for a circle radius of 3 feet, find the length of a central angle of 24’. Leave your answer in terms of pie.

Two triangles can be formed using the given measurements,

19. Triangle 1: A = 64°, B ≈ 53.07°, C ≈ 62.93°, a = 16, b ≈ 14.83, c ≈ 16.64

Triangle 2: A = 64°, B ≈ 126.93°, C ≈ 9.07°, a = 16, b ≈ 80.17, c ≈ 8.98

20. Triangle 1: A ≈ 52°, B = 38°, C ≈ 94°, a ≈ 22.57, b = b, c ≈ 34.60

Triangle 2: A ≈ 128°, B = 38°, C ≈ 14°, a ≈ 22.57, b = b, c ≈ 16.66

19. We are given angle A and the side opposite to it, a. We can use the law of sines to find the other sides and angles of the triangle:

a/sin(A) = b/sin(B) = c/sin(C)

b/sin(B) = a/sin(A)

b = a × sin(B)/sin(A)

b = 16 × sin(64°)/sin(180°-64°-90°)

b ≈ 14.83

c/sin(C) = a/sin(A)

c = a × sin(C)/sin(A)

c = 16 × sin(68°)/sin(64°)

c ≈ 16.64

Therefore, the two triangles are:

Triangle 1: A = 64°, B ≈ 53.07°, C ≈ 62.93°, a = 16, b ≈ 14.83, c ≈ 16.64

Triangle 2: A = 64°, B ≈ 126.93°, C ≈ 9.07°, a = 16, b ≈ 80.17, c ≈ 8.98

20. We are given angle B. Let the length of the side opposite to B be b. We can use the fact that the angles in a triangle add up to 180° to find angle A, and then use the law of sines to find the remaining sides and angles:

A = 180° - 90° - 38°

A = 52°

a/sin(A) = b/sin(B) = c/sin(C)

a/sin(52°) = b/sin(38°)

c/sin(C) = b/sin(38°)

c = b*sin(C)/sin(38°)

The angles in a triangle add up to 180°, so we have:

C = 180° - A - B

C ≈ 94°

Substituting the values of A, B, and C in the above equations, we get:

a ≈ 22.57

b = b

c ≈ 34.60

Therefore, the two triangles are:

Triangle 1: A ≈ 52°, B = 38°, C ≈ 94°, a ≈ 22.57, b = b, c ≈ 34.60

Triangle 2: A ≈ 128°, B = 38°, C ≈ 14°, a ≈ 22.57, b = b, c ≈ 16.66

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The question is -

In Exercises 19-22, two triangles can be formed using the given measurements.

Solve both triangles.

19. A = 64°, a = 16,

20. B 38°

Answer:

So if theres two people who can have a drink thats the same and a dessert thats different, then there are 40 different ways you can have one drink with a different dessert.

Step-by-step explanation:

Drinks: 4

Desserts: 10

There are ten desserts for every drink.

10*4, or 10 times 4, equals 40.

Answer:see below

Step-by-step explanation:

10.600

11.80000

12.17

13.48

14.4000

21. 1km=100m;0.5km=500m;0.1km=100m

22.50m=5000cm; 5m=500cm; 0.5m=50cm

On simplifying the expression (−1 3/4)²- √ [127−2(3)]  we get -127/16

Simplifying an expression:

To simplify the expression, we need to follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we simplify the exponent by squaring -1 3/4 to get 49/16. Then, we simplify the expression under the square root by subtracting 2 times 3 from 127 to get 121, and we take the square root of 121 to get 11.

Here we have

(−1 3/4)²- √ [127−2(3)]  

The above expression can be simplified as follows

=>  (−1 3/4)²- √ [127−2(3)]    

Convert the mixed fraction into an improper fraction  

=> 1 3/4 = 7/4    [ ∵ 4 × 1 + 3 = 7 ]  

So given expression can be

=>  (−7/4)²- √ [127−2(3)]      

=>  (49/16) - √ [121]      

=>  (49/16) - 11

=>  (49 - 176 /16)

=>  -127/16  

Therefore,

On simplifying the expression (−1 3/4)²- √ [127−2(3)]  we get -127/16

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The condition that speaks to the circumstance is 194.99 + 2p = 284.97 where p represents the price of one game.

