Determine the ratio of the number of molecules in a gas having a speed ten times as great as the root mean square speed to the number having a speed equal to the root mean square speed. Is this ratio independent of temperature

The correct function that describes the student's distance from the finish line after x minutes is f(x) = -1/4x + 10.

The correct function that describes the student's distance from the finish line after x minutes can be determined by analyzing the given information. We know that the student runs 1 kilometer every 4 minutes, and the race is a total of 10 kilometers.

Let's examine the options:

1. f(x) = 1/4x + 10

This function represents the distance covered by the student in x minutes, but it does not account for the fact that the total race distance is 10 kilometers.

2. f(x) = -1/10x + 4

This function has a negative coefficient for x, which would indicate that the student is getting farther away from the finish line as time progresses, which is not the case.

3. f(x) = 1/10 + 4

This function is a constant and does not change with time, so it cannot describe the student's distance from the finish line.

4. f(x) = -1/4x + 10

This function correctly represents the student's distance from the finish line. The negative coefficient for x indicates that the distance decreases as time progresses, and the constant term of 10 represents the initial distance from the finish line, which is 10 kilometers.

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On average, there is only 1 letter that will go into the right envelope.

It is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

There are three main types of average: mean, median and mode. Each of these techniques works slightly differently and often results in slightly different typical values. The mean is the most commonly used average. To get the mean value, you add up all the values and divide this total by the number of values.

To find Average, we add up all the values and then divide this total by the number of values.

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Answer:

1 9/10

Step-by-step explanation:

First, convert all the fractions with 5 to 10's.

2/5 would be 4/10, and 3/5 would be 6/10.

9/10 + 4/10 + 6/10 = 19/10

19/10 = 1 9/10

After the stock's value increases by 4.5% and then falls by the same percentage, the new value would be approximately $997.975.

Let's calculate the new value of the stock after the increase and decrease.

Starting with $1,000, a 4.5% increase in value would be calculated as (4.5/100) * 1000 = $45. This brings the value up to $1,045.

Next, a 4.5% decrease in value would be calculated as (4.5/100) * 1045 = $47.025. This amount is subtracted from the increased value of $1,045.

Subtracting $47.025 from $1,045 gives us $997.975, which is slightly less than $1,000.

Therefore, after the stock's value increases by 4.5% and then falls by the same percentage, the new value would be approximately $997.975. It's important to note that this calculation assumes a simple percentage increase and decrease without considering other factors that can affect stock market fluctuations.

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Answer:

The correct answer is b)

Step-by-step explanation:

Answer:

At 50 miles, the rental costs are the same from either company.

Company A:

0.3 x 50 = 15

15+50= 65

Company B:

0.7 x 50 = 35

35 + 30 = 65

Answer:

153.9 ft²

Step-by-step explanation:

The area for a circle formula is πr².

Using the radius, we get:

π×7² =

49π ≈

153.938 ≈ (Using the π key)

153.9 ft²

Answer:153.86

Step-by-step explanation:area of a circle is πr square

That is 3.14×49

=153.86

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

The speed of current and average speed of paddling is 3 and 7 respectively.

Let p represents paddling speed of kayack guide  and c represents speed of current.

If paddling downstream, the total speed is p + c because you’re paddling with the current. Similarly, if paddling upstream, the total speed is p - c because you would be paddling against the current.

Since paddling downstream took  2 hours so distance covered 2*(p + c)

which is equal to 20 miles.

2*(p + c) =20.

p + c = 10. -----i

Paddling upstream took 4 hours so distance covered 4*(p-c).

which is equal to 16 miles.

4*(p-c) = 16.

p - c = 4.  -------ii

adding both equation c will be cancelled. 2*p=14 p =7.

put value of p in equation i.

7 + c = 10  ,c = 3.

So the speed of current and average speed of paddling is 3 and 7 respectively.

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Answer:

r = 1

Step-by-step explanation:

first you have to expand the brackets.

3 x 7 = 21

3 x -2r = -6r

the equation is now 21-6r = 21r-6

now you simplify it so get the answer r = 1

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The ratio of the number of students who joined the class to the number of students who were initially in the class is 2:1.

Age ratio refers to the comparison of the number of individuals in different age groups in a population. It is often expressed as a ratio or percentage of the number of people in a particular age group to the total population or the number of people in another age group.

Given by the question.

Now, when the group of students with an average age of 16 years joins the class, the average age of all the students becomes 17 years. This means that the total age of all the students in the class would now be 17 times the total number of students.

Let "y" be the number of students who joined the class. Then, the total number of students in the class after they joined would be x + y.

So, we have two equations:

18x = 17(x+y) (because the total age of all the students remains the same before and after the group joins)

16y = (x+y)*1 (because the average age of the new group is 16)

Simplifying the above equations, we get:

x = 17y

x = 34y

Equating both the equations, we get:

17y = 34y

y = 2

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Answer:

Hi... U should do like this

Answer:

Step-by-step explanation:

The number that is greater than 52,136 is 142,136.

