Establish A Routine.

Focus On Understanding New Concepts.

Create A Practice Math Test.

3. The graph shows the relationship between
the distance a taxi travels and the cost
of the taxi ride. Is the relationship
proportional? Explain. 2-5 additional practice

Answers

Yes, The distances a taxi travels and the cost of the taxi ride Is the relationship proportional

What is a Proportional Relationship?

The idea of proportion is closely related to those ratios and fractions. Comparing two values with the same unit is what makes up a ratio. A ratio enables us to assess an item's size in relation to another quantity. Two ratios or two fractions are comparable according to the equation of proportion. In other words, when two ratios are equal, they are said to be proportionate. By applying mathematical operations to both sides of the ratio, we discovered that a ratio may be stated in a number of different ways.

In the given question we have to state the relationship between the distance of a taxi and the cost of a taxi ride.

As we know Distance is proportional to speed. and we know that as much we travel our traveling costs will also increase.

That means The fare of the taxi is directly proportional to distance.

Hence, The distance a taxi travels and the cost of the taxi ride is directly proportional to each other.

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caculate the following multiplication
\(67 \times 12\)

Answers

Answer:

804

Step-by-step explanation:

Just use a calculator.

804 ==“”” omg use calculator

The statement says: You find a partial report of a sturdy that investigated the relationship between self esteem and depression. You see they conducted a one-tailed Pearson’ se correlation with 52 people, and that the r = -0.25, calculate and report the coefficient of determinationWhat is the coefficient of determination of person’s correlation with 52 people and that the r = -0.25What is the degrees of freedom?

Answers

Given:

Sample size, n = 52

correlation coefficient, r = -0.25

Let's find the coefficient of determination of the person's correlation.

To find the coefficient of determination, we have:

coefficient of determination = r²

Thus, we have:

coefficient of determination = r² = -0.25² = 0.0625

Therefore, the coefficient of determination is 0.0625

To find the degrees of freedom, apply the formula:

df = n - 2

Where

df is the degrees of freedom

n is the sample size = 52

Hence, we have:

df = 52 - 2 = 50

The degrees of freedom is = 50

ANSWER:

• Coefficient of determination = 0.0625

,

• Degrees of freedom = 50

Help I’ll give BRAINLIEST !!!!

Help Ill give BRAINLIEST !!!!

Answers

Answer:

AC

Step-by-step explanation:

Answer:

-3, 2 & 3, -2

Step-by-step explanation:

If you plot the equation, the line goes through a and c

A recent poll found that 35% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that all three will be worried about aggressive drivers on the road?

Answers

The probability that all three people surveyed is an independent probability and the calculated probability is 0.1225

The probability a surveyed driver is worried = 35%

P(worried) = 0.35

Number of people surveyed = 3

Since the probability of being worried is independent ;

Probability = P(A) × P(B) × P(C)

The probability that all 3 surveyed are worried :

P(worried) × P(worried) × P(worried) (0.35 × 0.35 × 0.35) = 0.1225

Therefore, the probability that all three people surveyed are worried is : 0.1225

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10% of 25,000
\(\huge\red{\boxed{\tt{\colorbox{black}{///////////////:}}}}\:\)​

Answers

Answer:

0.04

Step-by-step explanation:

Answer:

2,500

Step-by-step explanation:

10% = \(\frac{10}{100} = \frac{1}{10}\)

\(25000\times\frac{1}{10}=2500\)

2. A shipping box should weigh 1.0 pound. If
there is a 10% error on the weight, what is the
range of acceptable weight?
A. 1.0 - 1.10
B. 0.9 - 1.0
C. 1.10 - 1.20
D. 0.9 - 1.10

Answers

Answer:

10% of 1 is .1

D. .90 - 1.10 lb

Answer:

The answer is D

Step-by-step explanation:

The answer is D because you don't know if the added 10% or took away 10%

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