calculate the distance that you will travel if you will drive for the following situations. write you answers on a seperate sheet of paper.

The area of the resulting surface is (2/3)π[tex](e^(3/2) - 2)[/tex], or approximately 58.87 square units.

To find the area of the resulting surface, we need to use the formula for surface area of a solid of revolution.

The formula is:

S = 2π∫[tex]a^b f(x)√(1 + [f'(x)]^2) dx[/tex]

Where a and b are the limits of integration, f(x) is the function being rotated (in this case, y = ex), and f'(x) is the derivative of f(x) with respect to x.

In this case, we have:

f(x) = ex
f'(x) = ex

So, the integral becomes:

S = 2π∫[tex]0^20 ex √(1 + e^2x) dx[/tex]

This integral can be solved using u-substitution, where [tex]u = 1 + e^2x.[/tex]

[tex]du/dx = 2e^2x \\dx = du/(2e^2x)[/tex]

So the integral becomes:

[tex]S = π∫1^e (1/2)(u-1/2) du\\S = π[(2/3)u^(3/2) - (2/3)]_1^e\\S = π[(2/3)e^(3/2) - (2/3) - (2/3)]\\S = (2/3)π(e^(3/2) - 2)\\[/tex]

Learn more about area here :-

https://brainly.com/question/13254462

#SPJ11

Step-by-step explanation:

C  rate =   1 chapter / 9 hr   = 1/ 9    chap/hr

P rate = 1/6

together  :

1 chapter / ( c rate + p rate)  =   1 /( 1/9 + 1/6) =  1/ ( 2/18 + 3/18) = 1/ (5/18) =

    18/5 hr   = 3  3/5 hr

It would take Cynthia and Phillip 3.6 hours working together to proof a chapter of Hawkes Learning Systems' Introductory Algebra book.

To find out how long it would take Cynthia and Phillip working together to proof a chapter of Hawkes Learning Systems' Introductory Algebra book, we can use the work formula:

Work = Rate × Time

First, we'll find the individual rates for Cynthia and Phillip:
- [tex]Cynthia's rate:\frac{1 chapter}{9 hours}[/tex]
- [tex]Phillip's rate:\frac{1 chapter}{6 hours}[/tex]
Now, we'll add their rates together to find their combined rate:
[tex]Combined rate = \frac{1}{9}  + \frac{1}{6}[/tex]

To add these fractions, we need a common denominator, which is 18:
[tex]Combined rate = \frac{2}{18}  + \frac{3}{18}=\frac{5}{18}[/tex]

Now, we'll use the work formula to find the time it would take for them to complete the proofreading together. Since they're working on 1 chapter, we can set Work equal to 1:
[tex]1 = \frac{5}{18} (time)[/tex]

Next, we'll solve for Time:
[tex]Time = 1 (\frac{5}{18})[/tex]
[tex]Time=1 (\frac{18}{5})[/tex]
[tex]Time = \frac{18}{5} = 3.6 hours[/tex]

So, it would take Cynthia and Phillip 3.6 hours working together to proof a chapter of Hawkes Learning Systems' Introductory Algebra book.

To know more about  "Algebra" refer here:

https://brainly.com/question/29131718#

#SPJ11

It is nonsensical to talk about the direction of specific differences in ANOVA because it is an omnibus test.

An omnibus test is a statistical test that evaluates whether there is a difference between groups or conditions, without specifying which groups or conditions differ from each other. In the case of ANOVA (Analysis of Variance), it tests whether the means of two or more groups are equal or not. However, it does not tell us which specific groups are different from each other.

Instead, to identify the specific group differences, post-hoc tests such as Tukey's test, Bonferroni's test, or Scheffe's test can be used. These tests compare the means of each group and identify which groups differ significantly from each other.

Therefore, talking about the direction of specific differences in ANOVA is nonsensical because ANOVA does not provide information about which groups differ from each other. It only tells us whether there is a significant difference between groups or not.

for such more question on omnibus test

https://brainly.com/question/26504675

#SPJ11

The answer to the question is 7

The leakage current ratio of a transistor can be determined by comparing the leakage current in different configurations. In this case, we are given the parameters y, n, Pr, VDD, T, and VTHo.

The leakage current ratio is the ratio of the leakage current in two different configurations. In this case, we need to compare the leakage current when VDD is 0 and 0.2 V.

Using the given parameters and the formula for the leakage current, we can calculate the leakage current for both configurations.

