The probability that the sample average exceeded 5100 is given as follows:
0%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 250, \sigma = 5000, n = 64, s = \frac{5000}{\sqrt{64}} = 625[/tex]
The probability that a sample average exceeds $5,100 is one subtracted by the p-value of Z when X = 5100, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (5100 - 250)/625
Z = 7.76
Z = 7.76 has a p-value of 1.
1 - 1 = 0.
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Oak City High School ordered jerseys to sell at the
opening game. The school paid $9.25 each for
225 jerseys. Each jersey sold for $15.75. The
school sold 165 jerseys. What percent of the
jerseys did NOT sell? Round to the nearest
percent.
Approximately 27% of the jerseys did not sell.
What is Percentage?
Percentage is a way of expressing a number as a fraction of 100. It is used to describe ratios, proportions, and changes in quantities in terms of a fraction of the whole.
Solution:
The school ordered 225 jerseys and sold 165, so the number of jerseys that did not sell is:
225 - 165 = 60
To find the percentage of jerseys that did not sell, we need to divide the number of unsold jerseys by the total number of jerseys ordered and then multiply by 100:
60 / 225 x 100% = 26.67%
Rounding this to the nearest percent gives: 27%
Therefore, approximately 27% of the jerseys did not sell.
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Nancy has 4,111 in an account that pays 1. 07 interest Compounded monthly what is her ending balance after two years
Nancy's ending balance after two years is $31,930.93. Below, you will learn how to solve the problem.
To find Nancy's ending balance after two years, we will use the formula for compound interest:Plugging in the given values:
A = 4,111(1 + 1.07/12)^(12*2)
A = 4,111(1.089166)^(24)
A = 4,111(7.767)
A = $31,930.93
Therefore, Nancy's ending balance after two years is $31,930.93.
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Let A be a matrix with linearly independent columns. Which one of these statements must be true? You have only three attempts at this problem. A. The equation Az b always has a solution for all b B. The equation Ab has a solution for all b precisely when it has more rows than columns. O C. There is no easy way to tell if Ax-b has a solution for all b D. The equation Az -b has a solution for all b precisely when it has more columns than rows. OE. The equation Ax -b never has a solution for all b F. The equation Az-b has a solution for all b precisely when it is a square matrix. G. none of the abovePrevious question
If A be a matrix with linearly independent columns, then the statement that must be true is (A) The equation Az=b always has a solution for all b.
Since the columns of A are linearly independent, the matrix A has full column rank, i.e., its column space is the entire space R^n. Here are the implications of this fact for each statement:
A. The equation Az=b always has a solution for all b.
This is true, because for any b in R^n, we can write it as a linear combination of the columns of A, say b=c_1a_1+c_2a_2+...+c_na_n. Then, the solution to Az=b is simply z=[c_1,c_2,...,c_n]^T.
B. The equation Ab has a solution for all b precisely when it has more rows than columns.
This statement is false. The equation Ab=b is always solvable, regardless of the dimensions of A and b. The solution is simply b expressed in the basis of the column space of A.
C. There is no easy way to tell if Ax-b has a solution for all b.
This statement is also false. Since the columns of A are linearly independent, the equation Ax=b has at most one solution for each b. Therefore, Ax=b has a solution for all b if and only if the columns of A span the entire space R^n. This can be checked by computing the rank of A.
D. The equation Az-b has a solution for all b precisely when it has more columns than rows.
This statement is false. The equation Az=b is always solvable, regardless of the dimensions of A and b, as we have seen in (A).
E. The equation Ax-b never has a solution for all b.
This statement is false. The equation Ax=b has at most one solution for each b, and it is solvable for all b if and only if the columns of A span the entire space R^n, as we have seen in (C).
F. The equation Az-b has a solution for all b precisely when it is a square matrix.
This statement is false. The equation Az=b is always solvable, regardless of whether A is square or not, as we have seen in (A).
Therefore, the only true statement among the given options is (A) The equation Az=b always has a solution for all b.
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How do you divide fractions with a whole number for dummies?
Even though dividing a fraction by a whole number might be challenging, it is simple to achieve with a few steps. By placing the full number above 1, you must first divide it into a fraction. After that, multiply the fraction you are dividing by the inverted version of the fraction. Lastly, simplify the response as much as possible.
For instance, to multiply 3/4 by 2:
Put 2 over 1, making it 2/1, to make it a fraction.
