A sample of a radioactive isotope had an initial mass of 440 mg in the year 1990 and decays exponentially over time. A measurement in the year 1998 found that the sample's mass had decayed to 40 mg. What would be the expected mass of the sample in the year 2001, to the nearest whole number?

Answers

Answer 1

Using an exponential function, the expected mass of the sample in the year 2001 would be of 16 mg.

What is the exponential function for the amount of a substance?

The function is:

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

In which:

A(0) is the initial amount.k is the decay rate.

The information given is as follows:

A(0) = 440, A(8) = 40.

Hence:

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

[tex]40 = 440e^{-8k}[/tex].

[tex]e^{-8k} = 0.09090909[/tex]

[tex]\ln{e^{-8k}} = \ln{0.09090909}[/tex]

[tex]-8k = \ln{0.09090909}[/tex]

[tex]k = -\frac{\ln{0.09090909}{8}[/tex]

k = 0.29973691

Then the function is:

[tex]A(t) = 440e^{-0.29973691t}[/tex]

2001 is 11 years after 1990, hence the amount is:

[tex]A(11) = 440e^{-0.29973691 \times 11} = 16[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1


Related Questions

Evaluate
ifr=9 and s = 2.
S

Answers

Answer:

(4 × 9) / 2 = 36/2 = 18 gitu yaaa

Answer:

18

Step-by-step explanation:

plug in r and s

4(9)/2

36/2

18

Select the correct answer.
What is the complete factorization of x2 + 2x - 63?
A. (x+ 21)(x-3)
B.
(x-9)(x+7)
C.
(x + 9)(x-7)
D.
(x-21)(x + 3)
Reset

Answers

Answer:

the answer of this question is

c

Why is it important that you put the polynomial in standard form (largest power
to smallest-power)? *

Answers

Answer: Polynomials like to be written in standard form. This means they contain no like terms and the exponents are in descending order (largest to smallest).

Step-by-step explanation:

origanal price $60 sale price $45

Answers

Answer:

di ko po alam ehh

Step-by-step explanation:

sorry po

Answer:

Step-by-step explanation:

What is the question?

Price reduced by $15

Percentage reduction = 15/60 = 0.25 = 25%

Find set A' n B'
U= {1, 2, 3, 4, 5, 6, 7}
A= {4, 5, 6, 7}
B = {3, 4, 7}

Answers

Answer:

its 1 and 2

Step-by-step explanation:

first find A' which is(1,2,3) since these are in the universal set but not in A.

similary B' which is (1,2,5,6)

and since (1,2) are both in A' and B' set A'nB'=(1,2)

Answer:

Step-by-step explanation:

U={1,2,3,4,5,6,7}

A={4,5,6,7}

B={3,4,7}

A'={1,2,3}

B'={1,2,5,6}

A'∩B'={1,2}

Guys I need help !! X=2 evaluate 5x-2

Answers

So x=2
5(2)-2. (2)because x=2
5(2)-2=8

Answer:

Step-by-step explanation:

Evaluate means to see what value the equation has given x is 2

substitute x for 2 (write instead of x, write 2)

5x-2 will be 5*2-2 , calculate 5*2-2= 10-2 = 8

estimate 5/8 - 1/10 explain

Answers

Answer:

21/40.

Step-by-step explanation:

Find the LCD (Least Common Denominator) of the fractions. The LCD of 5/8 and 1/10 is 40.

Convert both fractions into denominators of 40.

So then we have: 25/40 - 4/40 which is equal to: 21/40.

21/40 is the estimated value of the expression  5/8 -1/10

What is Number system?

A number system is defined as a system of writing to express numbers.

The given expression is 5/8 -1/10

The terms in the expression are in the form of fractions, A fraction represents a part of a whole.

To find the value of expression firstly find the LCM of 8 and 10

40 is the LCM

5(5)-1(4)/40

25-4/40

The value of 25 minus 4 is twenty one.

21/40 is the value of the expression  5/8 -1/10

Hence, 21/40 is the estimated value of the expression  5/8 -1/10

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ2

PLEASE HELP!!! WILL GIVE BRAINLIEST!!!

Instructions

Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.

Complete the following. Show all work for calculations.

List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Length: 6 inches

Width: 2 and a half inches

Height: 12 inches (1 foot)

Describe the shape of the cross section when the box is cut parallel to the base.





What is the surface area of the box?





