mason asked some classmates if they play video games or not. the ratio of friends who play video games to everyone he asked is . how many of his friends do not play video games?

Answer:

565.486677646 inches squared

Step-by-step explanation:

Let's recall the formula for the surface area of a cylinder:

[tex]A=2\pi rh+2\pi r^2[/tex]

Where r is the radius and h is the height.

We are given that the radius is 6 inches and the height is 9 inches.

Substitute the values and solve the equation, like so:

[tex]A=2\pi (6)(9)+2\pi (6)^2=\\A=2\pi (54) +2\pi(36)=\\A=108\pi +72\pi =\\A=180\pi[/tex]

Thus, in terms of pi, the surface area is equal to [tex]180\pi[/tex].

180 times pi is equal to approximately 565.486677646 inches squared.

Answer:

below

Step-by-step explanation:

26. yes because a straight line is formed

27. domain - -2 to 2

range -2 to 1

Answer:

Yes, the graph is a linear function.

Domain: x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Step-by-step explanation:

A linear function is an expression that will form a straight line when graphed (or a graph that forms a straight line). These points form a straight line, so the function is linear.

The domain of the function is everything that x can be equal to. We can see here that the ordered points are:

(-2, -1.5), (-1.5, -1), (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), (1.5, 2)

So, the domain of the function is all of the x values of the ordered pairs, or:

x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

(the symbol next to the x means "belongs to.")

As for the range, it is everything that y can be equal to. Let us look once again at the ordered pairs. The range of the function is equal to the y coordinates of these ordered pairs, or:

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Keep in mind that if the function contains more than one value for x or y, it is listed ONLY ONCE in the domain/range.

Sharon's desired percentile rank of 0.78.

To determine the goal Sharon set for herself, we need to understand the relationship between standardized scores and percentile ranks.

In a standardized test, such as Sharon's Statistics final, the standardized score represents how well a student performed relative to the average score of the test-takers.

The percentile rank, on the other hand, indicates the percentage of test-takers that scored below a particular student.

In Sharon's case, she wants her standardized score to be equal to her percentile rank.

Therefore, her goal is to achieve a standardized score of 0.78 (written as a decimal) on her Statistics final.

This means she aims to score better than approximately 78% of her classmates, as indicated by her desired percentile rank of 0.78.

Hence her desired percentile rank of 0.78.

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Answer:

1/4 > 3/16

Step-by-step explanation:

1/4 = 4/16

4/16 > 3/16

1/4 > 3/16

hope this helps:)

~~~Wdfads~~~

The value of the Central angle and Circumscribed angle are respectively: 97° and  83°

A circumscribed angle is the angle formed by the intersection of two tangent lines (lines that each touch the circle at exactly one point) to a circle.

The circumscribed angle theorem states that the measure of a circumscribed angle is the supplement of the central angle that intercepts the same arc (the supplement of an angle is the difference between 180° and the angle). Because a central angle has the same degree measure as its intercepted arc, it follows from the circumscribed angle theorem that the measure of a circumscribed angle is the supplement of the degree measure of the intercepted arc.

The formula for the circumscribed angle theorem is:

θ = 180° - C

Where:

θ is the circumscribed angle

C is the central angle

Thus:

3x + 11 = 180 - (5x - 23)

3x + 11 = 180 - 5x + 23

3x + 11 = 203 - 5x

8x = 203 - 11

8x = 192

x = 192/8

x = 24

Thus:

Central angle = 5(24) - 23

= 120 - 23

= 97°

Circumscribed angle = 180 - 97 = 83°

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The situation can be represented by the equation 2x + 150 = 5x is"Mary has 2 stamps and buys 150 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have the same number of stamps?" (option b)

The equation 2x + 150 = 5x means that two expressions, 2x + 150 and 5x, are equal. In other words, whatever value we substitute for x, these two expressions will always have the same value. We can use this equation to solve different situations by finding the value of x that satisfies the equation.

Mary starts with 2 stamps and buys 150 stamps each week, while Nick starts with no stamps and buys 5 stamps each week. To determine when they will have the same number of stamps, we need to use the equation 2x + 150 = 5x. We can rewrite the equation as 150 = 3x, and solve for x by dividing both sides by 3. This gives us x = 50, which means that it will take Mary 50 weeks to have the same number of stamps as Nick.

Hence the correct option is (b).

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The equation for the sinusoidal function that represents Jane's motion would be d(t) = 25 x sin(π/4 x (t + 4)) - 5

Let d(t) be the distance Jane is from the bank (in feet) at time t (in seconds). Since Jane's motion is sinusoidal, we can express it as:

d(t) = A x sin(B x (t - C)) + D

We need to find the values of A, B, C, and D that satisfy these conditions.

Since the amplitude is half the peak-to-peak amplitude, we have:

A = 50 / 2 = 25

The vertical shift (D) is the average of the maximum and minimum distances:

D = (20 + (-30)) / 2 = -10 / 2 = -5

Since the sine function is -1 at 3π/2 (270 degrees), we have:

π/4 x (2 - C) = 3π/2

2 - C = 6

C = -4

So, the equation of the sinusoidal function representing Jane's motion is:

d(t) = 25 x sin(π/4 x (t + 4)) - 5

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The question is:

Find the sinusoidal function that represents Jane's motion.

The researcher could use statistical analysis to compare the proportion of accidents that occur among older employees (e.g., those over 50 years old).

The proportion that occurs among younger employees (e.g., those under 30 years old).

If the proportions are similar, then the data would suggest that older and younger employees are equally prone to having accidents.

To determine whether older and younger employees are equally prone to having accidents.

The researcher at the light manufacturing plant would need to analyze the data collected on accident types and age of the employees involved in the accidents.

If the proportions are different, then the data would suggest that one age group is more prone to accidents than the other.

It is important to note that other factors, such as job type, experience level, and physical condition, could also influence the likelihood of accidents. Therefore, the researcher should also consider these factors when analyzing the data.

to ascertain if employees of different ages are similarly prone to accidents.

The light manufacturing plant researcher would have to examine the information gathered on accident kinds and the ages of the personnel involved in the incidents.

The data would indicate that one age group is more prone to accidents than the other if the proportions were different.

It is significant to remember that additional elements, such as work kind, amount of expertise, and physical condition, may also affect the chance of mishaps.

As a result, when the researcher analyses the data, they should also take these things into account.

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By collecting data, calculating and comparing percentages, and analyzing accident types, we can investigate whether older and younger employees are equally prone to having accidents at the manufacturing plant for random sample.

We will look at the data from the researcher's investigation at the light manufacturing plant. They classified a random sample of accidents by type and age of the employee.

Step 1: Collect data on the total number of accidents involving older and younger employees, as well as the types of accidents they were involved in.

Step 2: Calculate the percentage of accidents involving older employees and the percentage involving younger employees.