To get 1/2, invert 2/1.
To get 3/8, multiply 3/4 by 1/2.
Divide the numerator and denominator by 3 to get 1/4, which is the simplest representation of the fraction 3/8.
Hence, 1/4 is equivalent to 3/4 when divided by 2.
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Dude please anyone help can anyone show me how to do this
According to the model, -9 (7v + 9.7) = -63v - 87.3. The solution has been obtained by using area model.
What is an area model?
An area model is a rectangular graphic used in mathematics to multiply and divide two numbers or expressions. The length and breadth of the rectangle are determined by the factors, also known as the quotient and divisor.
We are given an expression as -9 (7v + 9.7).
Using area model,
-9 * 7v = -63v
Similarly,
-9 * 9.7 = -87.3
On combining both, we get
-9 (7v + 9.7) = -63v - 87.3
Hence, the value for the expression is -63v - 87.3.
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the perimiter of pqr is 75, pq=25, pqr~stu and st=10. whats the perimeter of stu?
Answer: If pqr ~ stu, then we know that the corresponding sides are proportional.
We have pq=25 and st=10, so we can find the ratio of corresponding sides as:
25 / 10 = 2.5
This means that each side of stu is 2.5 times smaller than the corresponding side of pqr.
The perimeter of pqr is 75, so we can find the length of the other sides by subtracting the length of pq from the perimeter and dividing by 2:
(pq + qr + rp)/2 = (25 + qr + rp)/2 = 75/2
25 + qr + rp = 75
qr + rp = 50
Since pqr ~ stu, we know that the ratio of perimeters is also 2.5. Therefore, the perimeter of stu is:
Perimeter of stu = 2.5 (st + tu + us)
We know st=10, so we can find the other sides as:
tu = qr / 2.5 = 50 / 2.5 = 20
us = rp / 2.5 = 50 / 2.5 = 20
Therefore, the perimeter of stu is:
Perimeter of stu = 2.5 (10 + 20 + 20) = 2.5 (50) = 125
So the perimeter of stu is 125.
Step-by-step explanation:
What is 68 weight in lbs?
The conversion of the weight 68 kg from Kilogram to lbs will be equal to 149.914 lbs.
The fundamental mass unit in the metric system is the kilogramme (kg). A kilogramme and 1,000 cubic centimetres of water have fairly similar masses.
One pound is approximately equal to 454 grams. One kilogram is the same as 2.20462 lbs.
One pound is equal to 0.45359237 kilograms.
To convert kilograms (kg) to pounds (lbs), you can use the following formula:
To convert kilograms to pounds, multiply your figure by 2.20462
To convert 68 kg to lbs, you can multiply 68 by 2.20462:
68 kg X 2.20462 lbs/kg
= 149.914 lbs
Therefore, 68 kg is equal to 149.914 lbs.
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The complete question may be:
What is 68 Kg weight in lbs?
1 pts
A box with an open top is formed by cutting squares
out of the corners of a rectangular piece of cardboard
and then folding up the sides. If x represents the
length of the side of the square cut from each corner,
and if the original piece of cardboard is 15 inches by
13 inches, what size square must be cut if the volume
of the box is to be 189 cubic inches?
Use: length: (15-2x)
Width: (132z)
Height: x
The square that must be cut from each corner of the cardboard to form a box with a volume of 189 cubic inches is 3 inches on each.
What is square?Four equal sides and four right angles make up the two-dimensional shape known as the square. It is one of the most prevalent geometric shapes. There are a variety of useful applications for squares, including constructing tiling, patterns, and grids.
Given:
Length = 15 - 2x
Width = 13 - 2x
So, volume = lwh
189 = (15- 2x) (13 -2x) x
189 = (195 - 30x - 26x + 4x²)x
195x -56x² + 4x³ = 189
4x³ - 56x² + 195x - 189 = 0
On solving the cubic equation we get
x= 1.69, 3 and 9.3
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Find the missing output value (y)
for the given input value (x).
(3,y)
y=x-5
y = [?]
Enter
The corresponding output value is y = -2 when x = 3 in the equation y = x - 5.
What is the missing output value (y)?Given the equation in the question;
y = x - 5
Input value x = 3
Output value y = ?
The equation given is y = x - 5.
This equation is in the form y = f(x), which means that given an input value x, we can find the corresponding output value y.