Let's begin by setting up the condition based on the data given.

Serena paid $194.99 for the amusement framework and two diversions that took a toll at the same cost, let's call it "p".

The whole sum that went through Serena was $284.97.

So able to set up the condition as:

194.99 + 2p = 284.97

The left-hand side of the condition represents the whole sum that went through the amusement framework and two diversions. The right-hand side speaks to the whole sum went through by Serena.

therefore, the equation that speaks to the circumstance is:

194.99 + 2p = 284.97 .

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In order to find the probability that the participant lifts weights given they don't run, you would need to know these probabilities from the survey data.

To answer this question, we need to use the concept of conditional probability. We are given that a randomly selected survey participant does not run, and we want to find the probability that the participant lifts weights.

Let's denote the events as follows:
- R: The participant runs
- W: The participant lifts weights

We are given that the participant does not run, which means we are looking at the event ¬R (not R).

Now, we want to find the probability of the participant lifting weights given that they do not run. This can be represented as P(W | ¬R).

Using the formula for conditional probability, we have:

P(W | ¬R) = P(W ∩ ¬R) / P(¬R)

Unfortunately, we don't have the specific probabilities for these events (P(W ∩ ¬R) and P(¬R)). In order to find the probability that the participant lifts weights given they don't run, you would need to know these probabilities from the survey data. Once you have that information, you can use the formula above to find the probability.

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In order to find the probability that the participant lifts weights given they don't run, you would need to know these probabilities from the survey data.

we need to use the concept of conditional probability. We are given that a randomly selected survey participant does not run, and we want to find the probability that the participant lifts weights.

Let's denote the events as follows:

- R: The participant runs

- W: The participant lifts weights

We are given that the participant does not run, which means we are looking at the event ¬R (not R).

Now, we want to find the probability of the participant lifting weights given that they do not run. This can be represented as P(W | ¬R).

Using the formula for conditional probability, we have:

P(W | ¬R) = P(W ∩ ¬R) / P(¬R)

Unfortunately, we don't have the specific probabilities for these events (P(W ∩ ¬R) and P(¬R)). In order to find the probability that the participant lifts weights given they don't run, you would need to know these probabilities from the survey data. Once you have that information, you can use the formula above to find the probability.

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The total distinguishable ways can the donors be in line is 362,736.

The total number of distinguishable ways:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

To subtract the number of in-distinguishable arrangements:

(4! x 3!) + (3! x 2!) = 144

There are 362,736 distinguishable ways in which four donors with type O blood, three donors with type A blood, and two donors with type B blood can be in line.

This is calculated by first determining the total number of distinguishable arrangements, which is 9!.

Then,

The number of indistinguishable arrangements is subtracted from the total.

Which is done by multiplying the number of arrangements for each blood type separately and then adding them together.

The result is then subtracted from the total, leaving the number of distinguishable ways.

The total number of distinguishable ways is:

362,880 - 144 = 362,736

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If a quiz has 20 multiple choice questions, then the expected number of correct answers is 5.

For each question, there are 4 possible choices, and only 1 of them is correct.

So, the probability of randomly guessing the "correct-answer" for any  question is = 1/4 = 0.25,

Each question is an independent event, we use the concept of linearity of expectation to calculate the expected number of correct answers for all 20 questions.

The "Expected" number of correct answers for a "single-question" is  probability of guessing it correctly, which is 0.25,

The "Expected-Number" of correct answers for 20 questions is the sum of the expected number of correct answers for each question,

⇒ Expected number of correct answers = (Probability of guessing a single question correctly) × (Number of questions),

Substituting the values,

We get,

⇒ Expected number of correct answers = 0.25 × 20,

⇒ Expected number of correct answers = 5

Therefore, the expected number of correct answers when making "random-guesses" on all 20 multiple choice questions is 5.