Answer:

sorry I can't understand the answer sorry

a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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the box with the largest volume has dimensions approximately 3.48 in. x 3.48 in. x 5.76 in.

Let x be the side length of the square cut from each corner of the tin sheet. Then the dimensions of the base of the box will be (10-2x) by (10-2x), and the height of the box will be x. Thus, the volume of the box is given by:

V = (10-2x)^2 * x = 4x^3 - 40x^2 + 100x

To maximize V, we take the derivative of this expression and set it equal to zero:

dV/dx = 12x^2 - 80x + 100 = 0

Solving for x using the quadratic formula, we get:

xx = (80 ± sqrt(80^2 - 4*12*100))/24 ≈ 1.74, 5.76

The solution x = 1.74 is extraneous, since it would result in negative dimensions for the box. Thus, the optimal size of the square to be cut from each corner is x = 5.76 inches.

The dimensions of the box with the largest volume are:

Length = Width = 10 - 2x = 10 - 2(5.76) ≈ 3.48 inches

Height = x = 5.76 inches

Therefore, the box with the largest volume has dimensions approximately 3.48 in. x 3.48 in. x 5.76 in.

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If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

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Answer:

The derivative of infinity is undefined. Infinity is not a number, but rather a concept that represents a quantity that is unbounded or limitless. The derivative of a function at a point is a measure of the rate of change of the function at that point. Since infinity itself does not have a numerical value or a well-defined location, it is not possible to take the derivative of infinity. This means that the concept of the derivative does not apply to infinity and the derivative of infinity is undefined.

Answer:

x=120 (opp. angles of //gram)

Step-by-step explanation:

Because DA//CB and AB//DC (given)

Therefore ABCD is a parallelogram (opp. sides equal)

Therefore,

∠DAB = ∠DCB (opp. ∠s of //gram)

x = 120

This is the answer to your problem

True. Using polynomial models in RD can produce bumps at the cutoff that are larger than they should be, which is known as the "overshoot" problem.

This happens because polynomial models are flexible and can fit high-frequency variations in the data, including noise, which can lead to an overfit of the data near the cutoff and create larger bumps than what should be expected.

To avoid this problem, alternative modeling strategies, such as local linear regression or spline-based models, can be used

True. Using polynomial models in RD can produce bumps at the cutoff that are larger than they should be, which is known as the "overshoot" problem.

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Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

Each time X increases, there is a perfectly predictable increase in Y  is indicated by a Pearson correlation of r= +1.00 between X and Y

A Pearson correlation coefficient of +1.00 indicates a perfect positive linear relationship between the variables X and Y. It means that as X increases, Y increases in a perfectly predictable manner. The correlation coefficient of +1.00 indicates a strong and direct relationship between the two variables, where the values of Y can be precisely determined based on the values of X.

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The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

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complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

To find the conditions on a, b, c, and d such that the matrix B = [a b; c d] commutes with both [1 0; 0 1] and [0 0; 0 1], we need to determine when the product of B and each of these matrices is equal regardless of the order.

The necessary conditions for commutation are:

1. a = 1: This condition ensures that the first column of B remains unchanged when multiplied with [1 0; 0 1], ensuring commutation.

2. b = 0: This condition ensures that the second column of B is multiplied by the first column of [0 0; 0 1], which is a zero vector, resulting in a zero column.  

3. c = 0: This condition ensures that the first column of B is multiplied by the second column of [0 0; 0 1], which is a zero vector, resulting in a zero column.

4. d = 1: This condition ensures that the second column of B remains unchanged when multiplied with [0 0; 0 1], ensuring commutation.

In summary, the conditions for B to commute with both [1 0; 0 1] and [0 0; 0 1] are a = 1, b = 0, c = 0, and d = 1. These conditions ensure that the product of B with each of the given matrices is equal regardless of the order, resulting in commutation.

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Answer:

answer of second question 12x-6 =6(2x-1)

Step-by-step explanation:

12x-6

= 6(2x-1) take the common

=Answer=6(2x-1)

The statement n2 + 3n − 5 is greater than 4n for all natural numbers n > 2 can be proved using induction. The standard induction method starts by proving the base case for a specific value of n, then proving that the statement is true for any n+1 if it is true for n.

In this case, the base case is when n = 3, and the statement becomes 32 + 3(3) − 5, which is equal to 18, which is indeed greater than 4(3). Now, assume that the statement is true for all n ≥ 3. Now if n+1 is plugged into the equation, the result is (n+1)2 + 3(n+1) − 5 = n2 + 2n + 1 + 3n + 3 − 5 = n2 + 3n − 5 + 2n + 2 ≥ 4n + 2. Therefore, the statement is true for n+1, and the proof is complete.

In conclusion, the statement n2 + 3n − 5 > 4n for all n > 2 is true due to the method of induction, which can prove that any statement is true when the base case is proven and when the statement is true for each consecutive n.

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