What is the surface area of the box if it is scaled up by a factor of 10?





What is the volume of the box?







What is the volume of the box if it is scaled down by a factor of 1/10?

Answers

Answer:

I chose a box of cereal-------> rectangular prism

see the attached figure

Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Length: 20 cm

Width: 8 cm

Height: 32 cm

Part 2).

Describe the shape of the cross-section when the box is cut parallel to the base

the shape of the cross-section would be a rectangle of dimensions

20 cm x 8 cm

Part 3)

What is the surface area of the box?

surface area=2*area of the base+perimeter of the base*height

area of the base=20*8=160 cm²

perimeter of the base=2*[20+8]-----> 56 cm

height=32 cm

surface area=2*160+56*32------> 2,112 cm²

the answer part 3) is

2,112 cm²

Part 4)

What is the surface area of the box if it is scaled up by a factor of 10?

we know that

surface area of the larger box=[scale factor]²*surface area original box

scale factor=10

surface area original box=2,112 cm²

so

surface area of the larger box=10²*2,112-----> 211,200 cm²

the answer part 4) is

211,200 cm²

Part 5)

What is the volume of the box?

volume of the box=L*W*H-----> 20*8*32------> 5,120 cm³

the answer Part 5) is

5,120 cm³

Part 6)

What is the volume of the box if it is scaled down by a factor of 1/10

we know that

volume of the smaller box=[scale factor]³*volume original box

scale factor=1/10

volume original box=5,120 cm³

so

volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³

the answer part 6) is

5.12 cm³

Step-by-step explanation:

Answer:

541/2 square

Step-by-step explanation:

we know that

the volume of the smaller box=[scale factor]³*volume original box

scale factor=1/10

volume original box=5,120 cm³

so

volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³

the answer part 6) is 541/2 square

7x= -42


What is the solution to this equation?​

Answers

Answer:

X= -6

Step-by-step explanation:

7x = -42

(÷7) (÷7)

X = -6

7x= -42
X = -6

Answer to the equation is -6

Evaluate (–6)^2 – 7^2.

A) 85

B) 169

C) –85

D) –13

Answers

C would be the correct answer

if the force acting on a body of mass 4kg accelerates it at a constant rate of 4m/s. what would be the acceleration of the mass is doubled?

Answers

Answer:

4kg=4m/s

8kg=?

3m/s

Step-by-step explanation:

12kgm/s/4kg

This year 0.3 of the x students at Mega Middle School are in 7th grade. There are 294 students in 7th grade.

Answers

Answer:

is that even a question ?

Step-by-step explanation:

3/10x=294

x=294*10/3

x=980 students

if you found my answer helpful please mark as brainliest.

To keep in shape, Vincent exercises at a track near his home. ​ ​He requires 40 minutes to do 4 laps running and 7 laps walking. ​In contrast, he requires 18 minutes to do 2 laps running and 3 laps walking. ​ ​Assuming he maintains a consistent pace while running and while walking, how long does Vincent take to complete a lap at each pace?

Answers

Answer:

He completes a lap running in 3 minutes, and walking in 4 minutes.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the time needed to complete a lap running.

y is the time needed to complete a lap walking.

He requires 40 minutes to do 4 laps running and 7 laps walking.

This means that:

[tex]4x + 7y = 40[/tex]

[tex]4x = 40 - 7y[/tex]

He requires 18 minutes to do 2 laps running and 3 laps walking.

This means that

[tex]2x + 3y = 18[/tex]

Multipluing everything by 2

[tex]4x + 6y = 36[/tex]

Since [tex]4x = 40 - 7y[/tex]

[tex]40 - 7y + 6y = 36[/tex]

[tex]y = 4[/tex]

And

[tex]4x = 40 - 7y[/tex]

[tex]4x = 40 - 7*4[/tex]

[tex]4x = 12[/tex]

[tex]x = \frac{12}{4}[/tex]

[tex]x = 3[/tex]

He completes a lap running in 3 minutes, and walking in 4 minutes.

Solve for x in the following equation.
X/5=25
X=?

Answers

Answer:

125

Step-by-step explanation:

25 × 5 = 125

x/5 = 25 × 5 = 125

x = 125

X=25
25 x 5 = 125 your welcome

A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information: Battery Pack Model 1 Battery Pack Model 2Sample Size 9 9Sample Mean 5 hours 5.5 hoursStandard Deviation 1.5 hours 1.3 hoursUsing the null and alternate hypothesis:H0:mu1-mu2=0 vs. Ha: mu1-mu2 not equal 0Calculate the test statistic for this test.

