derive an equation that relates the initial release height hx of block x and the speed vs of the two-block system after the collision in terms of mx , my , and fundamental constants, as appropriate.

Answer:

Step-by-step explanation:

10x+y=9(x+y)

10y+x=10x+y-63

now put x alone and solve for x then y and add the values of x and y and you will get your answer

Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.

What is arithmetic sequence ?

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

The sequence {12, 5, -2, -9, -16 ... } can be defined by the following items:

The first term: 12

The common difference: -7

The pattern of adding the common difference to find the next term.

Therefore, all the items that define the sequence are:

The first term: 12

The common difference: -7

This sequence is an arithmetic sequence.

Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.

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Classifying polynomials refers to categorizing polynomials based on the degree of the polynomial and the number of terms in the polynomial.

The degree of a polynomial is the highest exponent in the polynomial. Polynomials can be classified into several types, including constant polynomials (degree 0), linear polynomials (degree 1), quadratic polynomials (degree 2), and so on. Adding and subtracting polynomials is the process of combining two or more polynomials by combining like terms. Like terms are terms with the same variable and exponent. To add or subtract polynomials, simply line up the terms with the same variable and exponent and add or subtract the coefficients. The result will be a new polynomial with the combined terms.

For example, to add the polynomials [tex]2x^2 + 3x + 4[/tex] and [tex]-x^2 + 5x - 6[/tex], we line up the terms with the same variable and exponent and add the coefficients:

[tex](2x^2 + 3x + 4) + (-x^2 + 5x - 6) = (2x^2 - x^2) + (3x + 5x) + (4 - 6) \\[/tex]

                                                   [tex]= x^2 + 8x - 2.[/tex]

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Gena needs to add 2.5 liters of the 20% solution. Option B is correct.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the amount of 20% solution that Gena needs to add "x". Then the total amount of solution will be 5 + x liters. The total amount of apple cider vinegar in the solution will be:

0.20x + 0.05(5 + x) = 0.10(5 + x)

Expanding the right side:

0.20x + 0.05 * 5  = 0.10 * 5 + 0.10x

Solving for x:

0.20x - 0.10x   = 0.10 * 5  -0.05 * 5

0.1x = 0.25
x = 2.5

So, Gena needs to add 2.5 liters of the 20% solution. Option B is correct.

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The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

1. Place the graduated pipet on a flat surface and make sure it is level

2. Draw the liquid up until the meniscus is level with the etched line that corresponds to the desired volume

3. Make sure the liquid is not touching the etched line above it

4. Observe the bottom of the meniscus and take the reading at the point where the liquid level is between the two etched lines

The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

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On solving the provided question, we can say that the equation foe the rectangle will be = 34 = 12 + 2W

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Perimeter of rectangle is = 2(L+W)

the equation foe the rectangle will be =

34 = 2(6.5 + W)

34 = 12 + 2W

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The probability that the battery will last for 52 months is approximately 0.928, or 92.8%.

To calculate the probability that a battery will last for 52 months, we need to find the z-score of 52 months, using the formula:

z = (x - μ) / σ

Plugging in the values, we get:

z = (52 - 42.5) / 6.5 = 1.384615

Next, we can use a z-table to find the probability that a battery will last more than 52 months.

In this case, the z-score is positive, so we look up the area to the right of 1.384615 in the z-table. The area to the right of 1.384615 is approximately 0.928.

Therefore, the probability that a battery will last for 52 months or more is approximately 0.928, or 92.8%.

So the answer to the question is: A) 92.8%

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The proportionate equation for each problems are:

Let's discuss each problem we have:

1. Liv earns $9.50 for every 2 bracelets she sells.

y = 4.75x

because y = kx, then:

y = $9.50

x = 2

4.75 --> constant of proportionality

--> price per unit of bracelet sold

2. John ran 3 miles in 25.5 minutes

y = 8.5x

y = 25.5 minutes

x = 3 miles

8.5 --> constant of proportionality

--> minuntes per miles

--> times per distance

3. Lincoln bought 3 bottles of energy drink for $4.50

y = kx

y = $4.50

x = 3

$4.50 = k (3)

k = $1.50 --> price of a bottle of energy drink

4.  Total cost of 4 hours renting a cotton candy machine is $72.

y = kx

y = $72

x = 4 hours

$72 = k(4)

k = $18 --> price of renting per hour

5. 7 cups of water are used to make 4 loaves of French bread.

