In ARST, r = 58 cm, m/S=48° and m/T=29°. Find the length of s, to the nearest
centimeter.

F(4) = 16 - 8 In(4) = 8 - 4 In(2)

So the global minimum value is F(2) ≈ -2.6137 and the global maximum value is F(1) = 1 (since F(4) is not greater than 1).

To find the global minimum and maximum of the continuous function F(x) = x^2 - 8 In(x) on the interval [1, 4], we need to find the critical points of the function and evaluate the function at those points and at the endpoints of the interval.

First, we take the derivative of the function:
F'(x) = 2x - 8/x

Setting F'(x) = 0, we get:
2x - 8/x = 0
Multiplying both sides by x, we get:
2x^2 - 8 = 0
Dividing both sides by 2, we get:
x^2 - 4 = 0
Factoring, we get:
(x + 2)(x - 2) = 0

So the critical points are x = -2 and x = 2. However, x = -2 is not in the interval [1, 4], so we only need to consider x = 2.

Now we evaluate the function at the critical point and the endpoints of the interval:
F(1) = 1 - 8 In(1) = 1
F(2) = 4 - 8 In(2) ≈ -2.6137
F(4) = 16 - 8 In(4) = 8 - 4 In(2)

So the global minimum value is F(2) ≈ -2.6137 and the global maximum value is F(1) = 1 (since F(4) is not greater than 1).

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Answer:

Step-by-step explanation:

To find the equation that has the same solution as x^2 - 10x - 3 = 5, we can start by simplifying the left side of the equation by adding 8 to both sides:

x^2 - 10x - 3 = 5

x^2 - 10x - 8 = 0

Now we need to find an equation with the same solutions as this simplified equation. We can do this by factoring the quadratic equation into two linear factors:

x^2 - 10x - 8 = 0

(x - 2)(x - 8) = 0

Therefore, the solutions to the equation x^2 - 10x - 3 = 5 are x = 2 and x = 8. We can write two equations that have these solutions:

(x - 2) = 0

(x - 8) = 0

So the two equations that have the same solution as x^2 - 10x - 3 = 5 are x - 2 = 0 and x - 8 = 0. These equations can be simplified as x = 2 and x = 8, which are the same solutions as the original quadratic equation. Therefore, the equations x - 2 = 0 and x - 8 = 0 have the same solution as x^2 - 10x - 3 = 5.

(x - 5)^2 = 33

a) There are 1540 ways that the teacher can select the three students.

b) The probability that all three students selected are girls is approximately 0.176 or 17.6%.

c) The probability that at least one boy is selected is approximately 0.824 or 82.4%.

a)

To find the number of ways the teacher can select three students out of 22 students (7 boys and 15 girls), we can use the combination formula. The number of ways to select r items from a set of n items is given by:

nCr = n! / (r! * (n-r)!)

where n! represents the factorial of n (i.e., n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1), and r! represents the factorial of r. Applying this formula, we get:

22C3 = 22! / (3! * (22-3)!) = 22! / (3! * 19!) = (22 x 21 x 20) / (3 x 2 x 1) = 1540

Therefore, there are 1540 ways that the teacher can select the three students.

b)

To find the probability that all three students selected are girls, we can use the formula for the probability of an event occurring. Since there are 15 girls and 7 boys, the probability of selecting a girl is 15/22 for the first selection, 14/21 for the second selection (since there are now 14 girls left out of 21 remaining students), and 13/20 for the third selection. Applying the formula, we get:

P(all three are girls) = (15/22) x (14/21) x (13/20) ≈ 0.176

Therefore, the probability that all three students selected are girls is approximately 0.176 or 17.6%.

c)

To find the probability that at least one boy is selected, we can use the complement rule. The complement of selecting at least one boy is selecting all three girls, which we calculated in part (b) to be approximately 0.176. Therefore, the probability of selecting at least one boy is:

P(at least one boy) = 1 - P(all three are girls) ≈ 1 - 0.176 ≈ 0.824

Therefore, the probability that at least one boy is selected is approximately 0.824 or 82.4%.