In this case, we are given an input value of x = 3 and we need to find the corresponding output value y.
To do this, we simply substitute x = 3 into the equation and solve for y:
y = x - 5
Plug in x = 3
y = 3 - 5
y = -2
Therefore, when x = 3, the corresponding output value is y = -2.
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Please help I’ll give brainliest
The sum of the algebraic expressions 8x - 2 and -3x² - 7 is given as follows:
-3x² + 8x - 9.
How to add the algebraic expressions?The algebraic expressions for this problem are defined as follows:
8x - 2.-3x² - 7.To add them, we must combine the like terms, that is, add the terms that have the same variable and exponent, which are given as follows:
Like terms with x²: -3x².Like terms with x: 8x.Constant like terms: -2 - 7 = -9.Hence the sum has the result given as follows:
-3x² + 8x - 9.
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3.) Write the quadratic equation from the table. Use the y-intercept to solve for a.
X
-4
-3
-2
-1
0
2
y
-12
-5
0
3
4
3
0
3
-5
Answer and Step-by-step explanation:
To write the quadratic equation, we need to find the values of a, b, and c in the general form of a quadratic equation:
y = ax^2 + bx + c
Using the given data, we can plug in the x- and y-values to get a system of equations:
-12 = 16a - 4b + c
-5 = 9a - 3b + c
0 = 4a - 2b + c
We can solve this system of equations using substitution or elimination to get:
a = -1
b = 3
c = 4
Substituting these values into the general form of the quadratic equation, we get:
y = -x^2 + 3x + 4
Therefore, the quadratic equation from the table is:
y = -x^2 + 3x + 4
Convert 52 degrees to degrees Celsius. If necessary, round your answer to the nearest 10th of a degree. Here are the formulas.
The conversion of 52 degree F into Celsius is 11.11 Degree Celsius.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
C= 5/9 (F- 32)
and, F = 9/5C + 32
We have F= 52 F put the value to Celsius Formula
C = 5/9 (52- 32)
C = 5/9 (20)
C = 100/ 9
C= 11.11
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Marieme wants to build a rectangular garden whose area is
24
2424 square meters.
1. Write an equation that represents the garden's length in meters (
l
ll) based on its width in meters (
w
ww).
The equation representing the length of the garden in meters
is length = 24/width.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, A rectangular garden has an area of 24 square meters.
We know, Area = length×width.
Therefore, 24 = length×width.
Now, An equation that represents the garden's length in meters is,
24 = length×width.
length = 24/width (meters).
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how can you use proportional and nonproportional linear relationships to solve problems
Answer:
To solve problems using proportional linear relationships, we can use the formula [tex]y=kx[/tex], where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.
To solve problems using nonproportional linear relationships, we can use the slope-intercept form of a linear equation, which is [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
A recipe requires 1 1/2, cups of milk for every 1/2 of a cup of flour. What is the ratio of
cups of milk to one cup of flour?
Answer:
So the ratio of cups of milk to one cup of flour is 3:1.
Step-by-step explanation:
We can start by multiplying the denominator by 2 to get a denominator of 1:
1/2 * 2 = 1
Now we need to multiply the numerator by 2 as well to keep the ratio the same:
1 1/2 * 2 = 3
What is factors of 47 ?
Factors of 47 are 1 and 47 which implies that it can only be divided by one and itself.
The number 47 is a prime number, which implies that it can only be divided by one and itself. As a result, the components of 47 are 1 and 47.
Generally, a number's factors are the positive integers that divide it evenly with no residual. The factors of 12 are, for example, 1, 2, 3, 4, 6, and 12, since each of these numbers can be divided into 12 without leaving a leftover.
Yet, there are only two elements in the case of prime numbers, such as 47, which are always 1, and the number itself. This is because, by definition, prime numbers have no divisors other than 1 and themselves.
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which function has a period of pi
a radioactive substance has a decay rate of 0.044 per hour. how many grams of a 100 gram sample will remain radioactive after 2 hours? round the answer to the nearest tenth of a gram, and do not include the unit in your answer. if necessary, include a leading 0 with any decimals less than 1. for example, 0.4 instead of .4. note: the formula for radioactive substance is w
91.6 grams of a 100 gram sample will remain radioactive after 2 hours. The solution has been obtained by using the concept of radioactive decay.
What is Radioactive decay?