Step 3: Compare the percentages and determine if there is a significant difference between the accident rates for older and younger employees.

Step 4: Analyze the types of accidents each group is involved in to see if there are any patterns or trends that may suggest a higher risk for either age group.

By following these steps, we can investigate whether older and younger employees are equally prone to having accidents at the manufacturing plant.

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A statistician would reply that in order to determine if the generic drug is less effective than the name-brand drug, a hypothesis test needs to be conducted.

The null hypothesis (H0) would be that there is no difference in the average blood pressure reduction between the two drugs, while the alternative hypothesis (H1) would be that the name-brand drug has a higher average reduction in blood pressure than the generic drug.

To test these hypotheses, a t-test would be appropriate since we have two independent samples (control and treatment groups) with known means, standard deviations, and sample sizes. The t-test will provide a p-value, which can be compared to a chosen significance level (e.g., α = 0.05).

If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference in the average blood pressure reduction between the two drugs. If the p-value is greater than the significance level, we fail to reject the null hypothesis, meaning we do not have enough evidence to claim that the name-brand drug is more effective than the generic drug.

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If there is at-least one-song liked by those two girls but disliked by the third, then the "different-ways" this is possible is 132 ways.

There are ⁴C₃ ways to choose the "3-songs" which are liked by "3-pairs" of girls.

There are 3! ways to find the three songs are liked by which pair of girls.

In total, there are ⁴C₃×3! possibilities for the first "3-songs".

There are "3-cases" for fourth song, let that song be "D".

Case 1: Song "D" is disliked by all three girls means there is only one possibility.

Case 2: Song "D" is liked by exactly one girl means there are three possibility.

Case 3: Song "D" is liked by exactly two girls means there are three pairs of girls to choose from.

However, there is an overlap when "other-song" is liked by "same-pair" of girl is counted as "fourth-song" at some point, in which "case-D" will be counted as one of first "three-songs" liked by same girls.

Counting the overlaps, there are "three-ways" to choose pair with overlaps and 4×3=12 ways to choose what the other "two-pairs" like independently.

In total, there are 3×12=36 over-lapped possibilities,

Therefore, there are ⁴C₃ × 3! ×(3+1+3)-36 = 132 ways for the songs to be likely by the girls.

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The only solution for the equation is the one in option E, 49

Here we have the equation:

x = 49

A value of x is a solution only if the equation is true, this means, we have the same number in both sides.

Here obviously there exist only one solution, and it is when x takes the value 49.

49 = 49

So the only correct option is E.

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The height of the parabolic balloon arch for the prom is 12.25 feet.

Using these assumptions, we can find the equation of the parabola that the arch follows as x = a(y-k)² + h, where (h,k) is the vertex and a is a constant that determines the shape of the parabola. We can find the value of a by using one of the points that the arch passes through, say (3,0):

3 = a(0-k)² + h h = 3 - a(k²)

Similarly, using the other point that the arch passes through, say (7,0):

7 = a(0-k)² + h h = 7 - a(k²)

Equating the expressions for h, we get:

3 - a(k²) = 7 - a(k²) a = -1/4

Substituting this value of a into one of the equations for h, say h = 7 - a(k²), we get:

h = 7 + 1/4(k²)

So the vertex of the parabola is at (h,k) = (7,0), and the equation of the parabola is x = -1/4(y² - 28y + 49).

To find the height of the arch, we need to find the y-coordinate of the vertex, which is k = 0. So the height of the arch is given by the distance between the vertex and the lowest point of the arch, which is the x-intercept of the parabola. To find the x-intercept, we set y = 0 in the equation of the parabola:

x = -1/4(0² - 28(0) + 49)

x = -1/4(49) = -12.25

However, since we are dealing with a physical object, the height cannot be negative. Therefore, we take the absolute value of the x-intercept, which gives us:

| -12.25 | = 12.25 feet

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Number of  exercise classes must you take in one month so that the cost of Forever Fitness is the ​same​ as Peachtree Gym is 8

Let's denote by x the number of exercise classes taken in one month.

For Forever Fitness, the total cost in one month would be:

50 + 15x

For Peachtree Gym, the total cost in one month would be:

75 + 10x

We want to find out when these two costs are equal, so we can set them equal to each other and solve for x

50 + 15x = 75 + 10x

Simplifying this equation by subtracting 10x from both sides gives:

40 = 5x

Dividing both sides by 5 gives

x = 8

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The drive-thru with typically more wait time is Burger Quick, because it has a larger median. The Option A.

