one side of a triangle is 5 and the altitude to that side is 12. another side of the triangle is 13. can you tell what the length of the altitude to that side of the triangle is? if not, why not? if so, show what it is.

To Prove :

[tex] \sf \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} = \tan54\degree \\ \\ [/tex]

[tex] \sf LHS = \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} \\ \\ [/tex]

[tex] \sf RHS = \tan54\degree \\ \\ [/tex]

Solving for LHS :

Divide numerator and denominator by cos9°

[tex]\longrightarrow \: \: \sf\dfrac { \dfrac{ \cos9\degree}{ \cos9\degree} + { \dfrac{\sin9}{ \cos9} }}{ \dfrac{ \cos9\degree }{ \cos9\degree} - { \dfrac{ \sin9\degree}{ \cos9\degree}}} \\ \\ [/tex]

[tex] \longrightarrow \: \: \sf\dfrac{1 + { \dfrac {\sin9\degree}{ \cos9\degree}} }{1 - { \dfrac{ \sin9\degree}{ \cos9\degree} }} \\ \\ [/tex]

[tex]\longrightarrow \: \: \sf \dfrac{1 + \tan9\degree}{1 - \tan9\degree} \\ \\ [/tex]

[tex]\longrightarrow \: \: \sf{ \dfrac{ \tan45 \degree + \tan9\degree}{1 - \tan45 \degree \tan9 \degree}} \: \: \: \: \: \: \: \sf \red{\bigg( \tan(A + B) = \dfrac{ \tan A + \tan B}{1 - \tan A \tan B} \bigg)} \\ \\ [/tex]

[tex]\longrightarrow \: \: \sf \tan(45\degree + 9\degree) \\ \\ [/tex]

[tex]\longrightarrow \: \: \sf \tan54 \degree[/tex]

LHS = RHS

The length of the base of a parallelogram is 30 feet and the height is 40 feet.

Given that the height of a parallelogram is 10 feet more than the length of the base, and the area of the parallelogram is 1200 square feet. We have to find the length of the base and the height. Let the length of the base of a parallelogram be x. Then, the height of the parallelogram = x + 10.

We know that the area of a parallelogram is given by; A = base × height1200 = x(x + 10). Simplify the equation1200 = x² + 10x. Rearrange the equationx² + 10x - 1200 = 0. On solving this quadratic equation, we get; x = 30 and x = -40.

Since the length of the base cannot be negative, therefore, the length of the base is 30 feet. So, the height of the parallelogram is 30 + 10 = 40 feet. Therefore, the length of the base of a parallelogram is 30 feet and the height is 40 feet.

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Considering they left at precise noon, at 12:45 they will be 9 miles apart after they leave the intersection.

Let's call the time it takes for them to be 9 miles apart "t". During this time, the truck will have traveled a distance of 30t, and the car will have traveled a distance of 42t. Since they are traveling in the same direction, we can subtract the distances to find the distance between them:

42t - 30t = 12t

So they are separating at a rate of 12 miles per hour.

To find when they will be 9 miles apart, we can set up the equation:

12t = 9

Solving for t:

t = 9/12

t = 0.75 hours,

To convert 0.75 hours into minutes, we have to multiply it by 60.

= 0.75 × 60

= 45 minutes

So they will be 9 miles apart 45 minutes after they leave the intersection, or at 12:45pm.

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Using the given values, the values of the expression and equations are:

25. -0.8

28. S ≈ 137.22

29. V ≈ 50.94

From the question, we are to evaluate each of the expressions for the given values

25.

[-b + √(b² -4ac)]/2a

a = 2, b = 8, c = 5

Substituting the values into the expression

[-b + √(b² -4ac)]/2a

= [-8 + √((8)² - 4(2)(5))]/2(2)

= [-8 + √(64 - 40)]/4

= [-8 + √(24)]/4

= [-8 + 2√6]/4

= -2 + 1/2(√6)

= -0.775

≈ -0.8

28.

S = 2πrh + 2πr²

r = 2.3, h = 7.1 (Take π = 3.14)

Thus,

S = 2(3.14)(2.3)(7.2) + 2(3.14)(2.3)²

S = 103.9968 + 33.2212

S = 137.218

S ≈ 137.22

29.

V = 4/3 πr³

r = 2.3(Take π = 3.14)

V = 4/3 × 3.14 × (2.3)³

V = 50.939

V ≈ 50.94

Hence, the value of V is 50.94

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there are 30 different monograms possible, based on the given choices.