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Answer:

a)

[tex]m = \frac{15 - 10}{4 - 2} = \frac{5}{2} [/tex]

[tex]10 = \frac{5}{2} (2) + b[/tex]

[tex]10 = 5 + b[/tex]

[tex]b = 5[/tex]

[tex]y = \frac{5}{2}x + 5[/tex]

b) The function is already given.

c)

[tex]m = \frac{100 - 40}{30 - 10} = \frac{60}{20} = 3 [/tex]

[tex]100 = 3 (30) + b[/tex]

[tex]100 = 90 + b[/tex]

[tex]b = 10[/tex]

[tex] y = 3x + 10[/tex]

The fraction of the school days in February that you walked to school is 7/10 or 0.7 when expressed as a decimal.

The fraction of the school days in February that you walked to school can be represented as:

(number of days you walked) / (total number of school days in February)

Since you walked 14 out of 20 days in February, we can substitute these values into the formula:

(number of days you walked) / (total number of school days in February) = 14 / 20

Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor (2), we get:

(number of days you walked) / (total number of school days in February) = 7 / 10

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For the given case, there is evidence that the true mean number of hours of screen time for US adults is greater than 3.5.

Here, the researcher is 95% confidence interval from 3.6 hours to 8.1 hours captures  y = the true mean amount of daily screen time for US adults.
If 3.5 hours falls below this interval, it is likely that the true mean number of hours of screen time for US adults is greater than 3.5 hours.

A confidence interval is a measure of values that is used to evaluate a statistical parameter which tends to involve the true form of the parameter a predetermined proportion of the time if the procedure of searching the group of values is repeated numerous times.

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The total length of the race is approximately 28.24 miles.

To determine the total length of the race, we can use the given information: Piotr has completed 24 miles, which represents 85% of the race. We can set up a proportion to find the total length. Let 'x' represent the full length of the race:

(24 miles) / x = 85% / 100%

To solve for 'x', we can first convert the percentage to a decimal by dividing 85 by 100, resulting in 0.85:

24 / x = 0.85

Next, we can cross-multiply:

0.85 * x = 24

Now, we can solve for 'x' by dividing both sides by 0.85:

x = 24 / 0.85

x ≈ 28.24 miles

Therefore, the total length of the race is approximately 28.24 miles. Piotr has completed 85% of this distance, which means he has run 24 miles and has around 4.24 miles remaining to finish the race.

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The discrepancy in the results: The theoretical probability may not be calculated correctly and enough trials have not been performed to give the desired result

In the given scenario, 81% of money spent at full-service restaurants in America is through debit, credit, or pre-paid cards. However, one restaurant found that 421 out of 973 customers used these payment methods. Possible reasons for the discrepancy in the results are:

1. The theoretical probability may not be calculated correctly: The 81% figure might not accurately represent the actual proportion of customers using cards in full-service restaurants. It could be due to incorrect data collection or interpretation.

3. Enough trials have not been performed to give the desired result: The data from one restaurant for one week might not be enough to accurately reflect the overall trend. A larger sample size and longer time frame would give a more accurate representation.

It's important to note that there might not necessarily be a discrepancy in the result; it could be a difference due to variations in individual restaurant data compared to the overall average.

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Answer:

more i formation required

Step-by-step explanation:

Answer:

[tex]8x+71/2[/tex]

Step-by-step explanation:

I did the test

Hope this helps :)

The 10 cupcakes will weigh approximately 25.9 ounces when one cubic inch is about 0. 55 ounces, the diameter of the mold is 3 inches and the height of the mold is 2 inches.

Given data:

Diameter of the mold = 3 inches

Radius = 3/2 = 1.5 inches

Height of the mold = 2 inches.

One cubic inch = 0.55 ounces

π = 3. 14

We need to find how many ounces will 10 cupcakes weigh. to find that we need to find the volume of a cone and the weight of one cupcake. we can find  the volume of a cone given by the formula,

[tex]V = (1/3)πr^2h[/tex]

Where:

r = radius

h = height

By Substituting the r and h values into the formula we get:

[tex]V = (1/3)πr^2h[/tex]

[tex]= (1/3) π ((1.5)^2) × (2)[/tex]

[tex]= (1/3) π×(2.25)×(2)[/tex]

= 1.5π

When one cubic inch of the cone is about 0.55 ounces, the weight of one cupcake is approximately

= 1.5π × 0.55

= 0.825π ounces.