The median is a measure of central tendency that represents the middle value of a set of data. In this case, the median wait time at Burger Quick is 15.5 minutes, while the median wait time at Super Fast Food is 12 minutes.

This indicates that, on average, customers at Burger Quick experience a longer wait time compared to customers at Super Fast Food. The larger median at Burger Quick suggests that there may be some longer wait times skewing the data towards the higher end which could be due to various factors such as slower service, or other operational issues at Burger Quick resulting in a longer wait time for customers at their drive-thru.

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As this is a contradiction, the system cannot be solved. The parallel lines of the two equations do not intersect.

A mathematical expression called and equation demonstrates the parity of two factors or values. It typically includes exponents, parameters, constants, and mathematical like addition, subtraction, multiplication, and division. Finding an unknown variable's value or expressing a correlation between a number of variables is the goal of an equation. To simulate real-world occurrences and address issues, equations are utilised in many mathematical areas, science, and engineering. Systems of equations, linear equations, and quadratic equations are a few types of equations.

given

We can multiply the first equation by two and then add the second equation to the system to find the solution via elimination. This results in:

[tex]2(x - 3y = 7) = 2x - 6y = 14\\2x - 6y = 12[/tex]

To remove x, we may now subtract the second equation from the first equation:

[tex](2x - 6y = 14) - (2x - 6y = 12) = 0[/tex]

That amounts to:

0 = 2

As this is a contradiction, the system cannot be solved. The parallel lines of the two equations do not intersect.

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The point (1,2) is the point of intersection of the two lines.

It should be noted that to verify if the point (1,2) is a solution to the system of linear equations, we need to substitute x=1 and y=2 into both equations and check if they are true.

The equation is true, so (1,2) is a solution to the first equation.

Substituting x=1 and y=2 into the second equation also makes the equation true.

Therefore, the point (1,2) is the point of intersection of the two lines.

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The plant is not in the sprinkler's range since the distance between the sprinkler and the plant is greater than the radius of the sprinkler's range.

The distance between the sprinkler and the plant can be calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the distance between the sprinkler and the plant is the hypotenuse of a right triangle with legs of length 4 feet and 6 feet:

distance = sqrt(4^2 + 6^2)

distance = sqrt(16 + 36)

distance = sqrt(52)

distance ≈ 7.21 feet

Since the distance between the sprinkler and the plant is greater than the radius of the sprinkler's range (8 feet), the plant is not in the sprinkler's range. Therefore, the plant will not receive water from the sprinkler.

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The survey question that would produce a qualitative response is one that asks about qualities or attributes.

A qualitative response is a non-numeric response that describes the characteristics or qualities of something.

In a survey, a qualitative question typically asks about opinions.

Attitudes, behaviors, or other non-measurable factors.

Out of the following survey questions, the one that would produce a qualitative response is:

"What is your favorite food in the cafeteria?"

This question is asking for a subjective opinion, which is a qualitative response. The response could vary from student to student and cannot be quantified numerically.

A qualitative response is a response that is based on qualities or attributes, rather than numerical or measurable data.

Out of the listed questions, the survey question that would produce a qualitative response is:

What is your favorite color?

This question asks about a personal preference, which cannot be measured numerically. The response would be a word or phrase indicating the color, which is a qualitative attribute.

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The two options that represent circles with diameter 12 units and center on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

The diameter of a circle is a straight line segment that passes through the center of the circle and connects two points on its circumference. It is twice the length of the circle's radius.

The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

Explanation:

For a circle with diameter 12 units, the radius is half of the diameter, which is 6 units.

Since the center of the circle lies on the y-axis, the x-coordinate of the center is 0.

The general equation for a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².

Using the given information, we substitute h = 0, k = ±6, and r = 6 to get the two equations:

(x - 0)² + (y - 6)² = 6² => x² + (y - 6)² = 36

(x - 0)² + (y + 6)² = 6² => x² + (y + 6)² = 36

Therefore, the two options that represent circles with diameter 12 units and center on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

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Answer:

Let x be the measure of the angle we are trying to find, in degrees.

The complementary angle to x is 90° - x, since the sum of complementary angles is 90 degrees.

