At the beginning of an experiment, a scientist has 120 grams of radioactive goo. After 135 minutes, her sample has decayed to 3.75 grams. Find an exponential formula for G ( t ) G(t) , the amount of goo remaining at time t t .

Answers

Answer 1

Answer:

[tex]G(t) = 120e^{-0.0257t}[/tex]

Step-by-step explanation:

Amount of substance:

The amount of the substance after t minutes is given by:

[tex]G(t) = G(0)e^{-kt}[/tex]

In which G(0) is the initial amount and k is the decay rate.

At the beginning of an experiment, a scientist has 120 grams of radioactive goo.

This means that [tex]G(0) = 120[/tex], so:

[tex]G(t) = G(0)e^{-kt}[/tex]

[tex]G(t) = 120e^{-kt}[/tex]

After 135 minutes, her sample has decayed to 3.75 grams.

This means that [tex]G(135) = 3.75[/tex].

We use this to find k. So

[tex]G(t) = 120e^{-kt}[/tex]

[tex]3.75 = 120e^{-135k}[/tex]

[tex]e^{-135k} = \frac{3.75}{120}[/tex]

[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]

[tex]-135k = \ln{\frac{3.75}{120}}[/tex]

[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]

[tex]k = 0.0257[/tex]

So

[tex]G(t) = 120e^{-0.0257t}[/tex]


Related Questions

a test has 10 multiple-choice questions with 6 choices each, followed by 35 true/false questions. if a student guesses on each equation, how many ways can he answer the questions on the test

Answers

Answer:

6¹⁰×2³⁵

Step-by-step explanation:

he has 6 choices for the first multiple choice question.

and for each of those he had again 6 more choices to answer the second question. 6×6 = 36

so, for all 10 multiple choice questions he answer in

6¹⁰ different ways = 60466176 ways

then there are 35 true/false questions, which are Bausch again multiple choice questions but with only 2 options instead of 6.

so we get 2³⁵ different possibilities. a huge number.

and they're possible for each of the 60466176 ways of the multiple choice part.

so, in total we have

6¹⁰×2³⁵ different answer possibilities.

What is the minimum perimeter of a rectangle with an area of 625 mm^2

Answers

130 mm^2 your welcome

On a recent trip to the convenience Store you picked up 4 gallons of milk 4 bottles of water and 5 snack size bags of chips your total was $28.35 if a bottle of water cost twice as much as a bag of chips and a gallon of milk cost $2.10 more than a bottle of water how much does each item cost​

Answers

Answer:

The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each

Step-by-step explanation:

I think Im right

Hi I need help :( I can’t figure these out

Answers

Step-by-step explanation:

I do don't either ok wjshjddshsj

Answer:

Part A: A scatter diagram (Also known as scatter plot, scatter graph, and correlation chart) is a tool for analyzing relationships between two variables for determining how closely the two variables are related. One variable is plotted on the horizontal axis and the other is plotted on the vertical axis. The dots in a scatter plot not only report the values of individual data points, but also patterns when the data are taken as a whole. Identification of correlational relationships are common with scatter plots.

Part B: There are three types of correlation: positive, negative, and none (no correlation).

Part C: A scatter plot is a graph of points that show the relationship between two different pieces of data, while a line graph is a graph that shows information via a connected line.

Please mark me brainliest:))

Solve d – 0.31 ≥ 1.87 Question 1 options: A) d ≤ 2.18 B) d = 2.18 C) d ≥ 1.56 D) d ≥ 2.18

Answers

Answer:

D) d ≥ 2.18

Step-by-step explanation:

d – 0.31 ≥ 1.87

d >_ 1.87 + 0.31

d >_ 2.18

Power Function:

Analyze and model the power function: Exercise 1

(Correctly identify the function and later use it to answer the questions asked, including the development and the answer)

Answers

Answer:

The function is:

f(x) = axⁿ

According to data in the table we have:

f(1) = 3 ⇒ a(1)ⁿ = 3 ⇒ a*1 = 3 ⇒ a = 3f(2) = 12 ⇒ 3*2ⁿ = 12 ⇒ 2ⁿ = 4 ⇒ n = 2

Since we found the values of a and n, the function becomes:

f(x) = 3x²

The number of infected to the tenth day:

f(10) = 3*10² = 300

Of the travelers arriving at a small airport, 60% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 50% are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.

What is the probability that the person
a. is traveling on business?
b. is traveling for business on a privately owned plane?
c. arrived on a privately owned plane, given that the person is traveling for business reasons?
d. is traveling on business, given that the person is flying on a commercially owned plane?

Answers

Answer:

a) 0.55 = 55% probability that the person is traveling on business

b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.

c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.

d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

50% of 60%(major airlines)

70% of 20%(privately owned airplanes)

80% of 100 - (60+20) = 20%(comercially owned airplanes). So

[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]

0.55 = 55% probability that the person is traveling on business.

