Model the scenario with an explicit formula and a recursive formula using n for the day and Vn for the number of days. Explain your reasoning.​

Answer:

153.86 units²

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

Given circumference we can find r, that is

C = 2πr , so

2πr = 43.96 ( divide both sides by 2π )

r = \(\frac{43.96}{6.28}\) = 7 , then

A = πr² = 3.14 × 7² = 3.14 × 49 ≈ 153.86 units²

The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

To know more about probability, visit:

https://brainly.com/question/29120105

#SPJ11

The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.

Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:

Diameter in kilometers = Diameter in miles × Conversion factor

Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile

Diameter in kilometers = 12,681.6 kilometers

Rounding this value to the nearest whole number, we get 12,682 kilometers.

Therefore, the correct answer is option D: 12,682 km.

Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.

Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.

Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.

In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

For more such questions on diameter visit:

https://brainly.com/question/28162977

#SPJ8

We cannot use the normal distribution to approximate the random variable x in this case because the second condition (nq ≥ 5) is not satisfied since 4.64 is less than 5. The correct option is (OC) No, because np < 5 and ng <5.

To determine whether the normal distribution can be used to approximate the random variable x in a binomial experiment, we need to check if the conditions for using the normal approximation are met.

The conditions are typically based on the sample size (n) and the probabilities of success (p) and failure (q).

In this case, the given values are:

n = 16

p = 0.71

q = 0.29

To use the normal approximation, the following conditions should be satisfied:

1. np ≥ 5

2. nq ≥ 5

Let's check if these conditions are met:

1. np = 16 * 0.71 = 11.36

2. nq = 16 * 0.29 = 4.64

Based on the calculated values, we can see that the second condition (nq ≥ 5) is not satisfied since 4.64 is less than 5.

Therefore, we cannot use the normal distribution to approximate the random variable x in this case.

To know more about normal distribution refer here:

https://brainly.com/question/29509087#

#SPJ11

The three fishermen are discussing the best depth to submerge their hooks to catch fish.

The first fisherman believes that 2 meters is the best depth, the second fisherman believes that 4 meters is the best depth, and the third fisherman believes that 5 meters is the best depth.

The best depth will vary depending on the type of fish you are trying to catch, the time of year, the weather conditions, and the location.

In general, fish tend to be found in different depths of water depending on their species. For example, bass are typically found in shallow water, while trout are typically found in deeper water. The time of year can also affect the depth of water where fish are found. In the summer, fish tend to be found in deeper water, while in the winter, they tend to be found in shallower water.

Learn more about fishermen on

https://brainly.com/question/13735100

#SPJ1

Three fishermen are on a yacht fishing in a mangrove area. They meet on the deck of the boat one meter above sea level, and discuss the appropriate depth to which they should submerge their hooks to get more fish, one places it at 2 meters, another at 4 meters and the last one at 5 meters:

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

1.the number of people in the labor force is 38.

2.the unemployment rate in Napielodougou is 5.26%.

3.the participation rate in Napielodougou is 60.32

1. Calculation of the number of people in the labor force: The number of people in the labor force is equal to the sum of employed and unemployed persons.

That is, in Napielodougou, the number of people in the labor force is equal to the number of people who have full-time jobs and part-time jobs, plus the number of people who are jobless but would like to work.

Therefore, the number of people in the labor force is calculated as follows: Number of people in the labor force = Number of full-time jobs + Number of part-time jobs + Number of jobless people who want to work = 25 + 10 + (75 - 25 - 10 - 12 - 10 - 5 - 8 - 2) = 25 + 10 + 3 = 38.

Therefore, the number of people in the labor force is 38.

2. Calculation of the unemployment rate in the village of Napielodougou: The unemployment rate is calculated by dividing the number of unemployed people by the number of people in the labor force and then multiplying the result by 100%.

The number of unemployed persons is the number of jobless people who want to work but could not find a job. Therefore, the unemployment rate in Napielodougou is calculated as follows:

Unemployment rate = Number of unemployed people / Number of people in the labor force × 100% = (75 - 25 - 10 - 12 - 10 - 5 - 8 - 2 - 2) / 38 × 100% = 1 / 19 × 100% = 5.26%.

Thus, the unemployment rate in Napielodougou is 5.26%.

3. Calculation of the participation rate in the village of Napielodougou: The participation rate is calculated by dividing the number of people in the labor force by the total number of working-age people (excluding those under the age of 16).