The problem tells us that x is 3.4 degrees less than its complementary angle, so we can set up the following equation:

x = (90 - x) - 3.4

Simplifying and solving for x, we get:

x = 86.6/2

x = 43.3

Therefore, the angle we are trying to find has a measure of 43.3 degrees, and its complementary angle has a measure of 90 - 43.3 = 46.7 degrees.

If the measure of angle RST is 60°, and RS=4 units, then the area of sector RST is 8.374 square units.

In geometry, a "Sector" of a circle is defined as the portion of circle enclosed by two radii and the arc between them. It can be thought of as a slice or a wedge cut out of a circle.

To find the area of the "sector-RST" in circle centered at "S", we use the formula for area of a sector of a circle, which is :

⇒ Area of sector = (θ/360) × π × r²,

where θ = central angle of sector in degrees, π = 3.14159, and r = radius of circle,

In this case, we are given that m∠RST = 60 degrees and RS = 4 units. Since RS is the radius of the circle centered at "S", we use RS = r,

Substituting the values, θ = 60 degrees, r = RS = 4 units,

We get,

⇒ Area of sector RST = (60/360) × 3.14 × (4)²,

= (1/6) × 3.14 × 16,

= 8.374 square units,

Therefore, the required area of sector is 8.374 square units.

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The given question is incomplete, the complete question is

In circle centered at "S", R and T are the points on the circumference with m∠RST = 60 and RS=4 units .Find area of sector RST.

The best answer is (c) understanding others' emotions.

Women tend to have a more empathetic communication style compared to men, and they tend to prioritize relationships and emotions in their interactions. This communication style involves actively listening to others, being supportive, and expressing empathy towards their feelings. Women often seek to connect with others on an emotional level and understand their perspective, rather than simply giving orders or being self-centered.

Research has shown that women's communication style can be more effective in building and maintaining relationships, as it fosters trust, mutual respect, and understanding. This style also creates a supportive environment where individuals can express their emotions freely and receive validation for their feelings.

In conclusion, women's communication style involves understanding others' emotions, listening actively, and showing empathy towards their feelings.

This approach promotes positive relationships and creates an environment of mutual respect and trust.

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the length of the ladder is approximately 54.01 feet.We can use trigonometric ratios to solve this problem

what is trigonometric ratios ?

Trigonometric ratios are mathematical functions used to relate the angles and sides of a right triangle. In a right triangle, there are three sides: the hypotenuse (the longest side, opposite the right angle), the opposite side (opposite to the angle we are interested in), and the adjacent side

In the given question,

We can use trigonometric ratios to solve this problem. Let's label the ladder as the hypotenuse of a right triangle, the height of the electric box as the opposite side, and the distance from the base of the ladder to the house as the adjacent side. Then we have:

sin(62°) = opposite/hypotenuse

cos(62°) = adjacent/hypotenuse

We know the height of the electric box is 27 feet, and we want to find the length of the ladder (the hypotenuse). Let's use the cosine ratio to solve for the hypotenuse:

cos(62°) = adjacent/hypotenuse

hypotenuse = adjacent/cos(62°)

Now we need to find the adjacent side. We know the height of the electric box is the opposite side, and we can use the tangent ratio to find the adjacent side:

tan(62°) = opposite/adjacent

adjacent = opposite/tan(62°)

opposite = 27 feet

Substituting in the values, we get:

adjacent = 27/tan(62°) ≈ 24.39 feet

Then we can find the hypotenuse:

hypotenuse = adjacent/cos(62°) ≈ 54.01 feet

Therefore, the length of the ladder is approximately 54.01 feet.

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The number of papers they have left to grade is 39.

What is Subtraction?

Subtraction is a mathematical operation that involves taking away or removing a certain number of items or quantity from a larger group. It is the inverse of addition and is denoted by the minus sign (-).

Let p be the number of papers they have left to grade.

The total number of papers is 87, and Mr. Lewis has already graded 32 and Ms. Yonkers has graded 16, so the number of papers they have left to grade is:

p = 87 - 32 - 16

p = 39

Therefore, they have 39 papers left to grade.

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Nicky needs to score 32 points in her next Game to have a mean of 25 points per game.

Nicky needs to score in her next game to have a mean of 25 points per game, we need to use the formula for the mean (average):
Mean = (Sum of all the numbers) / (Number of numbers)
In this case, we know that Nicky has scored 18 points, 22 points, and 28 points in her last three basketball games.

To find out how many points she needs to score in her next game to have a mean of 25 points per game, we need to first find the sum of all the points she has scored so far.
Sum of all the points = 18 + 22 + 28 = 68
Next, we need to find out how many games Nicky has played so far.