Question b:

70% of 20%, so:

[tex]p = 0.7*0.2 = 0.14[/tex]

0.14 = 14% probability that the person is traveling for business on a privately owned plane.

Question c:

Event A: Traveling for business reasons.

Event B: Privately owned plane.

0.55 = 55% probability that the person is traveling on business.

This means that [tex]P(A) = 0.55[/tex]

0.14 = 14% probability that the person is traveling for business on a privately owned plane.

This means that [tex]P(A \cap B) = 0.14[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]

0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.

Question d:

Event A: Commercially owned plane.

Event B: Business

80% of those arriving on other commercially owned planes are traveling for business reasons.

This means that:

[tex]P(B|A) = 0.2[/tex]

0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.

solve the following ineuality -1+6(-1-3x) >-39-2x

Answers

Step-by-step explanation:

(=) 5 (-1-3x) >-39-2x

(=) -5-15x > -39-2x

(=) -13x > -34

=> x < 34/13

True or false? The polynomial 3xy + 4z - 8 is a trinomial.

Answers

Answer:

False is the answer.

Step-by-step explanation:

answer is False.

Answer:

True.

Step-by-step explanation:

A trinomial is an algebraic expression consisting of 3 terms. The terms in this instance are: 3xy, 4z, and -8.

Express 18 hours to 2 days in its lowest term

Answers

Answer:

1 : 3

Step-by-step explanation:

We know that 1 days is 24 hours

2 days = 2*24 = 48 hours

16 hours : 48 hours

Divide each by 16

16/16 : 48/16

1 : 3

Answer:

[tex]3 : 8[/tex]

Step-by-step explanation:

[tex]18h : 2d \\ 18h : 2 \times 24h \\ 18 :48 \\ 3 : 8[/tex]

A telephone call arrived at a switchboard at random within a one-minute interval. The switch board was fully busy for 10 seconds into this one-minute period. What is the probability that the call arrived when the switchboard was not fully busy

Answers

Answer:

50/60 = .8333=  83.33%

Step-by-step explanation:

The probability that the call arrived when the switchboard was not fully busy is 0.75.

What is Normal Distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Given:

Here X follows uniform distribution with parameter a and b.

Where,

a = 0 and b = 1.

Then,

The density function of Y is given by:

P( 15 < Y ≤ 60)

or, P( 0.25 < Y ≤ 1)

So,  P( 0.25 < Y ≤ 1) = [tex]\int\limits^{1}_{0.25}{f(y) \, dy[/tex]

                                = [tex][y]^1 _ {0.25}[/tex]

                                = (1- 0.25)

                                = 0.75

Hence, The probability that the call arrived when the switchboard was not fully busy is 0.75.

Learn more about Normal Distribution here:

https://brainly.com/question/29509087

#SPJ2

3)
Write an inequality for the graph below. If necessary, use
<= for < or >= for.



Kinda stuck and running out of time

Answers

Answer:

Step-by-step explanation:

In a certain year Congress debated a bill. A poll of 1000 Americans indicated 401 opposed 293 favored 306 not sure. What is the probability that random person was in favor

Answers

So actually you have 100%
401 + 239 + 306 = 1000

Now 293 from the 1000 is favored,
So in pregnant is 293/1000 = 0.293
That’s also the probability to random person is favor (or 29.3% chance)

For an ordered pair left parenthesis x comma y right parenthesis in a relation, the x element represents the

Answers

Answer:

the x éléments représente the domain

x represents the value on the x-axis and the coordinate is also known as abscissa.

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

For an ordered pair left parenthesis x comma y right parenthesis in a relation that is (x, y).

Here x represents the value on the x-axis and the coordinate is also known as abscissa.

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

Multiply:

2 × (–21) × 7


A)

294

B)

–273

C)

–7

D)

–294

Answers

Answer:

[tex]2\times \left(-21\right)\times \:7[/tex]

PEMDAS order of operations:

[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]

[tex]=-42\times \:7[/tex]

[tex]=-294[/tex]

D) -294 is your answer

OAmalOHopeO

Use pemdas order & that’ll get you to your answer which is D) -294

The distance from the plane to the building __ meters

Answers

Answer:

1200 ×90÷8 is not correct ans

Lesson 9.6: Steady-State Analysis.) Consider a particular data set of 100,000 stationary waiting times obtained from a large queueing system. Suppose your goal is to get a confidence interval for the unknown mean. Would you rather use (a) 50 batches of 2000 observations or (b) 10000 batches of 10 observations each?

Answers

Answer:

I would rather use:

(b) 10,000 batches of 10 observations each.

Step-by-step explanation:

It is easier to have 10,000 batches of 10 observations each than to have 50 batches of 2,000 observations.  Human errors are reduced with fewer observations. For example, Hadoop, a framework used for storing and processing big data, relies on batch processing.  Using batch processing that divides the 100,000 stationary waiting times into 10 observations with 10,000 batches each is more efficient than having 2,000 observations with 50 batches each.

