the surface area of a cylinder is 936pi squares meters. the radius is 13m use the formula sa=2b=ph. to find the height of cylinder.

The rms speed of the dust particles is 8.24 mm/s, which is the correct answer with the appropriate units.

The equation you used requires temperature to be in Kelvin, density to be in [tex]kg/m^3,[/tex]

Boltzmann constant in J/K, and diameter in meters.

After plugging in the values you provided, the units of your answer are mm/s, which are not consistent with the units of velocity.

Here are the steps to calculate vrms with the correct units:

Convert the diameter from µm to meters:

5 µm [tex]= 5 * 10^-6 m[/tex]

Convert the density from [tex]g/cm^3[/tex] to [tex]kg/m^3:[/tex]

[tex]2 g/cm^3[/tex][tex]= 2000 kg/m^3[/tex]

Calculate the mass of the particle using the density and volume of a sphere: [tex]m = (4/3)\pi(d/2)^3[/tex]ρ

[tex]m = (4/3)\pi (5 * 10^-6/2)^3 * 2000 = 2.62 * 10^-13 kg[/tex].

Convert Boltzmann constant from J/K to [tex]m^2 kg/s^2 K: kB = 1.38 * 10^-23 J/K = 1.38 * 10^-23 m^2 kg/s^2 K[/tex]

Assume a temperature for the system, for example, T = 300 K

Plug in the values into the equation:

[tex]vrms = \sqrt{((3kBT)/(m4/3\pi(d/2)^3))}[/tex]

[tex]vrms = \sqrt{((3 * 1.38 * 10^-23 * 300)/(2.62 * 10^-13 * 4/3 *\pi * (5 * 10^-6/2)^3)}[/tex]

[tex]vrms = 8.24 * 10^-3 m/s = 8.24 mm/s[/tex] ....(rounded to one decimal place).

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The total value of the 549 coins in pounds (£) is £378.20 (or £379), depending on whether there are 110 or 111 20p coins.

Let's start by finding the number of £1 coins in the bottle. We know that ſ (one-half) of the coins are £1 coins, so:

ſ × 549 = 1/2 × 549 = 274.50

Since we can't have half a coin, we know that there are either 274 or 275 £1 coins in the bottle.

Next, we know that there are 164 50p coins in the bottle.

To find the number of 20p coins, we can subtract the number of £1 and 50p coins from the total number of coins:

549 - 274 (or 275) - 164 = 111 (or 110)

So, there are either 110 or 111 20p coins in the bottle.

To calculate the total value of the coins, we can multiply the number of each type of coin by its value and then add them up:

Value of £1 coins = £1 × 274 (or 275) = £274 (or £275)

Value of 50p coins = £0.50 × 164 = £82

Value of 20p coins = £0.20 × 111 (or 110) = £22.20 (or £22)

Total value = £274 (or £275) + £82 + £22.20 (or £22) = £378.20 (or £379)

Therefore, the total value of the 549 coins in pounds (£) is £378.20 (or £379), depending on whether there are 110 or 111 20p coins.

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The mapping that is a function will be B). X

Every function got a set of input values called " Domain " and a set of respective output values as " Range"

And function worked as Function( Input value ) = Output value

There are basic rules for function :

1. There always exist output value for every single input value.

2. Every input value should have one and only one output value

For W : Rule 2 is violated

Here, Input value 6 result to two output value 2 and 4

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The statement for congruency is true is A. ∠SPQ corresponds to ∠SRQ.

In geometry, a scalene triangle is a triangle in which all three sides have different lengths, and all three interior angles are different. In other words, no two sides of a scalene triangle are congruent, and no two angles are congruent.

Scalene triangles can also be classified as acute, obtuse, or right triangles based on the measure of their angles. An acute scalene triangle has three acute angles, meaning all three angles are less than 90 degrees. An obtuse scalene triangle has one obtuse angle, meaning one angle is greater than 90 degrees. A right scalene triangle has one right angle, meaning one angle is exactly 90 degrees.

Since the triangles are similar, their corresponding angles are equal, and their corresponding sides are proportional.

Given that ∠RQS ≅ ∠QSP, we can say that these angles correspond to each other. Therefore, statement A is true.

However, we cannot determine that ∠RSQ corresponds to ∠QPS or vice versa based on the information given. So statement B is not necessarily true.