When VDD is 0, the leakage current is given by:

I_leakage = y * Pr * exp[(VTHo-VDD)/n*VT]

Plugging in the values, we get:

I_leakage(0) = 1 * 0.35 * exp[(0.4-0)/0.1*VT] = 7.79 × 10^-10 A

When VDD is 0.2 V, the leakage current is given by:

I_leakage = y * Pr * exp[(VTHo-VDD)/n*VT]

Plugging in the values, we get:

I_leakage(0.2) = 1 * 0.35 * exp[(0.4-0.2)/0.1*VT] = 5.11 × 10^-9 A

Therefore, the leakage current ratio is:

I_leakage(0.2)/I_leakage(0) = (5.11 × 10^-9)/(7.79 × 10^-10) = 6.56

Rounded to the nearest integer, the leakage current ratio is 7.

To learn more about leakage current : brainly.com/question/29545860

#SPJ11

True. Time series data refers to a collection of observations gathered over time, where the time dimension is a critical component of the data.

Each data point is linked to a specific point in time. In contrast, cross-sectional data is collected at a single point in time and does not have a time dimension. Therefore, the timing of each observation is crucial in time series data but not as important in cross-sectional data.

Time series data is a sequence of data points indexed in time order. It is used to track change over time.

Cross-sectional data is a snapshot of data at a specific point in time. It is used to compare different groups or variables .

Think about how the time at which each observation is made affects the analysis of time series data and cross-sectional data.

to learn more about Time series data click here:

brainly.com/question/29097191

#SPJ11

The statement that best describes the result of the data that Maya collected, would be D. Small - size drinks cost more than $ 1. 00 at restaurants in Maya's city.

We see that in Maya's city, there was no entry in the $ 0.91 to $ 1.00 category. This shows that there are no restaurants (according to the sample) that sell small - sized drinks for less than $ 1.00

The other statements are false because the largest restaurants fall in the $ 1. 51 to $ 1. 60 category and Maya conducted the sampling at 50 restaurants because there were 10 restaurants per sample.

Find out more on samples at https://brainly.com/question/27819027

#SPJ1

The length of the hypotenuse is 4.

Let the three sides of the right triangle be a, b, and c, where a is the shortest side, b is the middle side, and c is the hypotenuse. Since the sides form a geometric progression, we know that:

b/a = c/b

Multiplying both sides by b, we get:

[tex]b^2/a = c[/tex]

Since a = 2, we can substitute this into the above equation to get:

[tex]b^2/2 = c[/tex]

We also know that the Pythagorean theorem applies, so we have:

[tex]a^2 + b^2 = c^2[/tex]

Substituting a = 2 and [tex]c = b^2/2[/tex] , we get:

[tex]2^2 + b^2 = (b^2/2)^2[/tex]

Simplifying this equation, we get:

[tex]4 + b^2 = b^4/4[/tex]

Multiplying both sides by 4, we get:

[tex]16 + 4b^2 = b^4[/tex]

Rearranging and factoring, we get:

[tex](b^2 - 4)(b^2 - 12) = 0[/tex]

Since b is a positive length, we can discard the solution[tex]b^2 = 12.[/tex] Therefore, we have:

[tex]b^2 = 4[/tex]

Taking the square root of both sides, we get:

[tex]b = 2\sqrt{2 }[/tex]

Finally, we can use the equation [tex]c = b^2/2[/tex] to find the length of the hypotenuse:

[tex]c = (2\sqrt{2} )^2/2 = 4.[/tex]

For similar question on hypotenuse.

https://brainly.com/question/2217700

#SPJ11

The probability of both representatives being girls is 39/158, or approximately 0.247.

To find the probability of both representatives being girls, we first need to find the probability of selecting a girl as the first representative, and then the probability of selecting another girl as the second representative, given that the first one was a girl.

The probability of selecting a girl as the first representative is 40/80, or 1/2, since there are 40 girls in the group of 80 students.

Once a girl has been chosen as the first representative, there will be 39 girls left in the group of 79 students (since one student has already been chosen), so the probability of selecting another girl as the second representative is 39/79.

To find the probability of both events occurring (selecting a girl as the first representative and then selecting another girl as the second representative), we multiply the probabilities together:

1/2 x 39/79 = 39/158

Therefore, the probability is 39/158, or approximately 0.247.