y = kx

y = 7

x = 4

7 = k(4)

k = 7/4

Proportionate equation: y = 7/4 x

(x = 6)

y = 7/4 (6)

y = 21/2 = 10.5 cups of water

6. 6 3/4 yards of fabrics are used to make 3 elf costumes

y = kx

y = 6 3/4

x = 3

6 3/4 = k (3)

27/4 = 3k

--------------- x 4

27 = 12k

k = 9/4

Proportionate equation: y = 9/4 x

(x = 7)

y = 9/4 (7)

y = 63/4

y = 15 3/4 yards of fabric

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The domain and range of the ordered pair  {(-13, 9), (-7, -5), (5, 14). (11, -10)) is as follows:

domain = [-13, -7, 5, and 11]

range = {9, -5, 14 and -10}

The domain of a function is independent variable of a function. The domain is the input value of the function. The domain lies on the x axis of the function.

Therefore, the domain of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) is [-13, -7, 5, and 11]

The range is the dependent value of the function. The range is also called the output value of the function. The range lies on the y-axis of the function.

Therefore, the range of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) are {9, -5, 14 and -10}

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Substance Gallons         % Fruit Juice

Drink A              x                         20%

Drink B              y                          5%

Total         x + y = 30                  10%

To find the number of gallons of Drink A and Drink B that should be used, we can write two equations based on the percentage of fruit juice.

20% * x = 10% * (x + y)

5% * y = 10% * (x + y)

Simplifying and solving for x and y:

x = 1.5 * y

10% * (x + y) = 10% * 30

y = 15

x = 1.5 * 15 = 22.5

So, we would use 22.5 gallons of Drink A and 15 gallons of Drink B to make a 30 gallon mixture that is 10% fruit juice.

The number of batches of soup that Fabian can make is given as follows:

3 batches.

The number of batches of soup is obtained applying the proportions in the context of the problem.

He has 10 pounds, and sets aside 2.8 pounds of tomatoes to make spaghetti sauce, hence the amount remaining for soup is given as follows:

10 - 2.8 = 7.2 pounds.

He needs 2 and 2/5 = 2 + 0.4 = 2.4 pounds for each batch, hence the number of batches is obtained as follows:

7.2/2.4 = 3.

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The limit does not exist as x approaches 8 for (√(12−x) − 2)/ (√(24−x) − 4).

Therefore the answer is dne.

The square root of 12 - x approaches 2 as x approaches 8 and the square root of 24 - x approaches 4 as x approaches 8.

The limit fails to exist because both the numerator and the denominator approach 0 as x approaches 8, but the ratio of the two approaches positive infinity. This shows that the limit is undefined or "dne".

As both the numerator and denominator approach 0, the fraction they form can approach any real number or it can oscillate between two values, leading to an undefined limit. In such cases, the limit fails to exist.

--The question is not readable, answering to the question below--

"evaluate the limit, if it exists. (if an answer does not exist, enter dne.)

lim x → 8 (√(12−x) − 2)/ (√(24−x) − 4)"

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So, if Octavio scores 10 points higher than the class mean on the midterm, we may anticipate that he will score final = a + b * (x + 10) points higher on the final.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Given the regression equation for predicting final-exam score from midterm-exam score:

final = a + b * midterm

where a and b are the regression coefficients, we can use the class mean midterm score x as a reference point to predict the final exam score for a student who scored 10 points above the class mean on the midterm.

First, we need to find the class mean midterm score, which can be represented as x:

x = mean(midterm_scores)

Next, we find the predicted final exam score for the class mean midterm score:

final = a + b * x

Finally, we find the predicted final exam score for a student who scored 10 points above the class mean midterm score:

final = a + b * (x + 10)

So, if Octavio scores 10 points above the class mean on the midterm, we can predict that he will score final = a + b * (x + 10) points above the class mean on the final.

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Answer:

The point you would plot would be at -1/2

Explanation:

3/4 - 1 1/4 = -1/2

The slope of the line is zero because the line is parallel to the x-axis.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is zero because the line is parallel to the x-axis. Then the equation is given as,

y = - 2

The slope of the line is zero because the line is parallel to the x-axis.

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Answer:

$5,250 ≤ m ≤ $6,125

Step-by-step explanation:

A compound inequality is a mathematical statement that combines two inequality statements using "and" or "or". In this case, the compound inequality represents the range of possible monthly salary for an entry-level mechanical engineer in Texas.