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Answer:

Parallelogram

Step-by-step explanation:

given that the opposite sides are parallel, then

the figure is a parallelogram

The lower and upper control limits that the manufacturer should use in the resulting control chart are LCL = 0.023,UCL = 0.043

To calculate the lower and upper control limits for the control chart, we need to use the following formula:
Lower control limit (LCL) = average proportion of defects - 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Upper control limit (UCL) = average proportion of defects + 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Using the given information, we can plug in the values to get:
LCL = 0.01 - 3 x square root of [(0.01 x 0.99) / 30] = -0.023
UCL = 0.01 + 3 x square root of [(0.01 x 0.99) / 30] = 0.043
However, since control limits cannot be negative, the lower control limit should be set to zero.

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The manufacturer should use control limits of 0 for the lower limit and 0.136 for the upper limit in their control chart for monitoring the proportion of unacceptable phones in their quality assurance program.

Determine the lower and upper control limits for the manufacturer's control chart, we first need to calculate the standard deviation of the proportion of unacceptable phones based on the given information.
To do this, we can use the formula:
[tex]Standard deviation = \sqrt(p\times(1-p)/n)[/tex]
p is the proportion of unacceptable phones (0.01), and n is the sample size (30 phones per day for 7 days = 210 total phones).
Plugging in these values, we get:
[tex]Standard deviation = \sqrt(0.01\times(1-0.01)/210) = 0.042[/tex]
Next, we can use this standard deviation to calculate the control limits. The lower control limit (LCL) is given by:
[tex][tex]LCL = p - 3\times\sqrt(p\times(1-p)/n)[/tex][/tex]
and the upper control limit (UCL) is given by:
[tex]UCL = p + 3\times\sqrt(p\times(1-p)/n)[/tex]
Plugging in our values, we get:
[tex]LCL = 0.01 - 3\times0.042 = -0.075[/tex]
[tex]UCL = 0.01 + 3\times0.042 = 0.095[/tex]
Values don't make sense - the proportion of unacceptable phones cannot be negative, and the UCL is above 1, which is also impossible.
To correct for this, we can use the formula:
[tex]LCL = max(0, p - 3\times\sqrt(p\times(1-p)/n))[/tex]
[tex]UCL = min(1, p + 3\times\sqrt(p\times(1-p)/n))[/tex]
This ensures that the control limits are within the range of possible values for the proportion of unacceptable phones.
Plugging in our values with this formula, we get:
[tex]LCL = max(0, 0.01 - 3\times0.042) = 0[/tex]
[tex]UCL = min(1, 0.01 + 3\times0.042) = 0.136[/tex]

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Answer:

Step-by-step explanation:

You want the coordinates of the vertices of ∆E'F'G' after ∆EFG has been dilated with a scale factor of 1/4.

Dilation about the origin multiplies each preimage coordinate by the scale factor.

  E' = (1/4)E = (1/4)(-8, 8) = (-2, 2)

  F' = (1/4)F = (1/4)(0, 0) = (0, 0)

  G' = (1/4)G = (1/4)(-8, -8) = (-2, -2)

The coordinates after dilation are E'(-2, 2), F'(0, 0), G'(-2, -2).

<95141404393>

Therefore, the first term of the sequence is 3.

A sequence is an ordered list of numbers, usually generated by a pattern or a rule. Each number in the sequence is called a term, and the position of a term in the sequence is called its index. Sequences can have a finite or infinite number of terms, and they can be defined in various ways, such as recursively (where each term is defined in terms of the previous terms) or explicitly (where the formula for each term is given).

Here,

The given sequence is an arithmetic sequence, where the common difference between consecutive terms is 4. To find the first term, we can use the formula for the nth term of an arithmetic sequence, which is:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the position of the term in the sequence, and d is the common difference.

