# A sample of a radioactive substance decayed to 93.5% of its original amount after a year. (Round your answers to two decimal places.)

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### calculus

A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? (b) How long would it take the sample to decay to 65% of its original amount?

### Calc

A sample of a radioactive substance decayed to 93.5% of its original amount after a year. a) What is the half-life of the substance? ? years (b) How long would it take the sample to decay to 10% of its original amount? ? years

### MATH!

The mass of a radioactive substance follows an exponential decay model, with a decay rate of 5% per day. A sample of this radioactive substance was taken six days ago. If the sample has a mass of 3 kg today, find the initial mass of the sample. Round your answer to two decimal...

### pre calc

You have a sample of a certain radioactive substance. After two days, thirty percent of the sample has decayed. What is the half-life of the material and how much will have decayed after a week?

### pre calc

You have a sample of a certain radioactive substance. After two days, thirty percent of the sample has decayed. What is the half-life of the material and how much will have decayed after a week?

### calculus

The rate at which an amount of a radioactive substance decays is modeled by the differential equation dA/dt = kA, where A is the mass in grams, t is the time in years, and k is a constant. Answer the following. a) If a 100-gram sample of the radioactive substance decays to 95 ...

### Science

Radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.6)^(-t). a) Determine the function A’, which represent the rate of decay of the substance. b) what is the half-life for this substance? c) ...

### MATH Precalculus

1) A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a radioactive substance. After 26 hours, 75 mg of the substance remains. How many milligrams will remain after 46 hours? 2) A house was valued at $110,000 in the year 1988. The value ...

### Math algebra

The radioactive decay of a substance is expressed by A=A^0 e^ -kt, where the initial amount A^0, decays to an amount A after t years. The positive constant k differs for each substance. Strontium 90 decays such that k=.028. Find out how much of 1,000 mg of strontium 90 remains...

### math

The radioactive decay of a substance is expressed by A=A^0 e^ -kt, where the initial amount A^0, decays to an amount A after t years. The positive constant k differs for each substance. Strontium 90 decays such that k=.028. Find out how much of 1,000 mg of strontium 90 remains...

### Calculus-derivatives

Verify if these are correct answers. 1. The derivative of f(x)=e^2x -e^-2x is f'(x)=2e^2x - 2e^-2x? 2.A certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, given by the function f(x)=3e^-3t. What is the rate of...

### math

round result to two decimal places...the answer i have is: 7.023 so two decimal places would it be: 702.0 You're asked to round to two decimal places. 7.023 = 7.02. Your answer has only one decimal place. so i guess my answer is wrong then...so what do they mean by two decimal...

### math

Phosphorus-32 (P-32) has a half-life of 14.2 days. If 200 g of this substance are present initially, find the amount Q(t) present after t days. (Round your growth constant to four decimal places.) How fast is the P-32 decaying when t = 21.5? (Round your answer to three decimal...

### Math

Phosphorus-32 (P-32) has a half-life of 14.2 days. If 200 g of this substance are present initially, find the amount Q(t) present after t days. (Round your growth constant to four decimal places.) How fast is the P-32 decaying when t = 21.5? (Round your answer to three decimal...

### math

Phosphorus-32 (P-32) has a half-life of 14.2 days. If 200 g of this substance are present initially, find the amount Q(t) present after t days. (Round your growth constant to four decimal places.) How fast is the P-32 decaying when t = 21.5? (Round your answer to three decimal...

### Math

Phosphorus-32 (P-32) has a half-life of 14.2 days. If 200 g of this substance are present initially, find the amount Q(t) present after t days. (Round your growth constant to four decimal places.) How fast is the P-32 decaying when t = 21.5? (Round your answer to three decimal...

### Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay constant. (a) ...

### Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay constant. (a) ...

### pre calculus

32% of a particular radioactive substance disappears in 227 years. Part 1: Find the decay constant. Your answer must be correct to five decimal places. Part 2: Determine the time T in years required for 93% of the substance to disapper. Your answer must be correct to two ...

### Math

Cosmic ray bombardment of the atmosphere produces neutrons, which in turn react with nitrogen to produce radioactive carbon-14. Radioactive carbon-14 enters all living tissue through carbon dioxide (via plants). As long as a plant or animal is alive, carbon-14 is maintained in...