The weight of 10 cupcakes is determined by multiplying by the weight of one cupcake, it is given as:

= 10 × 0.825π

= 8.25π ounces

= 8.25 × 3.14

= 25.9 ounces.

Therefore, the 10 cupcakes will weigh approximately 25.9 ounces.

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The system of equations 3x + 2y = –2 and 6x + 4y = 15 can be classified as inconsistent systems.

To classify the given system of equations, we will analyze the coefficients of the variables and constants to determine if the equations are dependent, independent, or inconsistent. The system is:

1) 3x + 2y = -2
2) 6x + 4y = 15

First, let's check if the equations are multiples of each other. If we multiply the first equation by 2, we get:

1') 6x + 4y = -4

Comparing equation 1' with equation 2, we can see that the left-hand sides are equal, but the right-hand sides are different (-4 ≠ 15). Therefore, the equations are not multiples of each other.

Next, we'll examine the coefficients of x and y. In both equations, the ratio of the coefficients of x to y is the same (3/2 and 6/4). This means the lines represented by these equations are parallel.

Since the lines are parallel and not multiples of each other, they do not intersect, meaning there is no common solution for this system of equations. Therefore, we can classify this system as inconsistent system.

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Answer:

Step-by-step explanation:

git

Answer:

  (A)  alternate interior angles

Step-by-step explanation:

You want the missing statement in the proof that opposite angles of a parallelogram are congruent.

The proof here shows angles A and C are congruent because they are corresponding parts of congruent triangles. To get there, the triangles must be shown to be congruent.

In statement 5, the triangles area claimed congruent by the ASA theorem, which requires two corresponding pairs of angles and congruent sides.

In statement 4, the relevant sides are shown congruent, so it is left to statement 3 to show two pairs of angles are congruent.

Of the offered answer choices, only one of them deals with two pairs of angles. Answer choice A is the correct one.

Answer:

Congruent, impossible, not congruent.

Step-by-step explanation:

a) Congruent because of AAS congruency.

b) Impossible to tell. There is no congruency rule with 1 angle and 1 side.

c) Not congruent. Sides should not be equal.

The amplitude of the current I is 16.9 Amperes

To find the amplitude of the current I in the given circuit with an alternating current E(t) = 120sin(12t), inductance L = 0.31 H, resistance R = 7 ohms, and capacitance C = 0.029 F, we need to determine the impedance (Z) of the circuit first.

The impedance Z can be calculated using the formula:

Z = √((R²) + (XL - XC)²)

Where XL is the inductive reactance, and XC is the capacitive reactance. XL can be calculated as:

XL = 2πfL

And XC can be calculated as:

XC = 1/(2πfC)

Here, f is the frequency of the alternating current, which can be determined from the given function E(t) = 120sin(12t) as:

f = 12/(2π) = 1.91 Hz

Now, we can calculate XL and XC:

XL = 2π(1.91)(0.31) = 3.74 ohms

XC = 1/(2π(1.91)(0.029)) = 2.89 ohms

Next, we can find the impedance Z:

Z = √((7²) + (3.74 - 2.89)²) = √(49 + 0.72) = 7.1 ohms

Finally, we can find the amplitude of the current I using Ohm's law:

I = E(t)/Z

Since we're looking for the amplitude, we only need the maximum value of E(t), which is 120 V:

I = 120/7.1 = 16.9 A

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In this prism, lateral Area =  858.54 m² and surface area = 890.54 m².

Firstly, we will find the lateral area of the prism by applying the formula:

Lateral  area = perimeter × height

Perimeter = sum of all the sides of prism

= 4 + 8 + 8.94  = 20.94 m

Lateral Area = 20.94 * 41  =  858.54 m²

Now, we have to find the surface area of the prism.

Surface area = Lateral Area + 2 × ( Base Area)

Base Area = the area of a triangle with sides 4, 8, and 8.94.