Similarly, we cannot say that side SP corresponds to side RS or side PS corresponds to side QR. So statements C and D are not necessarily true.

Therefore, the answer is A.

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Therefore, the original price of the suit was $950.

Percent is a way of expressing a number as a fraction of 100, and is denoted by the symbol %. For example, 50% means 50 out of 100, or 0.5 as a decimal. Percentages are commonly used to express proportions, rates, discounts, and many other kinds of numerical information.

Here,

Let x be the original price of the suit. We know that the sale price, which is 34% less than the original price, is $627.

We can set up the equation:

x - 0.34x = 627

Simplifying this equation, we get:

0.66x = 627

Dividing both sides by 0.66, we get:

x = 950

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Since the calculated test statistic (2.54) is greater than the critical value (1.992), we can reject the null hypothesis at the 5% significance level. We can conclude that there is a statistically significant difference between the mean reduction in LDL for men and women after spending 6-weeks on a plant-based diet.

To compute the test statistic for the hypothesis test, we will use the two-sample t-test, assuming equal variances.

The formula for the test statistic is:

[tex]t = \frac{x_{1} -x_{2}}{s_{p}\sqrt{\frac{1}{n_{1} }+ \frac{1}{n_{2}} } }[/tex]

where x₁ and x₂ are the sample means for men and women, [tex]s_{p}[/tex] is the pooled standard deviation, n₁ and n₂ are the sample sizes for men and women.

First, we need to calculate the pooled standard deviation:

[tex]s_p = \sqrt{(n_1-1)(s_1)^2 + \frac{(n_2)s^2}{ (n_1 + n_2)^2} }[/tex]

where s1 and s₂ are the sample standard deviations for men and women.

Substituting the given values, we get:

[tex]s_p = \sqrt{(36-1)(1.3)^2 + \frac{(41-1)1.9^2}{ (36 + 41)^2} }[/tex]

[tex]s_{p}[/tex] = 1.611

Next, we can calculate the test statistic:

[tex]t = \frac{(15.4 - 13.3)}{(1.611 \sqrt{\frac{1}{36}+\frac{1}{41}}}[/tex]

t = 2.54

The critical value for a two-tailed test with alpha = 0.05 and degrees of freedom = 75 (n₁ + n₂ - 2) is ±1.992.

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---The question is incomplete, The complete question is:

To determine the effects, researchers measured the LDL levels of 36 randomly selected men and 41 randomly selected women before and after spending 6-weeks on a plant-based diet. The researchers then subtracted the two values corresponding to each individual and found the mean reduction for each group. For men, the mean reduction in LDL was 13.3 mg/dl with a standard deviation of 1.3 mg/dl. For women, the mean reduction in LDL was 15.4 mg/dl with a standard deviation of 1.9 mg/dl. Both the scatterplots for the mean LDL reduction in men and women resemble a normal distribution.

We will test H_0: µ1= µ2 vs. H_a: µ1≠ µ2. Compute the test statistic of interest (women - men), accurate to three digits beyond the decimal point. ---

A reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.

How to estimate the probability of given data?

To estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to use the given data to calculate the mean and standard deviation of the number of feathers she has sold in the past festivals.

The mean, denoted by μ, is calculated by adding up all the number of feathers sold and dividing by the total number of festivals. So,

μ = (3 + 6 + 1 + 4 + 2 + 3 + 7 + 2) / 8 = 3.375

The standard deviation, denoted by σ, is a measure of how spread out the data is. It is calculated by first finding the variance, which is the average of the squared differences between each data point and the mean, and then taking the square root of the variance. So,

Variance = ((3-3.375)² + (6-3.375)²+ (1-3.375)² + (4-3.375)² + (2-3.375)² + (3-3.375)² + (7-3.375)² + (2-3.375)²) / 8 = 4.0898

σ = √(4.0898) = 2.022

Now, to estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to standardize the value by subtracting the mean and dividing by the standard deviation. So, let X be the number of feathers sold at the next festival, then,

Z = (X - μ) / σ

Let's say we want to estimate the probability that Patsy sells fewer than 2 feathers at the next festival. Then,

Z = (2 - 3.375) / 2.022 = -0.679

We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -0.679, which is approximately 0.2485.

Therefore, a reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.