### Algebra ASAP

Suppose that $17,000 is invested in a savings account paying 5.1% interest per year. (a) Write the formula for the amount A in the account after t years if interest is compounded monthly. A(t) = (b) Find the amount in the account after 3 years if interest is compounded daily...

### pre-calc.

Problem 1. You ingest a certain dangerous bacteria at dinner by accident. When more than 1,000,000 of these organisms are in your gut, you will become violently ill. Their population doubles every 20 minutes. You ate dinner at 7pm and by 5am you are sick. At least how many of ...

### math

the amount of radioactive substance prsent at anytime is given by q(t)=Q0e-0.1 How will it take for the radioactive substance x to decay to 30% of its original amount?

### Pre-Calculus

At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount A, in mg, remaining in the body is given by A=13(0.82)^t. a) What was the initial amount taken? b) What percent of the drug leaves the body each hour? c) How much of the drug is left in the ...

### Math

Find the accumulated amount A if the principal, P = $3700 is invested at the interest rate r = 7%/year for t = 12.5 years compounded semiannually. Round your answers to two decimal places. a. The accumulated amount is $8544.01. b. The accumulated amount is $8592.56. c...

### college stats

Again sorry for all the questions. please help, I am not good at stats and find these questions very difficult. I would appreciate an explanation if possible. 1.What is the sample average? 2.What is the SD of the box? 3.What is the number of draws from the box (the sample size...

### Stats

Exercise 6-8 The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 235 customers on the number of hours cars are parked and the amount they are charged. Number of Hours Frequency Amount Charged 1 18 $3 2 33 7 3 49 10 4 44 15 5 34 ...

### CALCULUS

Let y(t) denote the mass of a radioactive substance at time t.t. Suppose this substance obeys the equation y′(t)=−14y(t). Assume that, initially, the mass of the substance is y(0)=M>0. At what time does half of the mass remain? (Round your answer to 3 decimal ...

### Math

There was a sample of 550 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 5.2% each year. Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function ...

### Exponential Modeling

The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 100 grams of this substance. How many grams of the substance would be left after a week?

### College algebra

Sample of 500gms radioactive substance decays according to the function A(t)-500-0.044t where t is the time in years. How much of the substance will be left in the sample after 20 years?round to the nearest whole gram

### Math

What is the difference between "Give your answer correct to two decimal places." and "Round your answers to two decimal places." ?? Are they the same thing or do the answers differ?

### Statistics

The Hill of Tara in Ireland is a place of great archaeological importance. This region has been occupied by people for more than 4,000 years. Geomagnetic surveys detect subsurface anomalies in the earth's magnetic field. These surveys have led to many significant ...

### statistics

Among 17 metal parts produced in a machine shop, 6 are defective. If a random sample of four of these metal parts is selected, find: (a) The probability that this sample will contain at least three defectives. (Do not round the intermediate answers. Round your answer to 4 ...

### calculus

Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of approximately 5730 years. Using this known piece of ...

### College Algebra

A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t) = 9e−0.012t b) How much of the mass remains after 49 days? (Round your answer to one decimal place.)

### Business Statistics

The Bureau of Labor Statistics’ American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged 0.30 hour (18 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend...

### Math/Calculus

After 5 days, a particular radioactive substance decays to 37% of its original amount. Find the half life of this substance. Is this right? Th= ln 2/ln(1/.37) x 5 days

### algebra

``If 18g of a radioactive substance are present initially and 5 yr later only 9 g remain, how much of the substance will be present after 11yr ? after 11yr there will be ___g of a radioactive substance. round the final answer to the nearest thousandth as needed. round all ...

### algebra

A radioactive substance decays according to the formula A=A0e^kt where A0 is the initial amount of substance (in grams) A is the amount of substance(in grams) after t years k is a constant The half-life of the substance is 10 years.If we begin with 20g of the substance,how ...

### Calculus

a certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, is given by the function f(t)=3e^-3t. What is the rate of decay of the substance after half a year: I first found the derivative of f(t)=3e^-3t which is f'(...

### math with application

If 12 % of a radioactive substance decays in 7 hours, what is the half-life of the substance? Carry out all calculations exactly, then round the final answer to three decimal places. The half life is what hours?

### Chemistry

A radioactive sample contains 3.25 1018 atoms of a nuclide that decays at a rate of 3.4 1013 disintegrations per 26 min. (a) What percentage of the nuclide will have decayed after 159 d? % (b) How many atoms of the nuclide will remain in the sample? atoms (c) What is the half-...