Therefore, the participation rate in Napielodougou is calculated as follows: Participation rate = Number of people in the labor force / Total number of working-age people × 100% = 38 / (75 - 12) × 100% = 38 / 63 × 100% ≈ 60.32%.

Hence, the participation rate in Napielodougou is 60.32

Learn more about labor force at

https://brainly.com/question/13962639

#SPJ11

The direction of the resultant vector (10, 4) Ө 0 + (−14, -16) is approximately 108.43° W.

To find the direction of the resultant vector, we can use trigonometry. The direction is given by the angle that the resultant vector makes with the positive x-axis.

Given the vectors (10, 4) and (−14, -16), we can calculate the direction of the resultant vector.

First, let's find the x-component and y-component of the resultant vector by adding the corresponding components of the given vectors:

x-component: 10 + (-14) = -4

y-component: 4 + (-16) = -12

Next, we can calculate the magnitude of the resultant vector using the Pythagorean theorem:

Magnitude of the resultant vector = √((-4)^2 + (-12)^2)

= √(16 + 144)

= √160

= 12.65 (rounded to the nearest hundredth)

To find the direction, we can use the arctan function:

θ = tan^(-1)(y-component / x-component)

= tan^(-1)(-12 / -4)

= tan^(-1)(3)

≈ 71.57° (rounded to the nearest hundredth)

However, we need to determine the direction with respect to the west (W) direction.

To do that, we subtract the angle from 180°:

θ_W = 180° - 71.57°

≈ 108.43° (rounded to the nearest hundredth)

For similar question on resultant vector.

https://brainly.com/question/110151  

#SPJ8

Answer: Your answer should be A.

Step-by-step explanation:

Answer:

71.9

Step-by-step explanation:

Whenever you want to round a number to a particular digit, look only at the digit immediately to its right. For example, if you want to round to the nearest tenth, look to the right of the tenths place: This would be the hundredths place digit. Then, if it is 5 or higher, you get to add one to the tenths digit.

After rounding 71.916476787 to 1 decimal place we get 71.9.

We round numbers to get an approximate value of the given number in more compact form and which is easy to work with.

According to the given question we have to round 71.916476787  to 1 decimal place.

So, to round 71.916476787 to 1 decimal place we'll look at the digit of 2 decimal place here in this number it is 1 hence it is less than 5 so we can make all the digits after 1 decimal places zero and rewrite this number as

71.900000000 and we know zeroes are meaning less to the right of the decimal so this can be written as 71.9.

learn more about rounding of numbers :

https://brainly.com/question/28562556

#SPJ2

Answer: y = 16807

Step-by-step explanation:

7 * 7 * 7 * 7 * 7 * 7 = 117649

7^16807 = 117649

Answer:

Option 3

Step-by-step explanation:

The slope is \(\frac{-2-6}{5-1}=-2\).

The equation of the line through \((x_1, y_1)\) with slope \(m\) is \(y-y_1=m(x-x_1)\).

y-6=-2(x-1) is the equation is a point slope form equation for line AB

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

point A, with coordinates (1, 6), and point B, with coordinates (5, -2)

m=-2-6/5-1

m=-8/4

=-2

So slope is -2.

The point slope intercept of line is

y-y₁=m(x-x₁)

y-6=-2(x-1)

Hence y-6=-2(x-1) is the equation is a point slope form equation for line AB

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ2

Answer:

17% of 13 is 2.21

13 + 2.21 = 15.21

Step-by-step explanation:

Joseph's lunch costs = $13 without taxes

He leaves tip for the waiter = 17% of cost of the lunch

= 17% of $13

= 13 ×  

= ( 13 × 0.17)

= $2.21

Total cost of lunch + tip = 13 + 2.21

                                      = $15.21

This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

Learn more about nonlinear problem: brainly.com/question/31457669

#SPJ11

Answer:

it's going to be the first one, (x+7,-y)

Step-by-step explanation:

take one point, A for example and count how far it moved left and right. left is negative, right is positive, do the same for y

The correct statements about given synthetic division are C, D, and F

"It is a polynomial with degree 2."

"It is defined as a way of dividing one polynomial by another polynomial of first degree."