Now, we will calculate the area of the triangle

Firstly, we will find s for calculating the area of triangle and then apply the formula.

s = ( 4 + 8 + 8.94)/2 = 10.47 m

Area of triangle =  [tex]\sqrt{ (10.47 (10.47 - 4)(10.47 - 8)(10.47 - 8.94))}[/tex]

= [tex]\sqrt{(10.47 (6.47)(2.47)(1.53))}[/tex]

= 16 m²

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Correct question:

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. The figure is not drawn to scale. The bases are right triangles.

Answer:

The triangular prism has two triangular bases and three rectangular lateral faces.

First, we need to find the area of each triangular base. Using the formula for the area of a triangle:

base x height / 2

We can calculate the area of one triangular base as:

(10 x 12) / 2 = 60 units²

Now we need to find the area of each rectangular lateral face. All three faces have the same dimensions of 10 units by 14 units, so the area of each face is:

10 x 14 = 140 units²

To find the total surface area of the prism, we add up the areas of both triangular bases and all three rectangular faces:

Total surface area = 2 x (area of triangular base) + 3 x (area of rectangular face)

Total surface area = 2 x 60 units² + 3 x 140 units²

Total surface area = 120 units² + 420 units²

Total surface area = 540 units²

Therefore, the surface area of the triangular prism is 540 square units.

The probability of  P(Ski) is 7 / 30, P(Snowboard) is 13 / 30,P(Ski & Snowboard) is 2/15 and P(ski or snowboard) is  8/15.

1. Probability of a student skiing (P(Ski)):
  P(Ski) = number of students who ski / total number of students = 28 / 120 = 7 / 30

2. Probability of a student snowboarding (P(Snowboard)):
  P(Snowboard) = number of students who snowboard / total number of students = 52 / 120 = 13 / 30

3. Probability of a student skiing and snowboarding (P(Ski & Snowboard)):
  P(Ski & Snowboard) = number of students who ski and snowboard / total number of students = 16 / 120 = 4 / 30

=2/15

4.Probability(ski or snowboard) = (7/30) + (13/30) - (2/15)

P(ski or snowboard) = 8/15
Therefore, the probabilities are:

P(ski) = 7/30

P(snowboard) = 13/30

P(ski and snowboard) = 2/15

P(ski or snowboard) = 8/15

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We can be 99% confident that the true average price of all foreclosed homes in Washington, DC is no higher than $460,794.81.

To find the upper 99% confidence limit for the average price of all foreclosed homes in Washington, DC, we can use the formula:

Upper limit = sample mean + (z-score)*(standard error)

First, we need to find the z-score for the 99% confidence level. From a standard normal distribution table, we can find that the z-score for a 99% confidence level is 2.576.

Next, we need to find the standard error, which is the standard deviation of the sample divided by the square root of the sample size:

standard error = standard deviation / √sample size

Plugging in the values given in the problem, we get:

standard error = 220,978 / √40

standard error = 34,955.84

Finally, we can plug in the values for the sample mean, z-score, and standard error into the formula to get the upper limit:

Upper limit = 375,334 + (2.576)*(34,955.84)

Upper limit = 460,794.81

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If the store advertises 60 square foot flooring for $253, then the cost for "per-square foot" is (c) $5.55.

To find the cost per square foot for the flooring, we need to divide the total cost of the flooring including the "installation-fee' by the total square footage of the flooring.

⇒ Total cost of flooring + installation fee = $253 + $80 = $333,

⇒ Total square footage of the flooring = 60 sq. ft.

So, Cost per square foot = (Total cost of flooring and installation fee)/(Total square footage of the flooring),

⇒ Cost per square-foot = 333/60,

⇒ Cost per square foot = $5.55/sq. ft.

Therefore, the correct option is (c).

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The 25 fluid ounces is greater than one pint is correct statement .

Relation between fluid ounces and pint ,

There are 16 fluid ounces in one pint.

Conversion of fluid ounces to pint

This implies that,

1 fluid ounces is equal to  one by sixteen pint.

To be precise,

25 fluid ounces is equal to 25 / 16pints

⇒  25 fluid ounces is equal to 1.5625.