### Calculus

The total worldwide box-office receipts for a long-running movie are approximated by the following function where T(x) is measured in millions of dollars and x is the number of years since the movie's release. T(x) = (120x^2)/(x^2 + 4) How fast are the total receipts changing ...

### STATISTIC

A survey of Internet users reported that 20% downloaded music onto their computers. The filing of lawsuits by the recording industry may be a reason why this percent has decreased from the estimate of 28% from a survey taken two years before. Assume that the sample sizes are ...

### Statistics

Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $120,000. This distribution follows the normal distribution with a standard deviation of $38,000. (A) If we select a random sample of 58 ...

### Calculus

The percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid oz of whiskey is given by the following equation. A(t) = 0.26te-0.3t , (0 t 12) (a) What is the percentage of alcohol in a person's bloodstream after 1/2 hr? After 6 hr? (Round your answers to four...

### Chemistry

How much a 2.00 g 239 Pu would have decayed after 1.6 x 10^4 years? The half-life for 239 Pu is 2.4 x 10^4 years. amount remaining= originalamount*(.5)^(1.6/2.4) amount decayed = original - amountremaining

### business Maths

On September 20, Jody Jansen went to Sunshine Bank to borrow $3,900 at 5% interest. Jody plans to repay the loan on January 27. Assume the loan is on ordinary interest. (Use table value) (a) What interest will Jody owe on January 27? (Use 360 days a year. Do not round ...

### Algebra ASAP

The half-life of krypton-91 ^(91Kr) is 10 seconds. At time t = 0 a heavy canister contains 6 g of this radioactive gas. (a) Find a function m(t) = m02^−t/h that models the amount of ^(91)Kr remaining in the canister after t seconds. m(t) = (b) Find a function m(t) = m0e...

### Algebra

5. The local soccer team won the championship a several years ago, and since then, ticket prices have been increasing $20 per year. The year they won the championship, tickets were $50. Write a recursive formula for a sequence that will model ticket prices. Is the sequence ...

### Quantitative Statistic

The following information is available. H0 : μ ≥ 220 H1 : μ < 220 A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 ...

### Quantitative Statistic

The following information is available. H0 : μ ≥ 220 H1 : μ < 220 A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 ...

### algebra 1 sequences

Year 2003 2004 2005 2006 Populatation 22.12 22.49 22.86 23.41 A. divide the population for each year by the population in the preceeding year. Round to the two decimal places and show the Texas population increase that is approximately geometric. 1.01 B. Write the general term...

### Algebra sequences

Year 2003 2004 2005 2006 Populatation 22.12 22.49 22.86 23.41 A. divide the population for each year by the population in the preceeding year. Round to the two decimal places and show the Texas population increase that is approximately geometric. 1.01 B. Write the general term...

### PRE-CAL

Complete the table assuming continuously compounded interest. (Round your answers to two decimal places.) Initial Investment== ? Annual % Rate== ? Time to Double== 11YRS Amount After 10 Years== $1600 Using formula A=Pe^rt ?

### math

Suppose that x is normally distributed with a mean of 10 and a standard deviation of 3. Find P(x ¡Ü 6). Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.

### Math

Can anybody show me step by step pls? A man invests $3000 in an account that pays 7.5% interest per year, compounded quarterly. 1. Find the amount after 3 years? (Round your answer to the nearest cent.) how much $? 2. How long will it take for the investment to double? (Round ...

### statistics

Chicken Delight claims that 86 percent of its orders are delivered within 10 minutes of the time the order is placed. A sample of 70 orders revealed that 57 were delivered within the promised time. At the .02 significance level, can we conclude that less than 86 percent of the...

### Chemistry

1. Calculate the pH of a buffer solution that contains 0.32 M benzoic acid (C6H5CO2H) and 0.17 M sodium benzoate (C6H5COONa). [Ka = 6.5 × 10-5 for benzoic acid] Round your answer to two places past the decimal. 2. A solution is prepared by mixing 470 mL of 0.18 M Tris·Base ...

### Chemistry

1. Calculate the pH of a buffer solution that contains 0.32 M benzoic acid (C6H5CO2H) and 0.17 M sodium benzoate (C6H5COONa). [Ka = 6.5 × 10-5 for benzoic acid] Round your answer to two places past the decimal. 2. A solution is prepared by mixing 470 mL of 0.18 M Tris·Base ...