The average salary for this position ranges from $63,000 to $73,500 per year. To find the monthly salary, we need to divide these amounts by 12 months, which gives us the minimum and maximum monthly salary:

$63,000/12 = $5,250

$73,500/12 = $6,125

Therefore, the compound inequality is:

$5,250 ≤ m ≤ $6,125

This means that the monthly salary of an entry-level mechanical engineer in Texas could be anywhere between $5,250 and $6,125.

Zero is the magnitude of the electric field inside the conducting shell, at a radial distance r where a < r < b.

Each point in space has an electric field associated with it when there is charge existing in any form. E, often known as electric field strength, electric field intensity, or just the electric field, is a mathematical constant that expresses the strength and direction of an electric field.

The electromagnetic region which surround electrically charged particles and acts to either attract or repel all those other positive ions in the field is known as an electric field (or E-field). A systems of charged particles' physical field is also referred to in this phrase.

By applying Gauss law, to the sphere of radius r with dotted lines:

∅(E) = ∫E. dA

∅(E) = E (4πr²) = Q/∈₀

E₁ = Q/4πr²∈₀

The electric field in a conductor is zero. a < r < b has an r value in the conductor.

E₂ = 0

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The probability of randomly selecting a pop CD is 15/74.

Probability is a measure of the likelihood of a certain event occurring, expressed as a number between 0 and 1.

An event with a probability of 1 is considered certain to occur, while an event with a probability of 0 is considered impossible. Events with probabilities between 0 and 1 are considered uncertain, with higher probabilities indicating greater likelihood of occurrence.

Probability is a mathematical concept that represents the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur. The calculation of probability involves using rules of probability theory and statistical analysis to determine the chance of a specific outcome or set of outcomes.

There are various methods for calculating probability, including classical probability, empirical probability, and subjective probability.

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The probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.

The probability that the digit 7 doesn't appear among 100 digits where each digit is one of (0-9) and all sequences are equally likely is given by the probability that all 100 digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 8, 9}. There are 10 choices for each digit, so there are 10^100 possible sequences of 100 digits. The number of sequences that don't contain the digit 7 is 9^100. Therefore, the probability that the digit 7 doesn't appear among 100 digits is: P(7 doesn't appear) = (9^100) / (10^100) = 9 / 10

Therefore, the probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.

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Saturn has the densest crown based on Gizmo densities, with a density of 687 kg/m³.

The density of an item is calculated theoretically as its mass divided by its volume.

The weight of an object is defined as its mass. The volume of a thing is the amount of space that the object or substance takes up.

As a result, density refers to the ratio or numerical connection between an object's mass and the quantity of space it occupies.

Saturn is the densest planet in terms of both mass and volume. Saturn is denser than a rock, quarter, cruise ship, or beach ball, according to what we can see from the Gizmos.

See the table below for their densities.

Objects     Relative Density

Rock                2.6g/cc³

Cruise Ship     9.0g/cm³

Quarter           8.9 g/ml³

Saturn            687 kg/m³

Beach ball       10 g/cc³

Thus, we selected Saturn as the Gizmo with the densest crown.

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The probability for getting the different numbers when two dice are thrown is: 5/6.

The sample space formed by rolling two dice are: 6*6 = 36.

Total number of pairs having same number = (1,1), (2,2),(3,3),(4,4),(5,5),(6,6) = 6 samples.

Thus,

Number of outcomes having different numbers:

36 - 6 = 30

Probability (different numbers) = total number of different number / total outcomes.

Probability (different numbers) = 30 / 36

Probability (different numbers) = 5/6

Thus, the probability for getting the different numbers when two dice are thrown is: 5/6.

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Answer:

I think its A even function

Step-by-step explanation:

To find f ( -4 ) - f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. Now that we have both values we can subtract them to get the answer of -67.

a.) f ( -4 ) = 3 ( -4 )2 - 4 ( -4 ) - 5 = -47  f ( 3 ) = 3 ( 3 )2 - 4 ( 3 ) - 5 = 20  f ( -4 ) f ( 3 ) = -47 ( 20 ) = -940

b.) f ( -4 ) - f ( 3 ) = -47 - 20 = -67

a.) To find f ( -4 ) f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. This gives us -47. To evaluate f ( 3 ) we plug 3 into the function and simplify. This gives us 20. Now that we have both values we can multiply them together to get the answer of -940.

b.) To find f ( -4 ) - f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. This gives us -47. To evaluate f ( 3 ) we plug 3 into the function and simplify. This gives us 20. Now that we have both values we can subtract them to get the answer of -67.