However, since 1.5625 is greater than 1,

This implies that 25 fluid ounces is greater than 1 pint.

So, 25 fluid ounces is greater than 1 pint.

Because 25 is greater than 16.

And 1 pint is not greater than 25 fluid ounces.

Therefore, the 25 fluid ounces is greater than one pint.

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Answer:

2(x - 3) < -24

x - 3 < -12

x < -9

The inequality that represents the given statement is 2(x-3) ≤ -24, where x is the unknown number.

The given statement can be translated into an inequality as "twice the difference of a number (x) and 3 is at most -24". Mathematically, this can be represented as 2(x-3) ≤ -24. Simplifying this inequality, we get 2x - 6 ≤ -24, or 2x ≤ -18, which gives x ≤ -9. Therefore, any number less than or equal to -9 satisfies the given statement.

For example, x = -10 satisfies 2(-10-3) = -26, which is less than or equal to -24. However, any number greater than -9 does not satisfy the given statement. For example, x = -8 gives 2(-8-3) = -22, which is greater than -24. Therefore, the solution set for the given inequality is x ≤ -9.

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The area of the triangle ∆WXY is derived to be 5.7 to the nearest tenth.

When two side length of a triangle and the angle between them is given, the area is half the multiplication of the two sides and the sine of the angle.

Area of the triangle = 1/2 × 4.7 × sin162

Area of the triangle = 11.4738/2

Area of the triangle = 5.7369.

Therefore, the area of the triangle ∆WXY is derived to be 5.7 to the nearest tenth.

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a) Parametrization for the curve of intersection of 9y2 + z2 = 1 and xyz = 1 is:
x = 1/(z(sqrt((1 - z^2)/9)))
y = ±sqrt((1 - z^2)/9)
z = t

b)Parametrization for the curve of intersection of  x=y_and x2 - y2 =z is

x = t
y = t
z = 0
c)Parametrization for the curve of intersection of  x2 + y2 + z = is

x = r cos(t)
y = r sin(t)
z = 1 - r

a) To find the curve of intersection of the two surfaces [tex]9y^2 + z^2 = 1[/tex] and xyz = 1:

We can solve for one variable in terms of the others.

For example, we can solve for y in terms of z and x using the first equation:
[tex]9y^2 + z^2 = 1[/tex]
[tex]9y^2 = 1 - z^2[/tex]
[tex]y^2 = (1 - z^2)/9[/tex]
y = ±sqrt([tex](1 - z^2)/9)[/tex]
Substituting this into the second equation, we get:
x(sqrt((1 - [tex]z^2)/9))z = 1[/tex]
x = 1/(z(sqrt((1 - [tex]z^2)/9)))[/tex]
So, a parametrization for the curve of intersection is:
x = 1/(z(sqrt((1 - [tex]z^2)/9)))[/tex]
y = ±sqrt((1 - z^2)/9)
z = t
This is defined for all t except at z = ±1.
b) To find the curve of intersection of the two surfaces x = y and [tex]x^2 - y^2 = z:[/tex]

We can substitute x = y into the second equation:
[tex]x^2 - y^2 = z[/tex]
[tex]y^2 - y^2 = z[/tex]
z = 0
So the curve of intersection is just the x = y line.

A parametrization for this line is:
x = t
y = t
z = 0
c) To find a parametrization for the surface [tex]x^2 + y^2 + z = 1:[/tex]

We can use cylindrical coordinates:
x = r cos(t)
y = r sin(t)
z = 1 - r
where 0 ≤ r ≤ 1 and 0 ≤ t < 2π.

This parameterization covers the surface of a unit cylinder with its top and bottom caps removed.

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Ines has 9/10 liter of juice, if Meg has 3/10 liter of juice left in her bottle and Ines has 3 times as much juice in her bottle as Meg has .

It is need to find how much juice does Ines have.To calculate it, it is need to know how much liter of juice does Meg have. Meg have 3/10 liter of juice left in her bottle, and Ines has 3 times as much juice her bottle as Meg has.

That is Ines has 3 times means multiplying how much juice meg have by 3.