### math

5. Cesium-137 is a radioactive isotope. The following formula represents the remaining amount of a 300 gram sample of cesium-137 in a storage tank after t years: N(t)=300e−0.02297t A) Determine the remaining amount of cesium-137 in the storage tank after 75 years. (Round...

### Physics

If a sample of a radioactive isotope has a half-life of 5 year(s), how much of the original sample will be left at the end of the second year? How much will be left at the end of the third year of thr original sample? How much will be left at the end of the fourth year of the ...

### statistics

A sample of n = 5 college students yielded the following observations on number of traffic citations for a moving violation during the previous year. Calculate s2 and s. (Round all answers to four decimal places.) s2 = 1 s = 2

### Math889

A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = te−t/4 (a) Find the velocity at time t (in ft/s). v(t) = (b) What is the velocity after 1 s? (Round your answer to two decimal places.) v(1) = ft/s (...

### Stats

Suppose the following data are selected randomly from a population of normally distributed values. 42 51 43 48 41 57 54 39 45 48 45 39 46 Construct a 95% confidence interval to estimate the population mean. Round the intermediate values to 2 decimal places. Round your answers ...

### stats

If a random sample of size n = 65 is drawn, find ¦Ìx, ¦Ò x and P(24 ¡Ü x ¡Ü 26). (Round ¦Ò x to two decimal places and the probability to four decimal places.) ¦Ìx = Correct: Your answer is correct.

### Calculus

The amount remaining of a radioactive substance after t hours is given by A(t) = 100ekt. After 12 hours, the initial amount has decreased by 4%. How much remains after 48 hours? What is the half-life of the substance?

### Trigonometry

Find all solutions between 0 and 2pi. Round to two decimal places. In radians. Find all solutions between 0 and 2 pi. Round to two decimal places for the final solutions. The answers should be in radian mode. If you can use exact values use them. At least one of the 3 problems...

### finance

You want to have $2 million in real dollars in an account when you retire in 30 years. The nominal return on your investment is 8 percent and the inflation rate is 5.3 percent. What real amount must you deposit each year to achieve your goal? (Do not round intermediate ...

### statistics

A sample of n = 9 has a mean of M = 72 with SS = 162. Use the sample to make a point estimate of ì and to construct the 90% confidence interval for ì. (Round all answers to two decimal places ì = ? ± ? ( ? ) The 90% confidence interval for ì: ( ? , ? )

### statistics

A sample of n = 9 has a mean of M = 72 with SS = 162. Use the sample to make a point estimate of ì and to construct the 90% confidence interval for U. (Round all answers to two decimal places.) U = ? ± ? ( ?) The 90% confidence interval for U: ( ? , ? )

### Math

The element strontium-90 is radioactive. The percent of strontium -90, A(t), left in a sample can be modelled by the half-life function A(t) = A0 (1/2)^t/29, where t represents the time, in years, after the initial time, and A0 represents the initial amount, 100% of the ...

### algebra

You deposit $3000 in an account earning 7% interest compounded continuously. The amount of money in the account after years is given by A(t)=3000 e^(0.07 t) . How much will you have in the account in 5 years? $ Round your answer to 2 decimal places. How long will it be until ...

### statistics

Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that ...

### Pre-calculus

Complete the table assuming continuously compounded interest. (Round your answers to two decimal places.) Initial Investment: Annual % Rate: Time to Double: 8 yr Amount After 10 Years: $1700 I don't understand how to get in the initial investment of annual % rate given only ...

### College Finance

1.A recent edition of The Wall Street Journal reported interest rates of 10.75 percent, 11.10 percent, 11.48 percent, and 11.75 percent for 3-, 4-, 5-, and 6-year Treasury security yields, respectively. According to the unbiased expectation theory of the term structure of ...

### QMB2100

Chicken Delight claims that 90 percent of its orders are delivered within 10 minutes of the time the order is placed. A sample of 70 orders revealed that 60 were delivered within the promised time. At the .02 significance level, can we conclude that less than 90 percent of the...

### Pre-calculus

Initially 600 milligrams of a radioactive substance was present. After 7 hours the mass had decreased by 3%. Construct an exponential model A(t) = A0ekt for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24 hours.

### Calculus

Find the amount of an annuity if $210/month is paid into it for a period of 20 yr, earning interest at the rate of 8%/year compounded continuously. (Round your answer to two decimal places.)