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Probability that more than 10 adults in the sample have hypertension is 0.768

Var(X) = 5.25

The probability that more than 10 adults in the sample have hypertension is 0.6086

The National and Nutrition survey reported that 30% of adults in the U. S have hypertension (high blood pressure). Let X be the number of adults in the U. S with hypertension.

A sample of 25 adults is studied:

Calculate the following probabilities using R guro and then fill in the blanks with your answers.

a) The probability that 12 or fewer adults in the sample have hypertension is  . Round your answers to three decimal places.

b) The probability that more than 10 adults in the sample have hypertension is  . Round your answers to three decimal places.

c) Calculate the Var(X)=n ∗p∗(1−p) = . Round the answer to the nearest whole number.

The National and Nutrition survey reported that 30% of adults in the U. S have hypertension

A sample of 25 adults is studied

therefore X = 25

adults in the U. S have hypertension = 30% of 25

                                                              = 7.5

a) the probability that 12 or fewer adults in the sample have hypertension is

Let X: Number of adults that were told they have hypertension.

The scenario here follows the Binomial distribution since trials are independent and the probability of success( i .e having hypertension) is equal from trial to trial.

X~ Binomial(n=12, p =0.30)

Required probability,

P(X≥2)=1−P(X=0)−P(X=1)

=1−( 12                                              ( 12

       0 )0.30^ 0(1−0.30) ^(12−0) −      1)0.30^ 1(1−0.30) ^(12−1)

=1−0.1660−0.0652

=0.768

b) the probability that more than 10 adults in the sample have hypertension is

Let X: Number of adults that were told they have hypertension.

The scenario here follows the Binomial distribution since trials are independent and the probability of success( i .e having hypertension) is equal from trial to trial.

X~ Binomial(n=10, p =0.30)

Required probability,

P(X≥2)=1−P(X=0)−P(X=1)

=1−( 10                                              ( 10

       0 )0.30^ 0(1−0.30) ^(10−0) −      1)0.30^ 1(1−0.30) ^(10−1)

=1−0.2824−0.1089

=0.6086

​c) Calculate the Var(X)=n ∗p∗(1−p)

n= 25

p=0.30

Var(X)=n ∗p∗(1−p)

         = 25*0.30*(1-0.30)

         =5.25

Probability that more than 10 adults in the sample have hypertension is 0.768

Var(X) = 5.25

The probability that more than 10 adults in the sample have hypertension is 0.6086

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Probability that more than 10 adults in the sample have hypertension is 0.768

Var(X) = 5.25

The probability that more than 10 adults in the sample have hypertension is 0.6086

The National and Nutrition survey reported that 30% of adults in the U. S have hypertension (high blood pressure). Let X be the number of adults in the U. S with hypertension.

A sample of 25 adults is studied:

Calculate the following probabilities using R guro and then fill in the blanks with your answers.

a) The probability that 12 or fewer adults in the sample have hypertension is  . Round your answers to three decimal places.

b) The probability that more than 10 adults in the sample have hypertension is  . Round your answers to three decimal places.

c) Calculate the Var(X)=n ∗p∗(1−p) = . Round the answer to the nearest whole number.

The National and Nutrition survey reported that 30% of adults in the U. S have hypertension

A sample of 25 adults is studied

therefore X = 25

adults in the U. S have hypertension = 30% of 25

                                                             = 7.5

a) the probability that 12 or fewer adults in the sample have hypertension is

Let X: Number of adults that were told they have hypertension.

The scenario here follows the Binomial distribution since trials are independent and the probability of success( i .e having hypertension) is equal from trial to trial.

X~ Binomial(n=12, p =0.30)

Required probability,

P(X≥2)=1−P(X=0)−P(X=1)

=1−( 12                                              ( 12

      0 )0.30^ 0(1−0.30) ^(12−0) −      1)0.30^ 1(1−0.30) ^(12−1)

=1−0.1660−0.0652

=0.768

b) the probability that more than 10 adults in the sample have hypertension is

Let X: Number of adults that were told they have hypertension.

The scenario here follows the Binomial distribution since trials are independent and the probability of success( i .e having hypertension) is equal from trial to trial.