Radioactive decay is the spontaneous destruction of an atomic nucleus in a radioactive substance that causes the emission of radiation from the nucleus. A parent nuclide in a radioactive process is one that decays, and a daughter nuclide is one that is created in the radioactive process.
We are given that a radioactive substance has a decay rate of 0.044 per hour.
Using the radioactive decay formula,
N(t) = N₀ [tex]e^{-kt}[/tex]
Initially, N = 100
k = 0.044
t = 2
So,
⇒N(t) = 100 * e⁽⁻⁰°⁰⁴⁴ ˣ ²⁾
⇒N(t) = 91.5761
⇒N(t) = 91.6
Hence, 91.6 grams of a 100 gram sample will remain radioactive after 2 hours.
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a golf ball has a circumference of 13.408 centimeters, and 336 dimples on its surface. approximately how many dimples per square centimeter are on the surface of a golf ball? (A)0.170 (B)1.468 (C)4.268 (D)5.872
The golf ball is a sphere with a curved surface area of 57.217 sq cm. The number of dimples per sq. cm on the ball is D) 5.872.
In geometry, a sphere is a three-dimensional geometric shape that is perfectly symmetrical and round in shape. It is a set of points in space that are equidistant from a fixed center point. The surface of a sphere is made up of all the points that are at an equal distance, known as the radius, from the center.
Let's assume that the radius of the golf ball is r cm.
Given that
the circumference of the golf ball = 13.408 cm
2πr = 13.408
r = [tex]\frac{13.408}{2\Pi}[/tex]
r = [tex]\frac{13.408}{2\times3.142}[/tex]
r = 2.134 cm.
The radius of the sphere is 2.134 sq. cm.
The curved surface area of the sphere is 4πr².
CSA = 4πr²
CSA = 4 × 3.142 × 2.134²
CSA = 57.217 sq cm.
It is also given that there are 336 dimples on its surface.
Number of dimples per sq. cm = [tex]\frac{Total\ dimples\ on\ ball}{CSA}[/tex]
[tex]= \frac{336}{57.217} \\= 5.872[/tex]
Hence, there are 5.872 dimples per square centimeter on the surface of a golf ball.
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What are 4 sides shapes called?
The closed shapes with four sides are called quadrilaterals.
Quadrilateral is the closed which has four sides.All the four sides are connected to each other known as vertex.Two adjacent side with vertex forms a interior angle of the quadrilateral.If the opposite sides are parallel to each other then it is known as parallelogram.There are three main types of parallelogram.Rectangle, Square, Rhombus.Rectangle with opposite pair of sides parallel and congruent to each other.Square and Rhombus all four sides are congruent.If only one pair of opposite side parallel to each other then it is known as trapezium.Kite is also formed by four sides.Therefore, the four sides closed shape is known as quadrilateral.
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why does gyro never never ever bet on even numbers
Gyro never bets on even numbers because the expected value of such a bet is always negative.
To understand this concept, let's look at what an even number bet involves. When a person bets on an even number, they are essentially risking their entire stake on a 50/50 chance of winning.
This means that if they win, they will get their stake back plus the amount they would have won if the bet had been successful – in other words, their returns will be twice their original stake.
However, if they lose the bet, they will lose their entire stake. This means that the expected value of a bet on an even number is always negative. In other words, the expected outcome of the bet is always a loss.
Therefore, it is never a good idea to bet on an even number, as the expected value is always negative
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What is the conversion of 3cm in inches ?
The value after conversion 3 centimeter into inches is equal to 1.1811 inches.
Centimeters and inches are the units used to measure the length of the object.The conversion value of the centimeter into inches is given by :
One centimeter is equal to 0.393701 inches
Substitute the value 3 centimeter into inches we have,
⇒ 3 centimeter = ( 3 ) × ( 0.393701 ) inches
⇒ 3 centimeter = ( 1.181103 ) inches
⇒ 3 centimeter = ( 1.1811 ) inches ( round upto the four decimals places )
Therefore, the converted value of the 3 centimeter to inches is given by ( 1.1811 ) inches ( round upto the four decimals places ) .
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Which equation shows that the Pythagorean identity is true for 0=0 Select the equation that is in the form sin^20 + cos^20 = 1.
Answer:
D
Step-by-step explanation:
the last one, because sin(0)=0, cos(0)=1.
10% of 75 is what number?