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Correct question is "The number of feathers Patsy 3, 6, 1, 4, 2, 3, 7, 2 Peacock sold at each of the festivals this year. Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than feathers next festival? "

The circumference of the circle with a radius of 10 cm is approximately 62.8 cm.

The ratio of a circle's circumference to its diameter is used to define the definition of Pi (). By d, divide both sides. The diameter (d) and both sides of the equation (C= d) will be divided by one another to provide a result that is about equal to.

To get a circle's circumference, use this formula:

C = 2πr

We get the following results when we plug the radius's provided value into the formula:

C = 2π(10 cm)

= 20π cm

Using the approximate value of π as 3.14, we can calculate the circumference to be:

C ≈ 20π cm ≈ 62.8 cm (rounded to the nearest tenth)

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the height of the mast is approximately 51.5 meters.

what is approximately ?

"Approximately" means that the value is an estimate that is very close to the true value but may not be exact. In the context of the answer I provided, "approximately" indicates that the height of the mast is very close to 51.5 meters but may be slightly more or less than that value.

In the given question,

Let's call the height of the mast "h". We can use trigonometry to find the value of "h".

If we draw a diagram, we can see that the angle of elevation of the mast is the same as the angle between the ground and a line from P to the top of the mast. We can call this angle "θ".

We know that tan(θ) = opposite/adjacent = h/150.

We also know that tan(19°) = 0.3431 (rounded to 4 decimal places).

So we can set up an equation:

0.3431 = h/150

To solve for "h", we can multiply both sides by 150:

h = 0.3431 x 150

h = 51.465 (rounded to 3 significant figures)

Therefore, the height of the mast is approximately 51.5 meters.

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Answer:

Eleven below Zero

Step-by-step explanation:

Every number below zero (less than zero) is a negative number.

Therefore, the measure of angle XOB is 60 degrees.

The radius is the distance around a circle from its centre to its edge. For instance, if the circle's radius is 7 cm, its diameter will be 7 x 2, or 14 cm. You can find the diameter of a circle if you know its circumference and divide it by a certain number.

Since O is the circle's center, the inscribed angle theorem states that the length of the arc XOY is twice the length of the angle XOB.

We know that the measure of the arc XOY is 120, so:

2 * measure of angle XOB = measure of arc XOY

2 * measure of angle XOB = 120

measure of angle XOB = 60

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The first step in finding the distance between vertex P and vertex V is find the length of diagonal between vertex P and vertex R.

option A.

To find the distance between vertex P and vertex V, we need to draw a diagonal line from vertex P to vertex V.

After drawing the diagonal line, we will notice that we have a new right angle triangle.

So since we know the height of the right triangle, we need to find the base of the right triangle first, which is equal to length of diagonal length PR or TV

So the correct answer will be "find the length of diagonal PR first.".

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Answer:

Step-by-step explanation:

You want to identify the lines among those listed that will intersect the line y = 4.

The line y = 4 is a horizontal line. Any line of the form y = c, for some constant c (not 4), will be parallel and will not intersect y = 4.

All of the other lines listed will intersect y = 4.

The intersecting lines are ...

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The probability that 3 of the 9 randomly selected subjects entered a profession closely related to their college major is approximately 0.1665, or 16.65%.

To find the probability that 3 out of 9 randomly selected subjects entered a profession closely related to their college major, we can use the binomial probability formula:
[tex]P(X = k) = (n choose k) * p^k * (1 - p)^{n - k}[/tex]
where:
- P(X = k) is the probability of k successes (in this case, 3 people entering a profession closely related to their major)
- n is the number of trials (9 subjects)
- k is the number of successes (3 people)
- p is the probability of success (53% or 0.53)
- (n choose k) is the number of combinations of n items taken k at a time, which can be calculated as C(n, k) = n! / (k! * (n - k)!)
Plugging in the values, we get:
[tex]P(X = 3) = C(9, 3) * (0.53)^3 * (1 - 0.53)^{9 - 3}[/tex]
First, calculate the combinations (n choose k):
C(9, 3) = 9! / (3! * (9 - 3)!)
C(9, 3) = 9! / (3! * 6!)
C(9, 3) = 362880 / (6 * 720)
C(9, 3) = 84
Now, calculate the probabilities:
[tex]P(X = 3) = 84 * (0.53)^3 * (0.47)^6[/tex]
P(X = 3) = 84 * 0.148877 * 0.013325
P(X = 3) ≈ 0.1665.