A monogram is a design that uses the initials of a person's name, usually in an artistic or decorative way. In the case of school class rings, the monogram is often engraved onto the surface of the ring. The monogram typically consists of the student's initials, with the first initial on the left, the middle initial (if applicable) in the centre, and the last initial on the right.

In this problem, we are given that there are two sizes of initials (presumably a larger size for the first and last initials, and a smaller size for the middle initial), five different type styles (i.e., different ways the letters can be designed), and three different border styles (i.e., different decorative borders around the monogram).

To calculate the total number of possible monograms, we need to multiply the number of choices for each category. This is known as the multiplication principle of counting.

So, we start by considering the number of choices for the initial sizes. We are given that there are two sizes, so there are two choices. Next, we consider the number of choices for the type styles. We are given that there are five different type styles, so there are five choices. Finally, we consider the number of choices for the border styles. We are given that there are three different border styles, so there are three choices.

To get the total number of possible monograms, we multiply the number of choices for each category together. So we get:

2 (initial sizes) x 5 (type styles) x 3 (border styles) = 30

Therefore, there are 30 different monograms possible, based on the given choices.
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Therefore, the average velocity of the person over the interval 0 ≤ t ≤ 12 can be calculated as follows:Average Velocity = Total distance travelled / Total time taken= 6.6 / 12= 0.55 m/s.

In the given question, we need to find the average velocity of a person running in a straight line across a field, given differentiable function v(t) on the interval [0,12]. Therefore, to calculate the average velocity of a person, we use the following formula:Average Velocity = Total distance travelled / Total time takenWe have a graph with the velocity of the person, which is a differentiable function v(t) given above on the interval 0 ≤ t ≤ 12.

We need to find the distance travelled by the person. Therefore, we use the following formula:Distance travelled = ∫v(t)dt From the given graph, the velocity of the person is zero when t = 0 and when t = 5. Similarly, the velocity of the person is 0 when t = 10 and when t = 12.So, we have to calculate the distance travelled from 0 to 5, from 5 to 10, and from 10 to 12 to determine the total distance travelled by the person over the given interval .Distance travelled from 0 to 5 can be calculated as follows :

Distance travelled from 0 to 5 = ∫v(t)dt from [tex]0 to 5= 5 x 0.6 = 3[/tex]Distance travelled from 5 to 10 can be calculated as follows :Distance travelled from 5 to 10 = [tex]∫v(t)dt[/tex] from [tex]5 to 10= 5 x 0.4 = 2[/tex]

Distance travelled from 10 to 12 can be calculated as follows: Distance travelled from 10 to 12 = ∫v(t)dt from 10 to 12= 2 x 0.8 = 1.6Total distance travelled = Distance travelled from 0 to 5 + Distance travelled from 5 to 10 + Distance travelled from 10 to [tex]12= 3 + 2 + 1.6= 6.6[/tex]

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Answer:

6.3cm

Step-by-step explanation:

73/5 = 92/x

cross multiply to get: 73x=460

divide both sides by 73

x=6.3

The empirical rule states that approximately 95% of the population lies within 2 standard deviations of the mean for a normal distribution, but you found that the z-scores that mark off the middle 95% of the standard normal distribution are -1.96 and 1.96. This does not represent a contradiction, and I will explain why is it so ?

The empirical rule, also known as the 68-95-99.7 rule, is a useful guideline to help us understand the proportions of data in a normal distribution. According to this rule, about 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. However, it is essential to note that the empirical rule is a simplified approximation.

On the other hand, the z-scores that you calculated, -1.96 and 1.96, are more precise values based on the actual standard normal distribution. These values come from a more accurate calculation using the cumulative distribution function (CDF) of the normal distribution, which gives the exact probability for any given range of z-scores.

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The two variables are said to have a correlation.

Correlation is a statistical measure of the relationship between two variables. When two variables are correlated, changes in one will be associated with changes in the other. For example, as the temperature increases, ice cream sales will also increase.

The correlation coefficient is a measure of the strength of the relationship between two variables. If the coefficient is close to +1, there is a strong positive correlation.

This means that as one variable increases, the other also increases. If the coefficient is close to -1, there is a strong negative correlation. This means that as one variable increases, the other decreases. If the coefficient is close to zero, the variables are said to have no correlation.

Correlation does not necessarily imply causation. It only indicates that two variables are related and does not necessarily explain why.

For example, two variables can be correlated because of a third variable. Therefore, correlation does not always indicate a causal relationship between two variables.

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Answer:

Eighty biscuits.