For this sequence, we know that a6 = 23 (since 23 is the last term given in the sequence), n = 6, and d = 4. Substituting these values into the formula, we get:

a6 = a1 + (6 - 1)4

23 = a1 + 20

a1 = 23 - 20

a1 = 3

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Complete question:

What’s the first term for the given sequence: 3, 7, 11, 15, 19, 23?

Choose the 3rd table .

Exactly one output value from a different set, known as the range, is what a function in mathematics does for each input value from the set known as the domain.

A function can be compared to a device that processes an input to create a particular output.

Given that the output value depends on the value of the input variable, the input value is sometimes referred to as the independent variable.

For instance, if a function is defined as

f(x) = 2x + 1, x

is the input variable and f is the output variable.(x).

A variable in mathematics is a symbol that designates a value or quantity that is subject to variation or change.

In order to solve equations and describe relationships between different quantities, variables are needed.

Variables in algebra are frequently denoted by letters like x, y, and z. They are used to express a relationship between two or more quantities or to represent undiscovered quantities that we are trying to locate.

For instance, x is the independent variable and y is the dependent variable in the equation y = 3x + 2.

According to question  

Substitute X=14 into f(x) =  4/3  |x+2 |  - 5

f (-14） = 4/3  |-14+2 |  - 5

           = 4/3  |-12 |  - 5

           = 4/3 X12 -5

           = 16 - 5

            = 11

hence when x=-14 fix=11

the first table is false

substitute x= -10 into  f(x) =  4/3  |x+2 |  - 5

                                          =  4/3  |-10+2 |  - 5

                                          =  4/3 X 8 -5

                                          = 32-15 =17/3 ≠ 11

hence the second table is false

HENCE , Choose the 3rd table .

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Step-by-step explanation:

If he read 10 % , then he has 90 % to go...and this 90% is 54 pages

x = number of pages in book

90% * x  = 54

.90x = 54

x = 54/.90 = 60 pages in book

The theoretical and experimental probability of rolling a 5 are 1/6 and 4/15 respectively.

We will calculate the theoretical probability by substituting 30 for the number of favorable outcomes as the die is rolled 30 times with one option each for 30 rolls and 180 for total number of outcomes in theoretical probability formula.

P(Theoretical probability of rolling a 5) = 30/180

P(Theoretical probability of rolling a 5) = 1/6.

The experimental probability is calculated by substituting 8 for the number of time the event occurs and 30 for the total number of trials.

P(Experimental probability of rolling a 5)= 8/30

P(Experimental probability of rolling a 5) =4/15

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Since quadrilateral H'I'J'K' is a translation of quadrilateral HIJK, the translation rule include the following: (x, y)  → (x - 8, y + 10).

In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

By translating the pre-image of quadrilateral HIJK horizontally left by 8 units and vertically up by 10 units, the coordinate J of quadrilateral H'I'J'K' include the following:

(x, y)                               →                  (x - 8, y + 10)

J (8, -2)                        →                  (8 - 8, -2 + 10) = J' (0, 8).

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Therefore (t) can  be written as **(2 - 3Q) / (Q + 4)**.

Within the given equation, Q is a variable. It stands for an unknowable amount or value that can be ascertained by equation-solving.

A quantity that can take on any one of a number of values is referred to as a variable. A variable in mathematics is a symbol or letter that denotes an unknowable amount or value. The variable Q in the given equation stands for an unknowable quantity or value that can be ascertained by resolving the equation.

The equation is as follows:

Q = (2 - 4t) / (t + 3)

When we divide both sides by (t + 3), we obtain:

Q(t + 3) = 2 - 4t

When we increase the left side of the equation, we obtain:

Qt + 3Q = 2 - 4t

The result of adding 4t to both sides of the equation is:

Qt + 3Q + 4t = 2

Combining related concepts gives us:

t(Q + 4) = 2 - 3Q

The result of dividing both sides by (Q + 4) is:

t = (2 - 3Q) / (Q + 4)

t can therefore be written as **(2 - 3Q) / (Q + 4)**.