For given question,

We have been given a quadratic polynomial \(F(x)=4x^{2} -17x-15\)

We can factorize above quadratic polynomial as,

\(F(x)\\=4x^{2} -17x-15\\=4x^{2} -20x+3x-15\\=4x(x-5)+3(x-5)\\=(x-5)(4x+3)\)

This means the factors of \(4x^{2} -17x-15\) are (x - 5) (4x + 3)

And the roots of the polynomial would be,

\(\Rightarrow F(x)=0\\\Rightarrow 4x^{2} -17x-15=0\\\Rightarrow (x-5)(4x+3)=0\\\Rightarrow x-5=0~~,~~4x+3=0\\\Rightarrow x=5~~,~~x=-\frac{3}{4}\)

This means, the roots of \(4x^{2} -17x-15\) are 5 and \(\frac{-3}{4}\)

Therefore, the correct statements about given synthetic division are C, D, and F

Learn more about polynomial here:
https://brainly.com/question/11536910

#SPJ2

The effective annual rate (EAR) for the investment account with a return of 14.00% (APR) compounded quarterly can be calculated using the formula:

EAR = (1 + (APR / n))^n - 1

Where APR is the annual percentage rate and n is the number of compounding periods per year. In this case, since interest is compounded quarterly (every 3 months), n would be 4.

Plugging in the values, we have:

EAR = (1 + (0.14 / 4))^4 - 1

Calculating this expression, we find that the effective annual rate is 14.62%.

The effective annual rate (EAR) is a measure of the true annual interest rate taking into account the effects of compounding. It allows for easy comparison of different interest rates that compound over different periods.

In this scenario, the investment account has an annual percentage rate (APR) of 14.00%, which represents the nominal interest rate per year. However, the interest is compounded quarterly, meaning it accrues and is added to the account balance every 3 months. To determine the actual annual rate accounting for compounding, we calculate the effective annual rate (EAR).

By using the formula mentioned above and plugging in the values, we can calculate the EAR. The APR is divided by the number of compounding periods per year (4, in this case), and then 1 is added to this result. The entire expression is raised to the power of the number of compounding periods per year (4) and then subtracted by 1.

The resulting EAR is 14.62%, indicating the equivalent annual rate considering the effects of compounding on the investment account.

Learn more about nominal interest rate here:

brainly.com/question/32615546

#SPJ11

Complete question:

Kono divides The numerator and the denominator of 48 over 72 by the greatest common factor to simplify the fraction in one step by what number does he divide

Answer:

2/3

Step-by-step explanation:

Given the number : 48 / 72

Obtain the greatest common factor of 48 and 72

- - - - 48 - - - - 72

- 2-- 24 - - - - 36

- 2 - 12 - - - - - 18

- 2 - 6 - - - - - - 9

- 3 - 2 - - - - - - 3

The greatest common factor of 48 and 72 is hence (2 * 2 * 2 * 3) = 24

Hence, divide both the numerator and denominator by 24 ;

Numerator = 48/24 = 2

Denominator = 72 / 24 = 3

= 2/3

One student correctly identified the sequence -6,1,8,15,22,... as an arithmetic sequence, and provided a sufficient explanation.

Arithmetic sequences have a constant difference between consecutive terms, while geometric sequences have a constant ratio between consecutive terms. To determine if a sequence is arithmetic or geometric, one can examine the difference or ratio between consecutive terms.

For the sequence -6,1,8,15,22,..., the difference between consecutive terms is 1-(-6) = 7, 8-1 = 7, 15-8 = 7, 22-15 = 7, and so on. Since there is a constant difference of 7 between consecutive terms, this sequence is an arithmetic sequence.

The student's explanation correctly identified the constant difference and used it to classify the sequence as arithmetic. Therefore, this student provided a correct and sufficient answer.

Learn more about Sequence:

brainly.com/question/30262438

#SPJ11

The point (-7,4) is the farthest from the point and the distance is 11 units away, the correct option is (d).

We have to find that which point is the farthest from the point (4,4),

The distance(d) between two points (x₁, y₁) and (x₂, y₂) can be calculated by the distance formula : √((x₂-x₁)² + (y₂-y₁)²);

Using this formula, we can find the distance between each of the points and (4, 4):

⇒ For point (-7, 4):

d = √((4 - (-7))² + (4 - 4)²)

d = √(11²)

d = 11 units

⇒ For point (4, 4):

d = √((4 - 4)² + (4 - 4)²)

d = 0 units

⇒ For point (4, -5):

d = √((4 - 4)² + (-5 - 4)²)

d = √(9²)

d = 9 units,

Therefore, the point farthest away from (4, 4) is (d) Point (-7, 4), and the distance is 11 units.