Answers

Answer:

-0.756

Step-by-step explanation:

N1 = 9

N2 = 9

Sd1 = 1.5 hours

Sd2 = 1.3 hours

X1 = 5 hours

X2 = 5.5 hours

Hypothesis

H0: mu1 - mu2 = 0

H1 : mu1 - mu2 not equal to 0

Test statistic

t = (x1 - x2)/SE

SE is the standard error, which is unknown

SE = √sd1²/n1 + sd2²/n2

= √1.5²/9 + 1.3²/9

= √0.25+0.1878

= √0.4378

= 0.66166

t statistics = (5-5.5)/0.66166

= -0.5/0.66166

= -0.756

7+9 x (3+8) Order of operations. Please explain.

Answers

Answer:

Not sure if that is "9x" or "9 times" but I will do both. I have attached a picture of me solving and explaining the steps. Hope this helps, thank you !!

To test the effectiveness of a drug proposed to relieve symptoms of depression, psychiatrists recruited volunteers for clinical tests. All of the volunteers were diagnosed with symptoms of depression. The psychiatrists provided the drug to first group and a sugar pill to the second group. In the description of the above situation, determine the control group.

Answers

Answer:

The control group is the group that takes the sugar pill

Step-by-step explanation:

In drug testing, to determine the efficacy of a drug, different groups of experimental subjects are recruited, one group is given the drug to be tested (treatment group) while another group is given a placebo.

A placebo is a fake version of the drug to be tested that does not have any therapeutic effect on the test subjects that receive it. In this case, the control group receives the placebo which is the sugar pill. They serve as the baseline of measurement when the outcome of the effect of the drug testing is done. The groups that received the actual drugs are compared against the groups that received the hoax treatment, and any change occuring  in the test subjects become the changes occuring as a result of the test drug used, when the observations on the control group has been ruled out.

four times a number increased by 8 is 54? ​

Answers

Answer:

4x+8=54 this is the correct answer

47. Health care costs per capita Rising health care costs
are a growing concern for everyone in the United
States. Using U.S. Centers for Medicare and
Medicaid Services data from 2006 and projected to
2021, U.S. per capita health care costs can be modeled
by
y = 20.61x? - 116.4x + 7406
where x is the number of years past 2000. Use this
equation to find, to the nearest dollar, the average rate
of change of U.S. per capita health care costs from 2010
to 2015 and from 2015 to 2020.

Answers

NHE grew 4.6% to $3.8 trillion in 2019, or $11,582 per person, and accounted for 17.7% of Gross Domestic Product (GDP).
Medicare spending grew 6.7% to $799.4 billion in 2019, or 21 percent of total NHE.
Medicaid spending grew 2.9% to $613.5 billion in 2019, or 16 percent of total NHE.
Private health insurance spending grew 3.7% to $1,195.1 billion in 2019, or 31 percent of total NHE.
Out of pocket spending grew 4.6% to $406.5 billion in 2019, or 11 percent of total NHE.
Hospital expenditures grew 6.2% to $1,192.0 billion in 2019, faster than the 4.2% growth in 2018.
Physician and clinical services expenditures grew 4.6% to $772.1 billion in 2019, a faster growth than the 4.0% in 2018.
Prescription drug spending increased 5.7% to $369.7 billion in 2019, faster than the 3.8% growth in 2018.
The largest shares of total health spending were sponsored by the federal government (29.0 percent) and the households (28.4 percent). The private business share of health spending accounted for 19.1 percent of total health care spending, state and local governments accounted for 16.1 percent, and other private revenues accounted for 7.5 percent.

If a sprinkler waters 1/20 of a lawn in 1/5 of an hour how much time will it take to water the entire lawn?