More on probability: https://brainly.com/question/11234923

#SPJ11

Answer:

Step-by-step explanation:

Assuming that the giant sugar cube is a perfect cube, we can calculate its volume by using the formula:

Volume = edge length³

To find the edge length, we need to first calculate the amount of wood used per unit of volume, which is given by:

wood per unit volume = 213.5 m³ / 1 unit of volume

We don't know the unit of volume of the sugar cube, but we can use any consistent unit, such as meters, centimeters, or millimeters. Let's use meters for consistency with the given material amount.

Now, we can find the edge length by solving the following equation for x:

wood per unit volume = 213.5 m³ / x³

x³ = 213.5 m³ / wood per unit volume

x³ = 213.5 m³ / (213.5 m³ / 1 unit of volume)

x³ = 1 unit of volume

Therefore, the edge length of the giant sugar cube is 1 meter.

Finally, we can calculate the volume inside the giant sugar cube by using the formula:

Volume = edge length³

Volume = 1³ = 1 cubic meter

Therefore, the volume inside the giant sugar cube is 1 cubic meter.

If a two-factor analysis of variance produces a statistically significant interaction, it means that the effect of one independent variable on the dependent variable changes depending on the level of the other independent variable.

In other words, the effect of one independent variable on the dependent variable is not the same across all levels of the other independent variable. Therefore, the interaction term is necessary to properly model the relationship between the independent variables and the dependent variable. It is important to interpret the interaction carefully to fully understand the relationship between the variables being studied.

Learn more about independent variable

https://brainly.com/question/29430246

#SPJ4

2.23% is the probability of a city with a population of 200,000, and there will be exactly 2 accidental drownings per year.

The Poisson distribution, is useful for modeling the number of events (in this case, accidental drownings) in a fixed interval (here, a year). Given the average rate of 3.0 drownings per 100,000 people per year, we first need to find the expected number of drownings in a city with a population of 200,000.

Expected drownings per year = (3.0 drownings / 100,000 people) * 200,000 people = 6 drownings

Now, we can use the Poisson probability formula to calculate the probability of exactly 2 accidental drownings per year in this city:

P(X = k) = (λ^k * e^(-λ)) / k!

Here, X represents the number of drownings, k is the desired number of drownings (2 in this case), λ (lambda) is the expected number of drownings per year (6), e is the base of the natural logarithm (approximately 2.718), and k! is the factorial of k.

P(X = 2) = (6^2 * e^(-6)) / 2! = (36 * e^(-6)) / 2 = (36 * 0.002478) / 2 = 0.04461 / 2 = 0.022305

Therefore, the probability that in a city with a population of 200,000, there will be exactly 2 accidental drownings per year is approximately 0.0223 or 2.23%.

Know more about Probability here:

https://brainly.com/question/13604758

#SPJ11

The value of {x} is 8 and the measure of angle A is 30°.

Refer to the image attached. We can see that ∠A and ∠B form a pair of co - interior angles. This means that we can write the relation as -

∠A + ∠B = 180°

So, we can write that -

6x - 18 + 14x + 38 = 180°

20x + 20 = 180°

20x = 160°

{x} = 8

∠A = 6x - 18

∠A = 6 x 8 - 18

∠A = 30°

So, the value of {x} is 8 and the measure of angle A is 30°.

To solve more questions on angles, visit the link-

brainly.com/question/11805053

#SPJ1

The volume of one piece of pizza is π cubic inches.

To find the volume of one piece of pizza, we need to first find the total

volume of the pizza and then divide by the number of pieces.

Find the volume of the entire pizza.

The pizza is a cylinder with a height (thickness) of 1/3 inches and a

diameter of 12 inches.

We can find the radius by dividing the diameter by 2, so the radius is 6

inches. The formula for the volume of a cylinder is

V = πr²h,

where V is the volume, r is the radius, and h is the height.

V = π(6²)(1/3) V = π(36)(1/3) V = 12π cubic inches

Divide the total volume by the number of pieces.

There are 12 congruent pieces, so we need to divide the total volume by 12.

Volume of one piece = (12π cubic inches) / 12 The 12's cancel out, leaving

us with: Volume of one piece = π cubic inches

So, the volume of one piece of pizza is π cubic inches.

for such more question on  volume

https://brainly.com/question/6204273

#SPJ11

8.) The surface area of the given shape would be =532ft²

9.) The surface area of the given circle = 24.62cm²

For question 8.)