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The minimum of the given expression can be found to be 3 x ∛(√2).

Use these inequalities to find the minimum of the given expression:

(a / (b + c)) + (b / (c + a)) + √(2c / (a + b)) ≥ (a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab)))

Now, simplify the expression:

(a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab))) = (√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))

Apply AM-GM inequality to the terms (√(a²/bc)), (√(b²/ac)), and (√(2c²/ab)):

AM = [(√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))] / 3 ≥ GM = ∛[(√(a²/bc)) * (√(b²/ac)) * (√(2c²/ab))]

The geometric mean (GM) is:

GM = ∛[(√(a²/bc)) x (√(b²/ac)) x (√(2c²/ab))]

GM = ∛(√(2a²b²c² / a²b²c²))

GM = ∛(√2)

Thus, the minimum of the given expression is:

= 3 x ∛(√2)

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The given statement "The radical expressions √2 and √12 can be combined to become one radical expression through addition or subtraction. " is true because a single radical expression that represents the two original expressions.

When we simplify a radical expression, we try to write it in its simplest form. For example, we know that √4 is equal to 2 because 2 multiplied by itself gives us 4. Similarly, we know that √9 is equal to 3 because 3 multiplied by itself gives us 9.

We can simplify radical expressions further by combining them using addition or subtraction. For example, √4 + √9 is equal to √13 because we can add 2 and 3 to get 5 and take the square root of 5 to get √5.

Now, let's look at √2 and √12. We can simplify √12 to √(4 × 3) because 4 is a perfect square. This gives us √4 × √3, which simplifies to 2√3.

Therefore, we can write √2 + √12 as √2 + 2√3. This is one radical expression that combines the two original expressions using addition. We can also subtract √12 from √2 to get √2 - 2√3, which is another radical expression that combines the two original expressions using subtraction.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{40}~,~\stackrel{y_1}{30})\qquad (\stackrel{x_2}{100}~,~\stackrel{y_2}{75}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{75}-\stackrel{y1}{30}}}{\underset{\textit{\large run}} {\underset{x_2}{100}-\underset{x_1}{40}}} \implies \cfrac{ 45 }{ 60 } \implies \cfrac{ 3 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{30}=\stackrel{m}{ \cfrac{ 3 }{ 4 }}(x-\stackrel{x_1}{40}) \\\\\\ y-30=\cfrac{ 3 }{ 4 }x-30\implies {\Large \begin{array}{llll} y=\cfrac{ 3 }{ 4 }x \end{array}}[/tex]

The probability that the point is in the smaller, shaded square is approximately 14.06%.

Probability is the measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will certainly occur. The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Probability is widely used in various fields, including mathematics, statistics, science, finance, and engineering.

The area of the large square is (8 cm)² = 64 cm², and the area of the shaded square is (3 cm)² = 9 cm². The probability of choosing a point at random that is in the shaded square is equal to the ratio of the area of the shaded square to the area of the large square:

Probability = (area of shaded square) / (area of large square)

Probability = 9 cm² / 64 cm²

Probability = 0.140625 or 14.06% (rounded to two decimal places)

Therefore, the probability that the point is in the smaller, shaded square is approximately 14.06%.

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Answer:

4x - y = 2,

Step-by-step explanation:

The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, we are given that the line passes through the points (4, -3) and (12, 1). The slope of the line is then m = (1 - (-3)) / (12 - 4) = 1/4.

Substituting the slope and the point (4, -3) into the point-slope form of the equation, we get y - (-3) = 1/4(x - 4). Simplifying, we get y + 3 = 1/4x - 1.

To convert the equation to standard form, we multiply both sides of the equation by 4. This gives 4y + 12 = x - 4. Simplifying, we get 4x - y = 8.

Therefore, the standard form of the equation of the line is 4x - y = 8.

The assertion that a distribution of sample means approaches a normal curve as sample size increases is called the Central Limit Theorem (CLT).

The CLT is a fundamental concept in statistics and is often used to make inferences about population parameters based on sample statistics.
The CLT states that for any population with a finite mean and standard deviation, the distribution of sample means for sufficiently large sample sizes (typically, n ≥ 30) will be approximately normal, regardless of the shape of the original population distribution.