### Calculus

Find the amount of an annuity if $210/month is paid into it for a period of 20 yr, earning interest at the rate of 8%/year compounded continuously. (Round your answer to two decimal places.) $

### personal finance

Hal Thomas wants to establish a savings fund from which a community organization could draw $800 a year for 20 years. If the account earns 3 percent, what amount would he have to deposit now to achieve this goal? (Round time value factors to 3 decimal places and final answer ...

### calculus

In 1970, the total enrollment in public universities and colleges in a country was 5.1 million students. By 2004, enrollment had risen to 14.3 million students. Assume enrollment can be modeled by exponential growth. (a) Estimate the total enrollments in 1980, 1990, and 2000...

### statistic

A random sample of size n = 72 is taken from a finite population of size N = 644 with mean μ = 239 and variance σ2 = 325. Use Table 1. a-1. Is it necessary to apply the finite population correction factor? Yes No a-2. Calculate the expected value and the standard ...

### math calculus (please help me)

In 1970, the total enrollment in public universities and colleges in a country was 5.1 million students. By 2004, enrollment had risen to 14.3 million students. Assume enrollment can be modeled by exponential growth. (a) Estimate the total enrollments in 1980, 1990, and 2000...

### math

The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) Estimate how long it takes the population to double. (Round your answer to two decimal places.) _______yr (b) Estimate how long it takes the population to triple...

### algebra

Two Questions: 1) A certain radioactive isotope has leaked into a small stream. 100 days later after the leak 10% of the original amount of the substance. Determine the half-life of this radioactive isotope. 2) During a research experiment, it was found that the number of ...

### college stats

Sorry for all the questions, I really need help and an explanation so I can fully understand. I really appreciate everything. Thank you. In a random sample of 519 judges, it was found that 285 had an introvert personality type. Construct a 95% confidence interval for the ...

### Urgent math

population growth model. Can anybody please help me out in trying to solve this problem? It's my homework and I don't seem to understand what I am getting. The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. (a) What is the relative rate of ...

### business Maths

On September 14, Jennifer Rick went to Park Bank to borrow $2,500 at interest. Jennifer plans to repay the loan on January 27. Assume the loan is on ordinary interest. Refer to Days in a year table. (a) What interest will Jennifer owe on January 27? (Use 360 days a year. Do ...

### math

If a ball is thrown directly upward with a velocity of 14 m/s, its height (in meters) after t seconds is given by y = 14t − 4.9t2. What is the maximum height attained by the ball? (Round to two decimal places.) ______ m After how many seconds is that height attained? (...

### Finance

If you put $10,000 at the end of each year into a savings account that pays interest at the rate of 5 percent a year, how much would you have after 4 years? Use the Appendix B. Round the answer to the nearest cent. Round FV-factor to three decimal places.

### 5 Pre-Calculus Questions

1. What is the value of x in the right triangle below? If needed, round your answer to two decimal places. 32 angle, 15 inches, find the x in base… 2. A 10-foot ladder is leaning up against the side of a building so that the top of the ladder reaches the top of the building...

### MATH

The value V of a machine t years after it is purchased is inversely proportional to the square root of t+2. The initial value of the machine is $10,000. Find the rate of depreciation when t=5 . Round your answer to two decimal places. A. -381.80 PER YEAR B. -1889.82 PER YEAR C...

### math ,correction

is this right? Find the standard deviation to the given data. The manager of a small dry cleaner employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. THe six ...

### probability

In a recent survey, 35 percent indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of ten people and ask them to name their favorite flavor of ice cream. (b) What is the probability exactly four of those in the sample name chocolate? (Do not ...

### Finite Math

Find the effective rate of interest corresponding to a nominal rate of 6%/year compounded annually, semiannually, quarterly, and monthly. (Round your answers to two decimal places.)

### Math

The null and alternate hypotheses are: H0: π1 ≤ π2 H1: π1> π2 A sample of 100 observations from the first population indicated that X1 is 70. A sample of 150 observations from the second population revealed X2 to be 90. Use the .05 significance ...

### Calc

I am having trouble with these two problems for my Calc class. I have tried answering a few times already, but i keep getting it wrong. Help please and thank you. For the limit below, find values of δ that correspond to the ε values. lim_(x->1)(3 + x - 3x^3) = 1...