To calculate the surface area of the square based pyramid the formula given below is used;

S.A = b² + 2bs

where;

b = 14ft

s = 12 ft

S.A = 14² + 2(14×12)

= 196+ 2(168)

= 196+336

= 532ft²

For question 9:

To calculate the area of the circle, the formula that should be used is given as follows:

S.A = πr²

where:

r = 2.8cm

π = 3.14

S.A = 3.14×2.8×2.8

= 24.62cm²

https://brainly.com/question/28470545

#SPJ1

Dakota rode his bike for 60 km. He understood that he could have been there 16 hours earlier if he had traveled 12 mph quicker. Dakota's actual speed during the bike ride was approximately 41.8 mph.

Let's assume that Dakota's actual speed during the bike ride was x miles per hour.

Using the distance formula:

distance = speed x time

We can calculate the time it took Dakota to complete the ride at his actual speed as:

60 = x * t

where t is the time in hours.

Now, according to the problem, if he had gone 12 mph faster, he would have arrived 16 hours sooner. This means that he would have covered the same distance in less time.

So we can set up another equation:

60 = (x + 12) * (t - 16)

Simplifying this equation:

60 = xt - 16x + 12t - 192

76 = xt - 16x + 12t

Substituting the value of t from the first equation, we get:

76 = 60 - 16x + 12(60/x)

Simplifying this equation:

[tex]16x^2 - 720x + 7200 = 0[/tex]

Dividing both sides by 16:

[tex]x^2 - 45x + 450 = 0[/tex]

Solving this quadratic equation using the quadratic formula:

[tex]$x = \frac{45 \pm \sqrt{45^2 - 41450}}{2}$[/tex]

[tex]$x = 22.5 \pm 7.5\sqrt{5}$[/tex]

We can reject the negative root because it doesn't make sense in the context of the problem.

To learn more about speed

https://brainly.com/question/28224010

#SPJ4

The true population mean of monthly incomes for workers in the factory falls between $1806 and $2263 with 98% of confidence intervals.

To calculate the 98% confidence interval for the mean of the population, we need to use the formula:

CI = sample mean ± Zα/2 * (σ/√n)

Where the sample mean, Zα/2 is the critical value for the given level of confidence (98% in this case), σ is the population standard deviation, and n is the sample size.

First, we need to find the sample mean from the given data:

sample mean = (2120 + 1980 + 2300 + ... + 1940) / 20 = 2034.5

Next, we need to find the critical value (Zα/2) using a standard normal distribution table or calculator. For a 98% confidence interval, the critical value is approximately 2.33.

Now, we can plug in the values and calculate the confidence interval:

CI = 2034.5 ± 2.33 * (518/√20) = (1806, 2263)

Therefore, we can say with 98% confidence that the true population mean of monthly incomes for workers in the factory falls between $1806 and $2263. This means that if we were to take many random samples of the same size from the population and calculate their confidence intervals, approximately 98% of these intervals would contain the true population mean.

To know more about confidence intervals, refer to the link below:

https://brainly.com/question/31420373#

#SPJ11

According to the flood recurrence interval equation, a flood that occurs in 2021, after 149 years of record keeping, and is the third largest ever recorded has a recurrence interval of approximately 50 years.

The flood recurrence interval equation is a statistical method used to estimate the likelihood of a flood of a certain magnitude occurring in any given year. It is based on historical records of floods and takes into account the size and frequency of floods that have occurred in the past.

In this case, the flood that occurred in 2021 is the third largest ever recorded. Based on the historical records of floods over the past 149 years, this flood has a recurrence interval of approximately 50 years. This means that there is a 2% chance of a flood of this magnitude occurring in any given year.

It is important to note that the flood recurrence interval equation is not a perfect predictor of future floods. It is only an estimation based on historical records. Other factors such as climate change and changes in land use can also impact the likelihood and severity of floods.

In conclusion, the recurrence interval for a flood that occurred in 2021, after 149 years of record keeping and is the third largest ever recorded is approximately 50 years. However, it is important to remember that the accuracy of this estimation may vary based on several factors.

To learn more about  interval equation, refer here:

https://brainly.com/question/12165844#

#SPJ11

Answer:

0.2515384615

Step-by-step explanation:

she makes 5/13

5/13*0.654

In order for the senator to have a confidence level of 90% that the sample proportion will not deviate from the actual proportion by more than 5%, they must conduct a survey of at least 273 voters.

To estimate the proportion of United States voters who favor abolishing the electoral college with a 90% confidence level and a margin of error of 5%, we need to use the formula :

n = (z² * p * (1-p)) / E²

where n is the sample size, z is the z-score for the desired confidence level (1.645 for 90% confidence level), p is the estimated proportion (0.5 is a conservative estimate since we don't know the true proportion), and E is the margin of error in proportion (0.05).