• 3/20 hour

• 1/4 hour

• 4 hours

• 5 hours​

Answers

Answer:

4 hours

Step-by-step explanation:

если x=6 то y=
если y=-4 то x=​

Answers

Step-by-step explanation:

ssshzvecucsussddyz wksoav

Answer:

X=6 To y=-6

y=-4 TO X = 4

꧁꧁꧁꧁꧂꧂꧂꧂

꧂꧂꧂꧂꧂

Pls help due in 10 minutes

Answers

Answer:

Boy I'm really boutta get to yo pickle chin ahh boy, egg head like collard greens head a//ss boy, oh hell nah boy yo dirt ahh boy stank ahh boy afro head ahh, lip gloss chin ahh boy ugly ahh boi

Step-by-step explanation:

Aawdadakdaw da  awdwa dadeefdcdcs

Need Trig Help plz Picture attached

Answers

Option B is the correct answer

Mr. Hernandez dilates the triangle shown below by a scale factor of 2 with the origin
as the center to obtain AA'B'C'.

Answers

Answer: only student 2

what is 3333 x 33 x 23 - 908

Answers

Answer:

2528839

Step-by-step explanation:

your welcome

I can’t tell if you are joking with this question or not but the answer is 2528839.

✨6 Grade Math✨ Pls help

Answers

Answer:

37

Step-by-step explanation:

89 - 4²×4 + 12 = 89 - 16×4 + 12                        = 89 - 64 + 12                        = 25 + 12                        = 37

Answer:

[tex]89 - 4 {}^{2} \times 4 + 12 = 89 \\ - 16 \times 4 + 12 \\ \\ = 89 - 64 + 12 \\ \\ = 25 + 12 \\ \\ = 37[/tex]

89-4^2×4+12=89-16×4+12

= 89-64+12

= 25+12

= 37

The 2010 U.S. Census asked every household to report information on each person living there. Suppose for a sample of 30 households selected, the number of persons living in each was reported as follows. 2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 9 3 2 1 1 3 Compute the mean, median, mode, range, lower and upper quartiles, and interquartile range for these data. (Round the mean to 2 decimal places.) Mean

Answers

Answer:

[tex]\bar x =2.53[/tex] -- Mean

[tex]Median= 2[/tex]

[tex]Mode = 2[/tex]

[tex]Range = 8[/tex]

[tex]Q_1 = 1[/tex]

[tex]Q_3 = 3[/tex]

[tex]IQR = 2[/tex]

Step-by-step explanation:

Given

n = 30

Data: 2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 9 3 2 1 1 3

Solving (a): The mean

This is calculated as:

[tex]\bar x =\frac{\sum x}{n}[/tex]

[tex]\bar x =\frac{2 +3 +1 +2 +6 +4 +2 +1 +5 +3 +2 +3+ 1+ 2 +2 +1 +3 +1 +2 +2 +4 +2 +1 +2 +9 +3 +2 +1 +1 +3}{30}[/tex]

[tex]\bar x =\frac{76}{30}[/tex]

[tex]\bar x =2.53[/tex]

Solving (b): The median

First arrange the given data

Arranged: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 5 6 9

[tex]Median =\frac{1}{2}(n+1)[/tex]

[tex]Median =\frac{1}{2}(30+1)[/tex]

[tex]Median =\frac{1}{2}(31)[/tex]

[tex]Median = 15.5th[/tex]

This implies that the median is the average of the 15th and 16th item

[tex]Median = \frac{2+2}{2}[/tex]

[tex]Median = \frac{4}{2}[/tex]

[tex]Median= 2[/tex]

Solving (c): The mode

From the given data; 2 has the highest frequency of 11.

So,

[tex]Mode = 2[/tex]

Solving (d): The Range

[tex]Range = Highest\ Data - Lowest\ Data[/tex]

The highest is 9 and the lowest is 1,

So:

[tex]Range = 9 - 1[/tex]

[tex]Range = 8[/tex]

Solving (e): Lower (Q1) and Upper (Q3) quartile.

Q1 is calculated as:

[tex]Q_1 = \frac{1}{4}(n+1)th[/tex]

[tex]Q_1 = \frac{1}{4}(30+1)th[/tex]

[tex]Q_1 = \frac{1}{4}(31)th[/tex]

[tex]Q_1 = 7.75th[/tex]

[tex]Q_1 = 8th\ item[/tex]

[tex]Q_1 = 1[/tex] -- from the arranged data

Q3 is calculated as:

[tex]Q_3 = \frac{3}{4}(n+1)th[/tex]

[tex]Q_3 = \frac{3}{4}(30+1)th[/tex]

[tex]Q_3 = \frac{3}{4}(31)th[/tex]

[tex]Q_3 = 23.25th[/tex]

[tex]Q_3 = 23rd\ item[/tex]

[tex]Q_3 = 3[/tex] -- from the arranged data

Solving (f): The interquartile range (IQR)

[tex]IQR = Q_3 - Q_1[/tex]

[tex]IQR = 3-1[/tex]

[tex]IQR = 2[/tex]

12 more than the square of a number is the same as 7 times the number.