That is Juice left in bottle of Ines = juice left in bottle of Meg * 3 = 3/10 liter x 3 = 9/10 liter. Therefore, Ines has 9/10 liter of juice in her bottle.

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The solution to the equation √8x + 4 = 6 is x = 0.5.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the equation in the question:

√8x + 4 = 6

To solve for x in the equation, isolate the term containing the variable x.

Subtract 4 from both sides of the equation:

√8x + 4 - 4 = 6 - 4

√8x = 6 - 4

√8x = 2

Square both sides of the equation:

( √8x )² = 2²

8x = 4

Divide both sides of the equation by 8:

x = 4/8

x = 1/2

x = 0.5

Therefore, the value of x is 0.5.

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The interval 4:00-4:59 represents the most number of cars.

How to determine the interval with the most number of cars based on the given time ranges?

To determine the interval that represents the most number of cars, we need to analyze the given options and find the one with the highest number of cars.

Unfortunately, we don't have any data about the actual number of cars during those intervals. Therefore, we cannot provide a definitive answer to this question. We could only make an educated guess based on certain assumptions.

For instance, if we assume that the traffic is usually higher during rush hour, we could say that the intervals between 4:00-4:59 and 3:00-3:59 are more likely to have the highest number of cars. However, without additional information or data, we cannot provide a more accurate answer.

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the side length of the large square is equal to 4 divided by the square root of π times the side length of the small square.

what is length  ?

Length is a physical quantity that refers to the measurement of a one-dimensional distance or extent, such as the distance between two points. It is typically measured in units such as meters, feet, inches, or centimeters. Length can be used to describe the size or dimensions

In the given question,

Let's assume that the side length of the small square is equal to the diameter of each small bubble.

When four bubbles in squares collide and merge into one large bubble in a square, the total area of the small squares is equal to the area of the large square. Since the side length of each small square is equal to the diameter of the small bubble, the area of each small square is equal to the square of the diameter of the small bubble.

So, if we let d be the diameter of each small bubble, then the area of each small square is equal to d². Therefore, the total area of the four small squares is equal to 4d², and the area of the large square is equal to the sum of the areas of the four small squares, which is 4d².

The area of a circle is equal to πr², where r is the radius of the circle. If we let R be the radius of the large bubble, then its area is equal to π².

We know that the area of the large square is equal to the area of the large bubble, so we have:

4d² = πR²

Solving for R, we get:

R =√(4d²/π)

R = 2d/√(π)

Since the side length of the large square is equal to twice the radius of the large bubble, we have:

Side length of large square = 2R = 4d/√(π)

Therefore, the side length of the large square is equal to 4 divided by the square root of π times the side length of the small square.

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Answer:V≈339.29m³

Step-by-step explanation:

V=π(d

2)2h=π·(6

2)2·12≈339.29201m³ Pls if you can answer my question if you have txvs.

The required answer is the nearest hundred dollars: $902.09 is approximately $900.

To find the value of the car 20 years after it was purchased, we can use the formula for exponential decay:

Value = Initial value * (1 - Depreciation rate) ^ (time elapsed / time for depreciation)

1. Determine the depreciation rate: The car's value depreciates by one half every 3.5 years, so the depreciation rate is 50% or 0.5.
Depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wears, and second, the allocation in accounting statements of the original cost of the assets to periods in which the assets are used (depreciation with the matching principle).

Depreciation is thus the decrease in the value of assets and the method used to reallocate, or "write down" the cost of a tangible asset (such as equipment) over its useful life span

2. Calculate the number of depreciation periods: Since the car's value halves every 3.5 years, we need to find out how many 3.5-year periods are in 20 years. To do this, divide 20 by 3.5: 20 / 3.5 ≈ 5.71 periods.

3. Use the exponential decay formula:
Value = 29,000 * (1 - 0.5) ^ (5.71)
Value ≈ 29,000 * (0.5) ^ (5.71)
Value ≈ 29,000 * 0.0311
Value ≈ 902.09

4. Round the value to the nearest hundred dollars: $902.09 is approximately $900.

So, the value of the car 20 years after it was purchased is approximately $900.

To know more about depreciation value. Click on the link.

https://brainly.com/question/28498512

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