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The correct interpretation of the 90% confidence interval is: "We estimate with 90% confidence that the true population mean is between 29.947 and 32.053 characters."

A confidence interval is a range of values that is likely to contain the true value of a population parameter (such as a population mean or proportion) with a certain level of confidence.

Confidence intervals are typically calculated from a sample of data and are used to estimate the range of values that the population parameter could take, based on the observed sample data. The level of confidence represents the degree of certainty that the true population parameter falls within the calculated interval. For example, a 95% confidence interval means that if we were to repeat the sampling process many times, 95% of the resulting intervals would contain the true population parameter.

The correct interpretation of the 90% confidence interval is: "We estimate with 90% confidence that the true population mean is between 29.947 and 32.053 characters."

The confidence interval provides a range of plausible values for the population mean based on the sample data. A 90% confidence level means that if we were to repeat the sampling process many times, 90% of the resulting confidence intervals would contain the true population mean.

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The wheel does 1,184 revolutions in the 1700 meters.

To find the number of revolutions we need to take the quotient between the distance and the circumference of the wheel.

The circumference of a circle of diameter D is:

C = 3.14*D

So here we have:

C = 3.14*18in = 56.52 in

And we know that:

1 meter ≈ 39.3701 inches

Then the circumference in meters is:

C = 56.52/39.3701 m = 1.435m

The number of revolutions is:

1700m/1.435m = 1,184

That is the correct answer.

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Answer:

Step-by-step explanation:

First find the circumference:

π × 18 = 3.14 × 18 = 56.52"

56.52÷ 39.3701 inches in one meter = 1.4356 meters for the circumference.

Divide 1700 meters by 39.3701 = 1184.173

round to 1184 revolutions

Answer:

-5d + 5.5 < 17

-5d < 11.5

d > -2.3

A is the correct solution.

Answer:

depends on the percentage of vat

Answer:

(-5,-4)

Step-by-step explanation:

i think this is correct because i tried to solve in paper.

Answer:

The answer is 28

Step-by-step explanation:

sin0=opp/hyp

let hyp be x

sin30=14/x

0.5x=14

divide both sides by 0.6

x=14/0.5

x=28

Answer:

Table D represents the linear function

y = x + 1.

The offered triangle's missing side measures 18.5 inches.

Two angles and one side of a triangle are measured as follows: A = 45°, B = 100°, and c = 15.

We need to find the side a. [opposite to angle A]

The Law of Sines indicates that we can use this formula to get the missing side (a) in the triangle given:

[tex]\mathrm{\frac{a}{sin(A)} = \frac{c}{sin(C)}}[/tex]

where A is the angle opposite side A, C is the angle opposite side C, and an is the unknown side.

Let's plug in the values we have:

A = 45°

B = 100°

c = 15

Now, we can find angle C using the fact that the sum of angles in a triangle is 180°:

C = 180° - A - B

C = 180° - 45° - 100°

C = 35°

Now we can apply the Law of Sines to find side a:

[tex]\mathrm {\frac{a}{sin(45)} = \frac{15}{sin(35)}}[/tex]

To find a, let's first calculate the values of sin(45°) and sin(35°):

sin(45°) ≈ 0.7071

sin(35°) ≈ 0.5736

Now, solve for a:

[tex]\frac{a}{0.7071} = \frac{15}{0.5736}[/tex]

a ≈ (15 × 0.7071) / 0.5736

a ≈ 18.54

Rounding to the nearest tenth:

a ≈ 18.5

So, the missing side (a) is approximately 18.5 units.

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The length of the garden is 99 m.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the area of the rectangle is 8811 [tex]m^{2}[/tex] and the width is 89 m. Substituting these values into the formula, we get:

8811 [tex]m^{2}[/tex] = Length x 89 m

To solve for the length, we can divide both sides of the equation by 89 m:

Length = 8811 [tex]m^{2}[/tex] / 89 m

Simplifying, we get:

Length = 99 m

Therefore, the length of the garden is 99 m.