Step-by-step explanation:

We need to find the limiting factor. We can do that by comparing ratio of mass of ingredient given to mass of ingredient needed for 20 biscuits

[tex]Butter:\\800:150\\=16:3\\=5.33\\Sugar:\\700:75=28:3\\=9.33\\Flour:\\1000:180\\=50:9\\=5.56\\Chocolate Chips:200:50\\=4:1\\=4\\[/tex]

We can clearly see that the choco. chips are the limiting factor since it has the lowest ratio, basically meaning we will run out of choco chips before anything else.

[tex]Biscuits=4*20=80[/tex]

Since we only have 4 times the choco chips needed to make 20 biscuits, we can only make 80 biscuits. Now you can see, we have other ingredients left, but choco chips have ran out which is why it was the limiting factor.

[tex]Flour:\\1000-4(180) = 280g[/tex]

After making 4 servings we still have 280g of flour left.

Answer:

12 and 78

Step-by-step explanation:

x + 2x+54 = 90 2x+54=2(12)+54

24+54

78

3x + 54 = 90

3x = 36

x=12

12 and 78

1. A proof is a step-by-step Argument/Explanation.

2. Informal proofs in this class are written in English language.

3. Formal proofs that we will soon learn are written in Fitch notation language.

4. Informal proofs should start with the word given and end with the word therefore.

1. A proof is used to show that a statement is true or that a given statement follows logically from given assumptions. A proof can be used to prove a theorem, corollary, or lemma, or to solve an equation.

2. Informal proofs in this class are written in English in order to make them easier to understand. The proof should explain the reasoning behind each step and provide clear evidence that the conclusion is valid.

3. Formal proofs that we will soon learn are written in Fitch notation language, which is a language used to represent logical proof structures. Fitch notation consists of lines of logical statements, linked together with arrows that indicate the structure of the proof.

4. Informal type of proof is often used in mathematics as it does not require a formal proof. It is used to explain why a certain statement is true. It usually involves making an assumption and then deriving a logical conclusion from that assumption.

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The complete question is:

1. A proof is a step-by-step ____________ . (Write one word; two possible correct answers.)

2. Informal proofs in this class are written in which language?

3. Formal proofs that we will soon learn are written in which language? _____________

4. Informal proofs should start with the word ______________ and end with the word _________________ .

The solution to the inequality 2sin(2x+π/3)≥√3 is:

x ∈ [-π/6, π/3]

What is inequality?

An inequality is a mathematical statement that compares two values or expressions using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to). Inequalities are used to express relationships between quantities that are not necessarily equal.

To solve the inequality 2sin(2x+π/3)≥√3, we can follow these steps:

Step 1: Subtract π/3 from both sides to get rid of the constant term on the right-hand side:

2sin(2x+π/3) - π/3 ≥ √3 - π/3

Step 2: Divide both sides by 2 to isolate sin(2x+π/3):

sin(2x+π/3) ≥ (√3 - π/3)/2

Step 3: Use the fact that sin(x) is positive in the first and second quadrants of the unit circle to find the interval of x that satisfies the inequality. To do this, we need to find the angles α and β such that sin(α) = (√3 - π/3)/2 and sin(β) = - (√3 + π/3)/2. Then, the solution interval will be:

α/2 - π/6 ≤ x ≤ β/2 + π/6

To find α and β, we can use the inverse sine function on a calculator or look them up in a table. We get:

α ≈ 0.4636 radians

β ≈ 2.6779 radians

Substituting these values into the solution interval, we get:

0.2318 - π/6 ≤ x ≤ 1.3389 + π/6

Simplifying, we get:

-π/6 ≤ x ≤ π/3

Therefore, the solution to the inequality 2sin(2x+π/3)≥√3 is:

x ∈ [-π/6, π/3]

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The prime factors or the prime numbers whose product is 51 are 3 and 17.

What is the operation of prime numbers?

The operation of prime numbers refers to the various mathematical operations that can be performed using prime numbers. Prime numbers are positive integers that have exactly two divisors, 1 and the number itself. Some of the important operations involving prime numbers include:

Now,

If you meant to ask for the prime factors of 51, then they are 3 and 17.

because 51 is divisible by 3 because 5+1=6

and after dividing 51/3=17 which is also a prime number.

Hence,

            the prime factors of 51 are 3 and 17.

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Answer:

Point I and Point II may not need to be main points.

Ann's main points are not balanced.

Parallel structure will not work with Ann's speech topic.

Step-by-step explanation:

This division indicates that Ann prioritized Point III above Points I and II. Point III was allocated the most of Ann's time (75%), while Point I and II were each given 10% and 15%, respectively. This is a sign that Ann placed a higher priority on Point III.