We know that she has played three games, so the number of games is 3.
formula for finding the mean to solve for the unknown variable, which is the number of points Nicky needs to score in her next game.
[tex]25 = (68 + x) / 4[/tex]
Multiplying both sides by 4, we get:
100 = 68 + x
Subtracting 68 from both sides, we get:
x = 32
In summary, to find out how many points Nicky needs to score in her next basketball game to have a mean of 25 points per game, we used the formula for finding the mean and solved for the unknown variable.

we got was 32 points, which means Nicky needs to score 32 points in her next game to maintain an average of 25 points per game.

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The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".

Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.

Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".

This is because each event does not depend on another one of the events being described.

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the probability that the emergency center will receive five calls on a given day is approximately 0.156, or 15.6%.

To find the probability of receiving five calls on a given day at the emergency center, we need to use the Poisson distribution formula:

[tex]P(x = 5) = (e^{-4})*\frac{(4^5)}{(5!)}[/tex]
Where:
- x = number of phone inquiries
- e = Euler's number (approximately 2.71828)

- ! = factorial (i.e. 5! = 5*4*3*2*1)

Given that the average number of phone inquiries per day is four, we can use that as our lambda (λ) value in the Poisson distribution formula, since lambda represents the mean number of events in a specific time interval:

λ = 4

Now we can substitute these values into the formula and solve:

P(x = 5) = (e^-4)*(4^5)/(5!) = (2.71828^-4)*(1024)/(120) ≈ 0.156

Therefore, the probability that the emergency center will receive five calls on a given day is approximately 0.156, or 15.6%.

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The probability that the emergency center will receive five calls on a given day is approximately 0.1755 or 17.55%.

To find the probability that the emergency center will receive five calls on a given day, given that the average number of phone inquiries per day is four, we can use the Poisson distribution formula.

Identify the average rate (λ): In this case, λ = 4 calls per day.

Identify the desired number of events (k): In this case, k = 5 calls.

Use the Poisson distribution formula: [tex]P(X = k) = (e^(-λ) \times (λ^k)) / k![/tex]

e is the base of the natural logarithm (approximately 2.71828)

λ is the average rate

k is the desired number of events

k! is the factorial of k

Plug in the values and calculate the probability:

[tex]P(X = 5) = (e^{(-4)} \TIMES (4^5)) / 5![/tex]

[tex]P(X = 5) = (0.0183 \times 1024) / 120[/tex]

P(X = 5) ≈ 0.1755

So, the probability that the emergency center will receive five calls on a given day is approximately 0.1755 or 17.55%.

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The average home size in the United States in 2004 was 7,000 square feet.

To solve this problem, we can use the concept of ratios. Let x be the average home size in 2004.

The concept of ratios involves comparing two or more quantities by expressing them as a fraction or a division of one quantity by another. It is used to determine how much larger or smaller one quantity is than another, and is often used in mathematics, science, finance, and other fields

We know that the average home size in 1970 was 1,400 square feet, and that the average size in 2004 was about 5 times greater. This can be expressed as:

x = 5(1,400)

Simplifying the right side of the equation, we get

x = 7,000 square feet

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If observer decides to count traffic in 30-second time intervals, then the probability of observer counting exactly 1 vehicles in an interval is 0.344.

The Vehicle headway follows an exponential distribution and the vehicle arrival follows a poison distribution.

We know that that, probability of getting headway greater than or  equal to 9 seconds is 65%,

So, P(h≥9) = 0.65         ...equation(1)

We know that, P(h≥t) = [tex]e^{-\lambda \times t}[/tex],

where, h is headway , t is time and λ is vehicle "arrival-rate",

So, P(h≥9) = [tex]e^{-\lambda \times 9}[/tex],      ....equation(2)

Equating both equation(1) and equation(2),

We get,

⇒ [tex]e^{-\lambda \times 9}[/tex] = 0.65,

⇒ -9λ = ln(0.65),

⇒ λ = 0.047 vehicles per second.

Since, the vehicle arrival follows poison distribution,

The probability of having "n" vehicles arrive in "t" time is P(n) ,

⇒ P(n) = {(λt)ⁿ[tex]e^{-\lambda \times t}[/tex]}/n!,

where, λ = average vehicle arrival rate = 0.047,

"t" = duration of time interval is = 30,

To find the probability of getting exactly 1 vehicle, we put n = 1,

So,

⇒ P(1) = {(0.047×30)¹ [tex]e^{-0.047 \times 30}[/tex]}/1!

⇒ P(1) = 0.344.

Therefore, the required probability is 0.344.

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The given question is incomplete, the complete question is

An observer has determined that the time headways between successive vehicles on a section of highway are exponentially distributed and that 65% of the headways between vehicles are 9 seconds or greater. If the observer decides to count traffic in 30-second time intervals,

Estimate the probability of the observer counting exactly 1 vehicles in an interval.