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the proportion of California college students who currently drink alcohol different from the proportion nationwide p0 = 0.60 (nationwide proportion from CDC)

Information provided; we can determine if the proportion of California college students who currently drink alcohol is different from the proportion nationwide by conducting a hypothesis test. Here are the steps:
The null hypothesis (H0) and alternative hypothesis (H1):
H0: The proportion of California college students who drink alcohol is the same as the nationwide proportion.

(p = 0.60).
H1: The proportion of California college students who drink alcohol is different from the nationwide proportion.

(p ≠ 0.60).
The sample proportion (p-hat), sample size (n), and the population proportion (p0):
p-hat = 0.66 (66% of the 450 California college students surveyed)
n = 450 (sample size)
p0 = 0.60 (nationwide proportion from CDC)
The test statistic (z) using the following formula:
[tex]z = (p-hat - p0) / \sqrt((p0 \times (1 - p0)) / n)[/tex]
A standard normal distribution table or calculator to find the p-value associated with the test statistic.
Compare the p-value to a predetermined significance level (α), usually set at 0.05.
- If the p-value is less than α, reject the null hypothesis (H0), suggesting that the proportion of California college students who drink alcohol is different from the nationwide proportion.
- If the p-value is greater than α, fail to reject the null hypothesis (H0), indicating that there is not enough evidence to suggest a difference between the two proportions.
Determine if the proportion of California college students who drink alcohol is significantly different from the nationwide proportion.

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Answer: Let's use the following variables to represent the unknown quantities in the problem:

x: the number of cupcakes purchased

y: the number of muffins purchased

From the problem statement, we can write two equations:

The total amount spent on cupcakes and muffins is $21.50:

2x + 1.25y = 21.50

The number of muffins purchased is one fewer than the number of cupcakes:

y = x - 1

These two equations form a system of equations that can be solved simultaneously to find the values of x and y.

Substituting equation 2 into equation 1, we get:

2x + 1.25(x - 1) = 21.50

Simplifying and solving for x:

2x + 1.25x - 1.25 = 21.50

3.25x = 22.75

x = 7

Now that we know x, we can use equation 2 to find y:

y = x - 1 = 7 - 1 = 6

Therefore, the customer purchased 7 cupcakes and 6 muffins, spending a total of $21.50.

Step-by-step explanation:

Boyle's law, which relates the pressure and volume of an ideal gas, has various applications in science, engineering, and everyday life. Some of the applications of this measuring technique include:

Gas storage: Boyle's law is used in designing and managing gas storage systems, such as gas cylinders and tanks. It helps in determining the volume of gas that can be stored at a given pressure and vice versa.

HVAC systems: Heating, ventilation, and air conditioning (HVAC) systems use Boyle's law to control the pressure and volume of gases in order to regulate temperature and air flow.

Scuba diving: Boyle's law is applied in scuba diving to calculate the changes in volume of gases in diving cylinders at different depths, which affects the diver's breathing and decompression requirements.

Medical applications: In respiratory therapy, Boyle's law is utilized in devices like ventilators, which deliver oxygen or other gases to patients at specific pressures and volumes.

Industrial processes: Boyle's law is used in industrial processes where gases are compressed or expanded, such as in manufacturing, chemical processing, and power generation.

As for measuring surfaces that are not flat, Boyle's law is not directly applicable for such measurements. It is a gas law that relates the pressure and volume of a gas, assuming the gas behaves as an ideal gas.

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The average distance of electric cars is 275.

The range of the data set is 300.

Given:

To find: Average distance of electric cars

Solution:

The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:

250, 250, 250, 400, 300, 300, 350, 100

To find the average distance of electric cars, we can use the formula:

Average = (Sum of all the data points) / (Number of data points)

Substituting the given values, we get:

Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8

Average = 2200 / 8

Average = 275

Therefore, the average distance of electric cars is 275.

Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.

Range = Maximum value - Minimum value

Range = 400 - 100

Range = 300

Therefore, the range of the data set is 300.

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