Plugging in the values, we get n = (1.645² * 0.5 * (1-0.5)) / 0.05² = 272.25. Since we cannot have a non-integer sample size, we round up to the nearest integer, so the minimum sample size needed is 273.

Therefore, the senator needs to survey at least 273 voters to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%.

To know more about confidence level, refer here:

https://brainly.com/question/22851322#

#SPJ11

Answer:

The correct answer is D.

Based on the given information, it seems that the number of left-handed desks in each classroom is adequate.

Based on the given information, we can calculate the expected number of left-handed students in a classroom:

Expected number of left-handed students = (total number of students in a classroom) x (proportion of left-handed students in the population)

Expected number of left-handed students = 30 x 0.11

Expected number of left-handed students = 3.3

Since each classroom contains four left-handed desks, it seems that the number of left-handed desks is more than enough to accommodate the expected number of left-handed students. In fact, there may even be some unused left-handed desks in each classroom.

Therefore, based on the given information, it seems that the number of left-handed desks in each classroom is adequate.

for such more question on adequate

https://brainly.com/question/28033296

#SPJ11

The number of child tickets sold that day was 81.

To solve the problem, let's use algebra. Let x be the number of child tickets sold and 3x be the number of adult tickets sold. The total sales can then be expressed as:

6.40x + 9.60(3x) = 950.40

Simplifying this equation:

6.40x + 28.80x = 950.40

35.20x = 950.40

x = 27

This means that 27 child tickets were sold. However, the problem asks for the number of child tickets sold on Friday, when three times as many adult tickets were sold.

So the number of child tickets sold on Friday is:

3x = 3(27) = 81

Therefore, 81 adult tickets and 27 child tickets were sold on Friday, and the revenue was $950.40.

To know more about tickets sold, refer here:

https://brainly.com/question/28491872#

#SPJ11

37% of all voters are Democrats. The probability is 0.137, and the option that matches this answer is "0.137".

To find the probability that two randomly selected voters from the town are both Democrats, we need to use the formula for the probability of independent events:
P(A and B) = P(A) x P(B)
where A and B are independent events. In this case, A is the event that the first voter is a Democrat, and B is the event that the second voter is a Democrat.
The probability of the first voter being a Democrat is 0.37, since 37% of all voters in the town are Democrats. The probability of the second voter being a Democrat is also 0.37, since the selection of the first voter does not affect the probability of the second voter being a Democrat. Therefore:
P(A and B) = P(A) x P(B) = 0.37 x 0.37 = 0.1369
Rounding to three decimal places, we get a probability of 0.137. Therefore, the answer is 0.137, and the option that matches this answer is "0.137".

Learn more about probability here

https://brainly.com/question/13604758

#SPJ11

The area of the original trapezoid is B. half the area of the rectangle in step 4.

Given a trapezoid which has the lengths of the parallel bases as b₁ and b₂.

We know that,

Area of a trapezoid = (b₁ + b₂) h / 2, where h is the height between the two bases.

Two trapezoids are joined to get a parallelogram and then rearrange it to form a rectangle.

Area of a rectangle = Length × width

Here, length = b₁ + b₂

Width = height of the trapezoid = h

Area of rectangle in step 4 = (b₁ + b₂) h

Area of trapezoid is half of this.

Hence the correct option is B.

Learn more about trapezoids here :

https://brainly.com/question/8643562

#SPJ1

To create a 90% confidence interval with a margin of error of 4%, the researcher should survey at least 424 students.

To calculate the sample size needed for a 90% confidence interval with a margin of error of 4% (0.04) when estimating the true proportion of students who have a job in addition to attending school, without a preliminary estimate, follow these steps:

1. Identify the desired confidence level (90%) and find the corresponding z-score (z-value). For a 90% confidence level, the z-score is 1.645.

2. Determine the margin of error, which is given as 4% or 0.04.

3. Since no preliminary estimate is available, use 0.5 (50%) as the proportion. This is the most conservative estimate and will result in the largest required sample size.

4. Use the formula for calculating the sample size (n) for proportions:

  n = (Z^2 * P * (1-P)) / E^2

  Where:
  - n is the required sample size
  - Z is the z-score (1.645 for a 90% confidence level)
  - P is the estimated proportion (0.5)
  - E is the margin of error (0.04)

5. Plug the values into the formula:

  n = (1.645^2 * 0.5 * (1-0.5)) / 0.04^2

6. Calculate the result:

  n ≈ 423.06

Since you cannot have a fraction of a student, round up the result to the nearest whole number:

  n = 424

Therefore, to create a 90% confidence interval with a margin of error of 4%, the researcher should survey at least 424 students.

to learn more about confidence interval click here:

brainly.com/question/17212516

#SPJ11

By using a seasonal sales forecast, Gabi can better plan her inventory and staffing levels throughout the year, which can help her optimize her business operations and maximize profits.