Answers

Answer: Sorry I don't know

Step-by-step explanation:

Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x − 20 x2 + x − 20 Incorrect: Your answer is incorrect. (b) x2 x2 + x + 20 Incorrect: Your answer is incorrect.

Answers

Answer:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]

Required

Decompose into partial fraction

Start by factorizing the denominator:

[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]

[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]

[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]

So, we have:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]

Take LCM

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]

Cancel out the denominator

[tex]x - 20 = A(x+5)+B(x-4)}[/tex]

Open brackets

[tex]x - 20 = Ax+5A+Bx-4B[/tex]

Collect Like Terms

[tex]x - 20 = Ax+Bx+5A-4B[/tex]

[tex]x - 20 = (A+B)x+5A-4B[/tex]

By comparison;

[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]

[tex]5A - 4B = 1[/tex]

Make A the subject in [tex]A + B = 1[/tex]

[tex]A = 1 - B[/tex]

Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]

[tex]5(1-B) -4B = 1[/tex]

[tex]5-5B -4B = 1[/tex]

[tex]5-9B = 1[/tex]

Collect Like Terms

[tex]-9B = 1 - 5[/tex]

[tex]-9B = - 4[/tex]

[tex]B = \frac{4}{9}[/tex]

[tex]A = 1 - B[/tex]

[tex]A = 1 - \frac{4}{9}[/tex]

[tex]A = \frac{9-4}{9}[/tex]

[tex]A = \frac{5}{9}[/tex]

So:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]

PLS Help While on a strenuous hike, Tara recorded her distance from the peak of the mountain at two different time intervals. The table shows the two pieces of data she collected.

Answers

Answer:

Step-by-step explanation:

Equation of a line  representing the relation between distance from the peak of the mountain and time is,

h = mt + b

Here, m = Slope of the line

b = y-intercept

Since, slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

From the table attached,

Slope of the line passing through (2, 2600) and (5, 950) will be,

m = [tex]\frac{2600-950}{2-5}[/tex]

   = -550

Therefore, equation of the line will be,

h = -550t + b

Since, point (2, 2600) lies on this line,

2600 = -550(2) + b

b = 2600 + 1100

b = 3700

So, equation of the line will be,

h = -550t + 3700

Input - output values for this line,

t            2             4            6  

h        2600      1500       400  

Now we can plot these points and get the graph of the line.

Other Questions
Does anyone know composite functions? What did the Farm Security Administration provide along the Great Plains and the west in orderto establish hope to those affected by the Dust Bowl? Give details! mindy bought five eights of almonds and three forths of walnuts witch pair of fractions cannot be used to find how many pounds of nuts she bought in all Senesh's poetry represent a specific point of view and unique cultural experience. South AfricaPublic DomainWhich of the following countries are compact states? (1 point)O Malawi and South AfricaO Somalia and LiberiaNigeria and LiberiaO Cameroon and SomaliaO The Gambia and Malawiwill give brainliest Find g(f(-1)).gf-1)) =( What were the characteristics of the Roman empire at its height please help me thank you One side of a fence is 22 feet long. If 3 feet = 1 yard, how many yards long is the fence? How many units down does susan need to move to get to the fourth point on the number line a. 1/2 b. 3/2 c. 2 d. 4 e. 6 Sarah's mother gives her $25 for each A she gets on her report card and $10 for each B. If Sarah's mother gave her $80 and Sarah had 3 B's, how many A's did she have on her report card? what organelle acts as a barrier of the cell? Please help me answer this question! The sun converts nuclear energy into what type of energy? Which types of plant cells must receive glucose from other plant cells? What is the surface area of this right rectangular prism?Enter your answer in the box.inA rectangular prism with a length of 3 inches, a width of 1 inch, and a height of 2 inches. Como es el proceso de adjudicacion An area of land that is not used by humans for agriculture, industry, or habitation is called __________.A)wildernessB)rangelandC)public landD)sustainable forestE)private land Words that describe Elie from the book night (5 pts) It takes Jack 3 hours longer to write holiday cards than it takes Jill. Together, they can write themin 2 hours. How long does it take each person to write the cards working alone?