Learn more about Distance here

https://brainly.com/question/14451972

#SPJ1

The given question is incomplete, the complete question is

A graph with the x-axis starting at -10, with tick marks every one unit up to 10. The y-axis starts at -10, with tick marks every one unit up to 10. A point is plotted at (-7, 4), at (4, 4) and at (4, -5).

Which of the points plotted is farther away from (4, 4), and what is the distance?

(a) Point (4, -5), and it is 9 units away

(b) Point (4, -5), and it is 11 units away

(c) Point (-7, 4), and it is 9 units away

(d) Point (-7, 4), and it is 11 units away

Answer:

Step-by-step explanation:

Answer:

help i help you

Step-by-step explanation:

where are the ansewrs at

Answer:

What you have is correct :)

Step-by-step explanation:

Answer:

34 feet

Step-by-step explanation:

let length of ladder be x

\( \ \sin(34) = \frac{17}{x} \)

\(x \sin(34) = 17\)

\(x = \frac{17}{ \sin(34) } \)

x = 32.131083564

The solution to the initial value problem. y' (t) - 2y = 6, y(2) = 2 is  y(t) = -3 + (5/e^4)e^(2t)..

To solve the initial value problem y'(t) - 2y = 6 with y(2) = 2,

we will use an integrating factor and the given initial condition. Here's the step-by-step solution:

1. Identify the integrating factor: The integrating factor is e^(-2t).

2. Multiply the equation by the integrating factor: e^(-2t)y'(t) - 2e^(-2t)y = 6e^(-2t).

3. Observe that the left side of the equation is the derivative of the product y(t)e^(-2t): (y(t)e^(-2t))' = 6e^(-2t).

4. Integrate both sides with respect to t: ∫(y(t)e^(-2t))' dt = ∫6e^(-2t) dt.

5. Integrate: y(t)e^(-2t) = -3e^(-2t) + C.

6. Solve for y(t): y(t) = -3 + Ce^(2t).

7. Apply the initial condition y(2) = 2: 2 = -3 + Ce^(4).

8. Solve for C: C = (5/e^4).

9. Substituting C back into the solution for y(t): y(t) = -3 + (5/e^4)e^(2t).
Learn more about integrating factor :  https://brainly.com/question/31400481

#SPJ11

Answer:

40

Step-by-step explanation:

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

For such more questions on solution

https://brainly.com/question/24644930

#SPJ8

The triangle ABC has a surface area of 17.7 square units. Rounding to the nearest tenth of a square unit,

Heron's Formula can be used to calculate the triangle ABC's area. The equation reads as follows:

A = √[s(s-a)(s-b)(s-c)]

Where s is one-half of the triangle's circumference and a, b, and c are its three sides.

By summing the triangle's sides, we can determine the perimeter:

P = a + b + c

The formula below is used to get the other half of the perimeter.

s = P/2

For the triangle ABC, we have the sides a=3, b=5, and c=4.

Therefore, half of the perimeter is s = 8.

Now, Heron's formula can be used to determine the triangle ABC's surface area:

A = √[s(s-a)(s-b)(s-c)]

= √[8(8-3)(8-5)(8-4)]

= √[8(5)(3)(4)]

= 17.7 square units

Therefore, the triangle ABC has a surface area of 17.7 square units, Rounding to the nearest tenth of a square unit.

To learn more about Heron's Formula, visit the link below:

https://brainly.com/question/29156195

#SPJ4

Answer:

Answer is b :D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The following calculation can be used to calculate the total number of extra pennies (p) that are required to reach the amount of $2: p = (200 - 25 - 12 * 10) / 1.

The value of the coins that have already been discovered is taken into consideration when determining how many further pennies are required to attain the target sum of $2. The value of a quarter is 25 cents, hence a pair of quarters is worth a total of 50 cents (25 times 2 equals 50). There are twelve dimes, and each one is worth ten cents, for a grand total of twelve times ten, which is one hundred and twenty cents. In the end, the 23 pennies amount to 23 cents (23 multiplied by 1 equals 23).

To determine how many more pennies are required to reach $2, we begin by deducting the total value of the coins that were discovered (193 cents) from $2 (which may be represented as 200 cents). This gives us the number of further pennies that are required. The equation is rewritten as follows: p = (200 - 25 - 12 * 10) / 1, where p is the number of additional pennies that are required. By solving the equation, we are able to find out how many pennies are necessary to attain a grand total of two dollars.

Learn more about equation here:

https://brainly.com/question/10724260

#SPJ11