To create this forecast, she will need to estimate the expected sales for each month based on historical data and market trends.

Here's an example of how Gabi could create a seasonal sales forecast:

Start with historical sales data: Gabi can use the previous owner's sales records to get an idea of how much revenue the store generated in each month. She should look for patterns or trends in the data that can help her predict future sales.

Identify seasonal trends: Based on the information she has been given, Gabi knows that 60 percent of sales occur during the Christmas holiday season. She should also consider other seasonal factors that could affect sales, such as the weather, local events, and school holidays.

Determine the baseline sales: Gabi can calculate the baseline sales by dividing the non-holiday sales (40 percent) by the number of non-holiday months (eight). This will give her an estimate of the average monthly sales during the non-holiday period.

Adjust for seasonal factors: Gabi should adjust her baseline sales estimate based on the seasonal trends she identified. For example, she might increase sales projections for November and December to reflect the holiday season, and adjust sales projections for other months based on other seasonal factors.

Review and adjust: Gabi should regularly review her sales forecast and adjust it as needed based on actual sales performance and any changes in market conditions.

for such more question on seasonal sales

https://brainly.com/question/14997249

#SPJ11

The dimensions of the cylindrical mailing tube of greatest volume that may be mailed using the US Postal Service are approximately:

Diameter: 3.45 inches

Length: 18.7 inches
Volume: 123.8 cubic inches.

To find the dimensions of the cylindrical mailing tube of greatest volume that may be mailed using the US Postal Service, we need to consider the dimensional restrictions set by the Postal Service. According to their regulations, the length and girth (circumference plus the diameter) of a package must not exceed 108 inches combined.

Let's assume that the tube has a diameter of "d" and a length of "L". The girth of the package is the sum of the circumference of the circular ends and the diameter of the tube, so we have:

Girth = 2π(d/2) + d = πd + d

The length and girth must satisfy the inequality:

L + Girth ≤ 108

Substituting the expression for Girth, we get:

L + πd + d ≤ 108

Solving for L in terms of d, we get:

L ≤ 108 - (π + 1)d

Now, let's consider the volume of the cylindrical tube, which is given by:

V = πr²L = (πd²/4) L

Substituting the expression for L, we get:

V = (πd²/4) (108 - (π + 1)d)

To find the maximum volume, we can take the derivative of V with respect to d, set it equal to zero, and solve for d:

dV/dd = 0

d[πd²/4 (108 - (π + 1)d)]/dd = 0

πd/2 - 3π²d/4 - π/4 + 27/4 = 0

Solving for d, we get:

d = 27/(4π - 6π²)

Substituting this value of d back into the expression for L and the equation for the maximum volume, we get:

L = 108 - (π + 1)d ≈ 18.7 inches

V = (πd²/4) (108 - (π + 1)d) ≈ 123.8 cubic inches

Know more about cylindrical here:

https://brainly.com/question/28995951

#SPJ11

It takes approximately 52.7 hours for the activity of a sample of gallium-67 to fall to 6.73 percent of its original value.

The decay of radioactive substances is governed by the following equation:

[tex]N(t) = N_{0} e^{(-\lambda t)[/tex]

where:

N(t) is the amount of the substance at time t

N₀ is the initial amount of the substance

λ is the decay constant

t is time

The half-life of gallium-67 is 78.2 hours, which means that:

λ = ln(2)/t₁/₂ = ln(2)/78.2 = 0.00887 h⁻¹

Let N be the amount of gallium-67 remaining after time t, and N₀ be the initial amount. Then, we can use the above equation to find the time t required for the activity of the sample to fall to 6.73 percent of its original value:

N/N₀ = 0.0673

[tex]0.0673 = e^{(-\lambda t)}[/tex]

Taking the natural logarithm of both sides:

ln(0.0673) = -λt

t = ln(1/0.0673)/λ

t = ln(14.84)/0.00887

t ≈ 52.7 hours

for such more question on word problem

https://brainly.com/question/13818690

#SPJ11

“My mother always used to say: The older you get, the better you get, unless you’re a banana.”

—Rose (Betty White), The Golden Girls