This means that as sample size increases, the variability in the sample means decreases, and the distribution of sample means becomes more and more symmetrical.
One of the key implications of the CLT is that it allows us to estimate population parameters, such as the mean and standard deviation, using sample statistics.

Multiple random samples from a population and calculate the mean of each sample, the distribution of those sample means will be approximately normal, and we can use that distribution to estimate the population mean with a certain level of confidence.
The CLT has broad applications in various fields, including finance, engineering, biology, and social sciences. It is important to note, however, that the CLT only holds under certain assumptions and conditions, and it is crucial to check these assumptions.

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Answer:

3x-y=1

Step-by-step explanation:

The surface density of the lights on the Rockefeller Center Christmas Tree is 9.38 lights per square foot.

The surface density of the lights on the Rockefeller Center Christmas Tree can be found by dividing the total number of lights by the surface area of the tree.

To find the surface area of the tree, we need to first find the slant height of the cone. We can use the Pythagorean theorem to find the slant height, which is the square root of the sum of the height squared and the radius squared:

The slant height:

= sqrt(72^2 + (45/2)^2)

= 75.43 feet

The lateral area of a right cone can be found using the formula: πrs

r = 45/2 = 22.5 feet

Substituting the given values into the formula for the lateral area, we get:

Lateral area = π(22.5)(75.43)

Lateral area = 5329.1295 square feet

To find the surface density of the lights, we can divide the total number of lights by the lateral area:

Surface density = 50,000 / 5329.1295

Surface density = 9.38239537996

Surface density= 9.38 lights/square foot.

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Answer:The easiest method is to draw a possibility space first. The grid shows the totals for two dice. There are: 6×6=36 possible outcomes. Of these there are 10 totals which are less than 6 .

Step-by-step explanation:

pls give me brainliest and have a good day and night:)

The H. C. F of 80,215,245 and 720 using long division method is 5.

The long division method to find the Highest Common Factor (H.C.F.) of 80, 215, 245, and 720.

Divide the largest number by the smallest number.

720 ÷ 80 = 9 with a remainder of 0

Divide the smallest number by the remainder from the previous step.

80 ÷ 40 = 2 with a remainder of 0

Divide the remainder from the previous step by the next smallest number.

40 ÷ 5 = 8 with a remainder of 0

Divide the remainder from the previous step by the next smallest number.

5 ÷ 5 = 1 with a remainder of 0

We have reached a remainder of 0, which means that 5 is the H.C.F. of the given numbers.

Therefore, the H.C.F. of 80, 215, 245, and 720 is 5.

We can also verify this by listing the factors of each number and finding the common factors:

80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

215: 1, 5, 43, 215

245: 1, 5, 7, 35, 49, 245

720: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720

The common factors are 1, 5, and 40.

The largest common factor is 5, which is the same as what we obtained using the long division method.

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Answer:

20

Step-by-step explanation:

So start with the ones you know like 2+2. So what I did is add the 2,s and then add the 4,s then I added 3,s which then added the 6,s the 8+12= 20 and that's how I got my answer.

The trains will be 380 miles apart at 3:00 PM, which is 4 hours after the freight train leaves the station at 12 noon.

We can use the formula d = rt (distance = rate x time) to calculate the distance each train has traveled during this time:

Let's call the time elapsed from 12 noon until the trains meet as t hours.

During this time, the freight train has traveled at a rate of 50 mph for t hours and the passenger train has traveled at a rate of 60 mph for (t-1) hours (since it started one hour after the freight train).

Distance traveled by freight train = 50t

Distance traveled by passenger train = 60(t-1)

The total distance between the two trains at time t is the sum of these distances, which we can write as:

Total distance = 50t + 60(t-1)

We want to find the time t at which the total distance is 380 miles. So we can set up the equation:

50t + 60(t-1) = 380

Simplifying this equation, we get:

110t - 60 = 380

110t = 440

t = 4

Therefore, the time elapsed from 12 noon until the trains meet is 4 hours. Since the passenger train left one hour after the freight train, it has been traveling for 3 hours.

So the time at which the trains are 380 miles apart is 3:00 PM (12 noon + 4 hours).

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Answer:

0.6

Step-by-step explanation:

it just math