Answer:
7.5
Step-by-step explanation:
the proportions of families with various numbers of children age 18 or under in a small town are given in the following table. one family is randomly selected from this town. x 0 1 2 3 4 5 p(x) .10 .40 .13 .10 .22 .05 find the probability that the selected family has at least 3 children age 18 or under.
The probability that at least 3 children age 18 or under will be selected is 0.50
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/total possible outcome
at least 3 children means x≥ 3
therefore ;
probability of atleast 3 children age 18 or under are selected =
.13+ .10 +.22 +.05
= 0.50
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The price of petrol is increased from R 12.58 per litre to R 13.28per litre Determine the percentage increase in the price
The percentage increase in the price of petrol is approximately 5.56%.
What is percentage?Percentages are used to compare and express parts of a whole, and to express changes or differences in values. For instance, we can use percentages to express:
A discount or a markup in prices
The increase or decrease in a quantity or value
The proportion of a quantity compared to a whole
The probability of an event occurring.
In the given question,
To determine the percentage increase in the price of petrol, we need to calculate the difference between the old price and the new price, divide that by the old price, and then multiply by 100 to convert to a percentage.
The difference between the old price and the new price is:
R 13.28 - R 12.58 = R 0.70
Dividing the difference by the old price:
R 0.70 ÷ R 12.58 ≈ 0.0556
Multiplying by 100 to convert to a percentage:
0.0556 × 100 ≈ 5.56%
Therefore, the percentage increase in the price of petrol is approximately 5.56%.
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what is tsp into grams?
Water weighs 4.92892 grams in a US teaspoon. Thus, 1 g of water is equivalent to around 1/5 teaspoon.
The acronym "Tsp" stands for teaspoon, a volumetric measurement commonly used in baking and cooking. A "gram" is a measure of mass or weight. As a result, converting between tsp and grams is not possible.
The density of the material being measured determines how to convert teaspoons to grams. For instance, a teaspoon of water weighs around 5 grams, but a teaspoon of sugar weighs roughly 4 grams.
I'll do my best to estimate the substance's weight in grams if you tell me what it is that you are quantifying in teaspoons.
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Lacrosse players receive a randomly assigned numbered jersey to wear at games. If the jerseys are numbered 0−29, what is the probability the first player to be assigned a jersey gets #16
The probability that the first player to be assigned a jersey gets #16 is 0.0333 (or 1/30).
What is probability?
The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%.
If there are 30 jerseys numbered 0-29 and they are all equally likely to be assigned, then the probability that the first player to be assigned a jersey gets #16 is 1/30 or approximately 0.0333 (rounded to four decimal places).
Hence, the probability that the first player to be assigned a jersey gets #16 is 0.0333 (or 1/30).
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What separate the population into nonoverlapping groups?
Stratified Sampling separates the population into nonoverlapping groups. By using specific criteria to split the population, we may use this strategy to draw a proportional random sample from each division.
The population is divided into non-overlapping groups or strata, and a proportional simple random sample is taken from each stratum to create a stratified sample. Each group's members ought to have some things in common. We must choose the number of people to choose from each stratum after the strata have been established. Here, the proportionality of the chosen number is crucial. In order to make the characteristic of interest more homogeneous inside a stratum than between strata, strata are based on information other than the characteristic being measured that is known to or thought to fluctuate with the characteristic of interest. Hence, strata can be defined based on any property that explains variation in the characteristic of interest.
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Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel
Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel so the value of distance l is l = fs - fa.
In a partly ionized plasma with several species, we investigate the propagation of electromagnetic waves (or incompressible waves with little thermal pressure) through the magnetic field. Due of variances in mass and density, each species responds to and hence influences electromagnetic field disturbances differently.
For the first lens , ray of light from distant object are parallel , so image will formed at the focal length of first lens.
For second lens,
object distance (u) = fa + l
image distance (v) = ∞
By lens formula,
1/v - 1/u = -1/fs
u = fs
fa + l = fs
l = fs - fa
Collisions between all of the species complicate the process even further. Based on a multi-fluid treatment and Faraday's and Ampere's laws, including the displacement current, a linear analysis is used to derive the dispersion relation of parallel propagation covering a wide range of frequencies, from magnetohydrodynamics (MHD) waves to light waves, with an arbitrary combination of multiple positively charged species, negatively charged species, and neutral species.
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Complete question:
Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel.
For this set up to work, what must be the distance l ?