In terms of the actual percentages, this could indicate a variety of things. It could mean that Ann felt Point III was more important than the other two points, or that Point III took more time to complete than the other two points. It could also mean that Ann was trying to achieve a specific ratio of her time dedicated to each point.
Regardless of the reasoning, this division of Ann's time shows that she placed a higher priority on Point III. This could mean that Point III was more important to her overall goal than the other two points, or that Point III required a larger amount of her time.

By understanding this division of Ann's time, we can gain insight into what she felt was important, and how she chose to prioritize her time. This can be used to better understand Ann's thought process and her overall goal.

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Answer: 12

Step-by-step explanation: if you take the number 64 and devide it by 8 you get 8. then add 4 to eight and you get twelve

Answer: 14x + 10

Step-by-step explanation: The perimeter of the room without the door can be found by adding up the lengths of all four sides:

Perimeter = 2(4x-1) + 2(3x+6)

Simplifying and combining like terms, we get:

Perimeter = 14x + 10

Therefore, the perimeter of the room without the door in simplest form is 14x + 10.

Answer:

We can begin by simplifying each equation:

A. 52 = 8n + 4 can be rewritten as 48 = 8n or 6 = n

B. 4(2n + 1) = 52 can be simplified to 8n + 4 = 52 or 8n = 48 or 6 = n

C. 4=52-8n can be rewritten as 8n = 48 or 6 = n

D. 4n = 48 can be simplified to n = 12

Therefore, equations A, B, and C are equivalent, and equation D is not equivalent to the others.

So, the correct answers are A, B, and C.

Answer:

Step-by-step explanation:first you have to multiply then divide then add then subtract and then substitute and then you will get the answer.

Answer:

(5,2)

Step-by-step explanation:

Let's solve your system by substitution.

[tex]x+y=7{\text{ ; }}x=y+3[/tex]

Step 2: let Solve [tex]$x+y=7$[/tex] for[tex]$x$[/tex]

[tex]x+y=7[/tex]

[tex]x+y +(-x)=7+(-x)[/tex] (Add (-x) on both sides)

[tex]y=-x+7[/tex]

0+(x)=7-x-y+(x)   (Add (x) on both sides)

x = -y + 7

x/1 = -y+7/1  (divide through by 1)

x = -y + 7

Substitute -y+7 for x in x = y + 3, then solve for u

(-y + 7) = y + 3

-y + 7 = y + 3 (simplify)

-y+7+(-7) = y + 3 + (-7)    (Add (-7) on both sides)

-y=y-4

-y = y-4 (simplify)

-y+(-y)=y-4+(-y)  (Add (-y) on both sides)

-2y-=-4

-2y/-2 = -4/-2  (Divide through by -2)

y = 2

Substitute in 2 for y in x = -y + 7

x =  -y+7

x = -2+7

x = 5

Answer:

x = 5 and y = 2

After answering the provided question, we can conclude that You can expression run this code several times to simulate the winner receiving different prizes at random.

In mathematics, an expression is a group of representations, digits, and conglomerates that resemble a statistical correlation or regimen. An expression can be a real number, a mutable, or a combination of the two. Addition, subtraction, rapid spread, division, and exponentiation are examples of mathematical operators. Arithmetic, mathematics, and shape all make extensive use of expressions. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

To simulate the winner receiving a prize at random, use a random number generator to generate a number between 1 and 5, with each number representing a prize. Here's some Python code to help you out:

# create a list of prizes

prizes = ['prize A', 'prize B', 'prize C', 'prize D', 'prize E']

# simulate the winner being given a prize

winner_prize = random.choice(prizes)

print('The winner has been given', winner_prize)

In this case, the random.choice() function chooses one prize at random from a list of prizes and assigns it to the winner prize variable. The code's output will be a message displaying the prize awarded to the winner. You can run this code several times to simulate the winner receiving different prizes at random.

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Answer:

If you want to decrease 144 in the ratio of 4:3, you can do so by first finding the difference between the two parts of the ratio (4-3=1) and then dividing 144 by this difference (144/1=144). This gives you the value of one part of the ratio. You can then multiply this value by 3 to find how much you need to decrease 144 by: 144 * 3 = 432. So if you decrease 144 by 432, it will be in the ratio of 4:3.

Step-by-step explanation:

The aquarium tank that holds 190 liters of water equals to 50.15 gallons. Therefore, the answer to the given problem is 50.15 gallons.

Conversion factors are the ratios that describe the numerical relationship between two units of measurement.

The conversion factor of liters to gallons is 1 gallon is 3.8 liters.

Therefore, by multiplying the given value of liters by the conversion factor of liters to gallons, we can convert liters to gallons.