X~ Binomial(n=10, p =0.30)

Required probability,

P(X≥2)=1−P(X=0)−P(X=1)

=1−( 10                                              ( 10

      0 )0.30^ 0(1−0.30) ^(10−0) −      1)0.30^ 1(1−0.30) ^(10−1)

=1−0.2824−0.1089

=0.6086

​c) Calculate the Var(X)=n ∗p∗(1−p)

n= 25

p=0.30

Var(X)=n ∗p∗(1−p)

        = 25*0.30*(1-0.30)

        =5.25

Probability that more than 10 adults in the sample have hypertension is 0.768

Var(X) = 5.25

The probability that more than 10 adults in the sample have hypertension is 0.6086

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The two possible locations for the fourth vertex of the parallelogram are p and q.

The fourth vertex of a parallelogram can be obtained by adding the vector difference between two of its vertices to the third vertex. In this case, the vector difference between two vertices can be found by subtracting one vertex from the other, i.e. p-o and q-o. So, the fourth vertex can be found by adding either of these vectors to vertex o, i.e. r = p - o + o = p or r = q - o + o = q.

Therefore, the two possible locations for the fourth vertex of the parallelogram are p and q.

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Answer:

False. The two sides evaluate to different numbers.

Step-by-step explanation:

Let's evaluate each side:

4 × (3 + 5) - 10 = 4 × 8 - 10 = 32 - 10 = 22

4 × 3 + 5 - 10 = 12 + 5 - 10 = 17 - 10 = 7

Answer:

Step-by-step explanation:

-4

Work Shown:

[tex]a_1 = -1 = \text{ first term} \\\\d = 0.5 = \text{ common difference} \\\\a_n = a_1 + d(n-1)\\\\a_n = -1 + 0.5(n-1)\\\\a_6 = -1 + 0.5(6-1)\\\\a_6 = -1 + 0.5(5)\\\\a_6 = -1 + 2.5\\\\a_6 = 1.5\\\\[/tex]

3/4 and 5 18 is fraction have a leat common denominator of 36.

3/4 and 5 18 is fraction have a leat common denominator of 36.

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The value of the sample variance rounded to one decimal place is 76.0.

What is the Mean?

The mean is a measure of the central tendency of a set of data, calculated as the sum of the values divided by the number of values in the set.

The sample variance of a set of data is a measure of the spread or dispersion of the data around the mean. To calculate the sample variance, you can follow these steps:

Calculate the mean of the data: First, find the sum of all the data points and divide by the number of data points (n).

For the given data, the mean is: (-11 + -5 + -5 + -11 + 13 + -11 + -5) / 7 = -7

Subtract the mean from each data point: Next, subtract the mean from each data point to get the deviations from the mean.

For the given data, the deviations are: (-11 - -7) = -4, (-5 - -7) = 2, (-5 - -7) = 2, (-11 - -7) = -4, (13 - -7) = 20, (-11 - -7) = -4, (-5 - -7) = 2

Square the deviations: Square each deviation to get rid of negative values.

For the given data, the squared deviations are: (-4)^2 = 16, (2)^2 = 4, (2)^2 = 4, (-4)^2 = 16, (20)^2 = 400, (-4)^2 = 16, (2)^2 = 4

Sum the squared deviations: Sum all the squared deviations.

For the given data, the sum of the squared deviations is: 16 + 4 + 4 + 16 + 400 + 16 + 4 = 456

Divide the sum by n - 1: Finally, divide the sum of the squared deviations by the number of data points minus 1 (n - 1). This gives us the sample variance.

For the given data, the sample variance is: 456 / (7 - 1) = 456 / 6 = 76

Hence, the value of the sample variance rounded to one decimal place is 76.0.

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The Probability that only one of John's pot crack while being fired is 0.06.

The probability that only one of John's pots cracks while being fired can be calculated using the formula for the binomial distribution:

P(X = 1) = C(2, 1) * (0.03)^1 * (1 - 0.03)^(2 - 1)

= 2 * 0.03 * 0.97

= 0.0582

Where C(2, 1) is the number of combinations of 2 items taken 1 at a time, and (0.03)^1 and (1 - 0.03)^(2 - 1) are the probabilities of the first pot cracking and the second pot not cracking, respectively.

So, the probability that only one of John's pots cracks while being fired is approximately 0.06.

To learn more about Probability.

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