A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)

Answers

Answer:

The answer is "-3.04"

Step-by-step explanation:

[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]

Sample distribution:

[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]

   [tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]

A line is perpendicular to the line y = 4x - 3 and has x-intercept (2,0). Which of the following is an equation of the line?

Answers

Answer:

y = -1/4x+1/2

Step-by-step explanation:

y = 4x - 3

This is in slope intercept form, y = mx+b where the slope is m

The slope is 4

Perpendicular lines have slopes that are negative reciprocals

-1/4 is the slope of the perpendicular line

y = -1/4x+b

Using the point (2,0)

0 = -1/4(2)+b

0 = -1/2+b

b = 1/2

y = -1/4x+1/2

7+4i+1-3i simplify as much as possible

Answers

Answer:

8+i

Step-by-step explanation:

7+4i+1-3i

Combine like terms.

8+i

I hope this helps!

pls ❤ and give brainliest pls

How much state tax is withheld from $36,200 if the tax rate is 4%?

Answers

Answer:

$1448

Step-by-step explanation:

Tax=rate*amount=(4/100)*36200=1448

-1/5y+7=7
What is the value of y?

Answers

The answer is y=0

See the attached photo for details

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

find the derivative of e power ax divide by log bx​

Answers

Answer:

Step-by-step explanation:

A scientist is studying the growth and development of an epidemic virus with a growth rate of 9% per month that has infected 3,124 people. If this rate continues, what will be the number of infected people in another 9 months? Round your answer to the nearest whole number.

Answers

Answer:

About 6,785 people will be infected about nine months.

Step-by-step explanation:

We can write an exponential function to represent the situation. The standard exponential function is given by:

[tex]\displaystyle f(x) = a(r)^x[/tex]

Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.

3,124 people have already been infected. Thus, our initial value a = 3124.

And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.

Hence, our function is:

[tex]\displaystyle f(x) = 3124(1.09)^x[/tex]

Then after nine months, the total amount of infected people will be f(9):

[tex]\displaystyle f(9) = 3124(1.09)^{(9)}[/tex]

Use a calculator:

[tex]\displaystyle f(9) \approx 6785[/tex]

About 6,785 people will be infected about nine months.

Answer:

7,022

Step-by-step explanation:

please help me with this question!

Answers

I am un able to see the photo please re try so I can help

How many real solutions does this system of equations have? x2 +3 = y
3х — у+1 = 0

Answers

Answer:

Step-by-step explanation:

y = x²+3

y = 3x+1

x² + 3 = 3x +1

x² - 3x + 2 = 0

(x-2)(x-1) = 0

x = 2, 1

Two solutions

(2,7) and (1,4)

An employee makes $11.20 per hour but is getting a 6.5% increase. What is his new wage per hour to the nearest cent? His new wage per hour is?​

Answers

Answer:

11.93

Step-by-step explanation:

First find the amount of increase

11.20 *6.5%

11.20 *.065

0.728

Rounding to the nearest cent

.73

Add this to the original wage

11.20+.73

11.93

What fraction is equivalent to 0.46464646...


A)

46∕999

B)

46∕99

C)

23∕50

D)

46∕100

Answers

Answer:

Hello,

answer is B

Step-by-step explanation:

[tex]0.\overline{46}=\dfrac{46}{99}[/tex]

The answer is a fraction with numerator is the period (46) and the denominator is a number made with 9 as longer that there are digits in the  periode (here 2 digits ==> 99)

10 times as much as 9

Answers

Answer:

90

Step-by-step explanation:

10 x 9

=> 90

10 times 9 is 90.

A data set includes data from student evaluations of courses. The summary statistics are n=89​, x=3.44​, s=0.67. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative​ hypotheses?
A.
H0​: μ=3.50
H1​: μ>3.50
B.
H0​: μ=3.50
H1​: μ<3.50
C.
H0​: μ≠3.50
H1​: μ=3.50
D.
H0​: μ=3.50
H1​: μ≠
(I also need the test statistic and p-value) thank you so much in advance :)

Answers

We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0

The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.

We go with answer choice D to form the null and alternative hypotheses.

The sign ≠ in the alternative hypothesis tell us that we have a two tail test.

---------------------------------------

Let's compute the test statistic

z = (xbar - mu)/(s/sqrt(n))

z = (3.44 - 3.50)/(0.67/sqrt(89))

z = -0.84483413122896

z = -0.84

The test statistic is roughly -0.84

---------------------------------------

Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.

Use a calculator or a Z table to determine that

P(Z < -0.84) = 0.2005

which is approximate

Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401

The p-value is roughly 0.401

-----------------------------------------

Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.

The conclusion based on that means that μ=3.50  must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50

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