190 liters x 1 gallon/3.8 liters = 50.15 gallons

Thus, the aquarium tank that holds 190 liters of water equals to 50.15 gallons.

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Answer:

no

Step-by-step explanation:

using Pythagorean theorem:

[tex]26^{2} +42^{2}=50^{2}[/tex]

676+1764=2500

2440=2500

2440<2500

Answer:no

Answer:

Step-by-step explanation:

Not sure.

The angle in question measures 60 degrees.

What are supplementary angles?

Supplementary angles are two angles that has sum of 180 degrees. In other words, if you have two angles that are next to each other, and when you add them together, they equal 180 degrees, then those angles are considered to be supplementary.

Let x be the measure of the angle in question.

The supplement of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. So, the supplement of x is 180 - x.

The problem tells us that the given angle (x) is 120 degrees less than its supplement (180 - x).

Therefore, we can set up the equation:

x = (180 - x) - 120

Simplifying this equation, we get:

x = 60

So, the angle in question measures 60 degrees.

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The probability of three or more goals being scored in an EPL match is approximately 0.522, or 52.2%.

To find the probability that three or more goals will be scored in a game, we need to calculate the cumulative probability of the Poisson distribution for x = 3, 4, 5, and so on, up to infinity. This can be written as:

P(X ≥ 3) = 1 - P(X < 3)

where X is the random variable representing the number of goals scored in a match.

To calculate P(X < 3), we can use the Poisson distribution formula:

[tex]P(X = x) = (e^{(-\lambda)} \times \lambda^x) / x![/tex]

where e is the mathematical constant approximately equal to 2.71828, and x! represents the factorial of x.

Using this formula, we can calculate the probabilities of scoring 0, 1, and 2 goals:

[tex]P(X = 0) = (e^{(-2.768)} \times 2.768^0) / 0! = 0.063\\\\P(X = 1) = (e^{(-2.768)} \times 2.768^1) / 1! = 0.174\\\\P(X = 2) = (e^{(-2.768)} \times 2.768^2) / 2! = 0.241[/tex]

To find P(X < 3), we add these probabilities:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.063 + 0.174 + 0.241 = 0.478

Finally, we can calculate the probability of scoring three or more goals using the formula we derived earlier:

P(X ≥ 3) = 1 - P(X < 3) = 1 - 0.478 = 0.522 or 52.2%

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Answer: k898

iiii

Step-by-step explanation:

k8ni7mrvnyrt

The probability that both marbles are red is 2/14 or 1/7.

This is because there are only two red marbles in the box, so the probability of the first being drawn is 2/14 (or 1/7). Since the first marble is not replaced, the probability of the second being drawn is also 2/14 (or 1/7). Mathematically, this can be expressed as: P(Both Red) = P(Red 1) x P(Red 2) = (2/14) x (2/14) = 1/7

In general, when dealing with probability questions involving drawing multiple objects from a box, the probability of drawing one object followed by another is calculated by multiplying the probability of drawing each individual object.

In the case of two marbles being drawn without replacement, the probability of both marbles being the same color is calculated by multiplying the probability of the first marble being of that color by the probability of the second marble being of that color.

The probability of the second marble being of the same color is lower than the probability of the first marble being of that color since it is drawn from a reduced set (the original set minus the first marble).

In this case, the probability of the second marble being of the same color as the first is 2/14, or 1/7. In conclusion, the probability of both marbles being red is 2/14, or 1/7.

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The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store, with both stores having the same price.

The difference between the two terms is that "difference" refers to the way in which two or more things are not the same, whereas "difference" is more of a comparison between two or more things.

The difference between the lowest price in store 1 and the lowest price in store 2 is the difference between the first digit of each store's key. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1.

The difference between the highest prices in store 1 and store 2 is the difference between the last digit of each store's key. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0.

The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1. This difference is reflected in the lowest prices of each store, with store 1 having a lower price than store 2.

The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0. This difference is reflected in the highest prices of each store, with both stores having the same price.

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Answer: To find the mean of this data set, we need to add up all the amounts of rainfall and divide by the number of weeks. From the line graph, we can estimate the following amounts of rainfall:

Week 1: 2 inches

Week 2: 3 inches

Week 3: 1 inch

Week 4: 3 inches

Week 5: 5 inches

Week 6: 4 inches

To calculate the mean, we need to add up these amounts and divide by 6 (the number of weeks):

(2 + 3 + 1 + 3 + 5 + 4) / 6

= 18 / 6

= 3

Therefore, the mean amount of rainfall in this data set is 3 inches. The answer is (B) 3.

Step-by-step explanation: