Verify Associative property: 2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5..

Please help tomorrow is my final exam ​

the sequence of transformations that produces R'S'T' from RST is translation 2 units to the right and 3 units down, followed by a rotation of 90 degrees clockwise, and finally a reflection across the x-axis.

A triangle is a polygon since it has a total of three faces along with three vertices. It belongs to the fundamental geometric shapes. Triangles having vertex positions alternating between A and B are referred to as triangles ABC. A unique plane and a triangle in Euclidean geometry appear when the three vertices are not collinear. Due to its three sides and three corners, triangles are considered polygons. The corners of a triangle are defined as the locations where its three sides meet. Three triangle angles are multiplied to get 180 degrees.

To transform triangle RST to R'S'T', we can use the following sequence of transformations:

Translation: Move the triangle 2 units to the right and 3 units down. This will result in triangle R''S''T'' with vertices (2, -3), (-2, 0), (-3, -2).

Rotation: Rotate triangle R''S''T'' 90 degrees clockwise about the origin. This will result in triangle R'''S'''T''' with vertices (3, 2), (0, 2), (2, 3).

Reflection: Reflect triangle R'''S'''T''' across the x-axis. This will result in triangle R'S'T' with vertices (3, -2), (0, -2), (2, -3).

Therefore, the sequence of transformations that produces R'S'T' from RST is translation 2 units to the right and 3 units down, followed by a rotation of 90 degrees clockwise, and finally a reflection across the x-axis.

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(16x)=4\implies 2^{\log_2(16x)}=2^4\implies 16x=2^4\implies x=\cfrac{2^4}{16}\implies x=1[/tex]

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as the goodness of fit test.

Option C is the correct answer.

We have,

A goodness of fit test is conducted to determine whether a hypothesized probability distribution for a population adequately fits or matches the observed data.

It compares the observed data to the expected distribution specified by the hypothesis and assesses whether there is sufficient evidence to reject the hypothesis.

This test is commonly used when testing the fit of categorical data to a specified distribution, such as testing whether the observed data follows a specific discrete probability distribution

(e.g., Poisson, binomial, multinomial) or whether the observed data matches the expected proportions in different categories.

The goodness of fit test evaluates the degree of discrepancy between the observed and expected frequencies or proportions and provides a statistical measure, such as the chi-squared test statistic, to assess the level of agreement or disagreement between the observed data and the hypothesized distribution.

Therefore,

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known

the goodness of fit test.

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If the probability of winning a game is 0.3, then the probability of losing a game is 0.7

Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of losing a game can be calculated as the complement of the probability of winning the game.

Since the probability of winning the game is 0.3, the probability of losing the game would be

Probability of losing = 1 - Probability of winning

Substitute the values in the equation

= 1 - 0.3

Subtract the numbers

= 0.7

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I have solved the question in general, as the given question is incomplete.

The complete question is:

If the probability of winning a game is 0.3, then what is the probability of losing it?

The function computes the test statistic for the relationship between total serum cholesterol and coronary heart disease, given a table with two columns: "totchol" and "anychd".

The function in Python that computes the test statistic:

import pandas as pd

import numpy as np

from scipy.stats import t

def compute_test_statistic(data):

   """

   Compute the test statistic for the relationship between total serum cholesterol and coronary heart disease.

   Parameters:

   -----------

   data: pandas.DataFrame

       A DataFrame with two columns: "totchol" (total serum cholesterol) and "anychd" (whether or not the person had coronary heart disease)

   Returns:

   --------

   float

       The test statistic

   """

   # Compute the mean total serum cholesterol for each group (with and without coronary heart disease)

   group_means = data.groupby("anychd").mean()["totchol"].values

   # Compute the standard deviation of the total serum cholesterol for each group

   group_std = data.groupby("anychd").std(ddof=1)["totchol"].values

   # Compute the sample size for each group

   group_n = data.groupby("anychd").count()["totchol"].values

   # Compute the pooled standard error

   pooled_se = np.sqrt(np.sum((group_n - 1) * group_std ** 2) / np.sum(group_n - 2))

   # Compute the t-value

   t_value = (group_means[1] - group_means[0]) / (pooled_se * np.sqrt(1/group_n[0] + 1/group_n[1]))

   # Compute the degrees of freedom

   df = np.sum(group_n) - 2

   # Compute the p-value (two-sided test)

   p_value = 2 * t.cdf(-np.abs(t_value), df)

   # Return the test statistic

   return t_value

This function assumes that the input table is in the form of a pandas DataFrame, with columns "totchol" and "anychd".

It uses the groupby method to split the data into two groups based on the "anychd" column, and then computes the mean, standard deviation, and sample size for each group. It then uses these values to compute the test statistic using the formula given in the prompt.

Finally, it uses the t.cdf function from the scipy.stats module to compute the p-value for a two-sided test.

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The Moon and Sun's gravitational pull on the waters of Earth is what causes tides.

The Moon and Sun's gravitational pull on the waters of Earth is what causes tides. The gravitational pull between any two objects is determined by both their masses and their separation from one another. Although having a far larger mass than the Moon, the Sun is located much distant from Earth. This indicates that the Moon's gravitational pull on the oceans of Earth is greater than that of the Sun.

The water on the side of the Earth that faces the Moon is drawn towards it by the Moon's gravitational attraction, creating a high tide. Another high tide results from simultaneous pulls on the opposite side of the Earth's water towards the Moon.

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The moon has a greater effect on Earth's tides than the sun because it is much closer to Earth.

Gravitational pull is the force by which a planet or other body draws objects toward its center. The force of gravity keeps all of the planets in orbit around the sun. It also keeps the moon in orbit around Earth.

The Moon and Earth exert a gravitational pull on each other. On Earth, the Moon's gravitational pull causes the oceans to bulge out on both the side closest to the Moon and the side farthest from the Moon. These bulges create high tides. The low points are where low tides occur.

The moon has a greater effect on Earth's tides than the sun because it is much closer to Earth. The gravitational force between two objects decreases as the distance between them increases, so the moon's gravitational pull on Earth's oceans is much stronger than the sun's. However, during certain times of the year, when the sun and moon are aligned, their combined gravitational pull can create especially high or low tides, known as spring tides.

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The statement that express 9(x + 7) is product of constant factors 9 and x + 7. The Option B.

The expression 9(x + 7) represents the product of constant factors 9 and x + 7. To evaluate the expression, you would distribute the 9 to both terms inside the parentheses, resulting in 9x + 63.

This expression can also be written as a 2-term factor of 9 and x + 7. It is important to understand the different terms and factors in an expression to simplify and solve equations.

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a. The dimensions that maximize the area of the pen are 33 meters by 100 meters.

b. The dimensions of each rectangular pen that minimize the amount of fence used are 10sqrt(2) meters by 10sqrt(2) meters.

a. To maximize the area of the rectangular pen, we need to find the dimensions that use up all 200 meters of fencing, except for the side that is against the barn. Let the length of the pen be x and the width be y. Then we have:

Perimeter of the pen = 2x + y = 200 - x (since one side is against the barn)

Simplifying this equation, we get:

3x + y = 200

Area of the pen = xy

Now we can express y in terms of x using the equation above:

y = 200 - 3x

Substituting this into the expression for area, we get:

A(x) = x(200 - 3x) = 200x - 3x^2

To maximize the area, we need to find the value of x that makes A(x) as large as possible. We can do this by taking the derivative of A(x) with respect to x and setting it equal to 0:

A'(x) = 200 - 6x

200 - 6x = 0

x = 33.33

Since we can't have a fractional length, we choose x = 33 meters (rounded to the nearest meter). Then y = 200 - 3x = 100 meters.

b. Let the dimensions of each rectangular pen be x and y. Then we have:

Area of each pen = xy = 100

Perimeter of each pen = 2x + 2y

We want to minimize the amount of fence used, which is equal to the total perimeter of all four pens. So, we need to find the dimensions that minimize the total perimeter subject to the constraint that the area of each pen is 100. We can use Lagrange multipliers to solve this problem:

L(x, y, λ) = 2x + 2y + λ(xy - 100)

Taking the partial derivatives with respect to x, y, and λ, we get:

∂L/∂x = 2 + λy = 0

∂L/∂y = 2 + λx = 0

∂L/∂λ = xy - 100 = 0

Solving these equations simultaneously, we get:

x = y = sqrt(200/λ)

xy = 100

Substituting the first equation into the second equation, we get:

sqrt(200/λ)^2 = 100

λ = 2

Substituting λ = 2 back into the first equation, we get:

x = y = sqrt(200/λ) = 10sqrt(2)

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Using quadratic formula, the dimensions for the rectangular garden is 12 feet by 25 feet

a- To represent this situation with a quadratic equation, we can start by letting "x" represent the width of the planter in feet. According to the problem, the length of the planter is twice as long as the width plus one foot. Therefore, the length can be represented by the expression "2x + 1".

The area of a rectangle is given by the formula A = l x w, where A is the area, l is the length, and w is the width. In this case, we know that the total area of the planter is 300ft^2. Therefore, we can write the following quadratic equation to represent the situation:

A = l x w

300 = (2x + 1) * x

300 = 2x^2 + x

2x² + x - 300 = 0

b- To find the dimensions of Mrs. Greenthumb's garden, we can solve the quadratic equation 2x² + x - 300 = 0 for "x". We can use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 2, b = 1, and c = -300. Therefore, we can plug these values into the quadratic formula and simplify to find the solutions:

x = (-1 ± √(1^2 - 4(2)(-300))) / 2(2)

x = (-1 ± √(1 + 2400)) / 4

x = (-1 ± √(2401)) / 4

We can simplify this expression further by noting that sqrt(2401) = 49. Therefore:

x = (-1 ± 49) / 4

The two solutions are:

x = 12 or x = -25/2

Since the width of the planter cannot be negative, we can discard the solution x = -25/2. Therefore, the width of the planter is x = 12 feet.

To find the length, we can use the expression for the length we found earlier: 2x + 1. Plugging in x = 12, we get:

length = 2x + 1 = 2(12) + 1 = 25

Therefore, the dimensions of Mrs. Greenthumb's garden are 12 feet by 25 feet.

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Answer:

0.0003

Step-by-step explanation:

u don't count the zeros as a significant figure

5 rounds 2 up to 3

Applying the right triangle altitude theorem and the leg rule, we have:

5. x = 6; y ≈ 6.7; z ≈ 13.4       6. x = 32; y ≈ 35.8; z ≈ 17.9

The right triangle altitude theorem states that the altitude drawn on the hypotenuse of a right triangle is equal to the geometric mean of the two line segments into which the altitude divides the hypotenuse.

5. To find x, apply the right triangle altitude theorem, which is:

x = √(3*12)

x = √36

x = 6

Using the leg rule, we can find y and z. It is expressed as:

hypotenuse/leg = leg/part

Therefore, substitute and find y:

(3 + 12) / y = y / 3

Cross multiply:

y² = 15 * 3

y = √45

y ≈ 6.7

Find z using the leg rule:

15/z = z/12

z² = 180

z = √180

z ≈ 13.4

6. Use the same theorem and leg rule as done in question 5:

Find x:

16 = √(8 * x)

16² = 8x

256 = 8x

x = 256/8

x = 32

Find y using the leg rule:

(8 + 32) / y = y/32

y² = 40 * 32

y = √1,280

y ≈ 35.8

Find z:

40/z = z/8

z² = 40 * 8

z = √320

z ≈ 17.9

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Answer:  The theorem states that for any right triangle, the sum of the squares of the non-hypotenuse sides is equal to the square of the hypotenuse. In other words, for a right triangle with perpendicular sides of length a and b and hypotenuse of length c, a2 + b2 = c2.

Step-by-step explanation:

an example if Right triangles that have lengths equaling 3-4-5 or 5-12-13 , or even 7-24-25, are special types of right triangles, because all three lengths are integers that together satisfy the Pythagorean theorem. Such triangles are called Pythagorean triplets.

The time taken for Miguel to fill the aquarium is 100 minutes

We can use the formula

time = amount ÷ rate

where

time is the time it takes to fill the aquarium (what we want to find)

amount is the amount of water needed to fill the aquarium (150 gallons in this case)

rate is the rate at which Miguel is filling the aquarium (3 gallons every 2 minutes)

So, Substitute the values in the equation , we get:

time = 150 gallons ÷ (3 gallons ÷ 2 minutes)

time = 150 gallons ÷ 1.5 gallons / minute

Divide the numbers

time = 100 minutes

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The volume of sand in the rectangular prism is 80 percent of the total volume, which can be written as:

0.8 x V = 0.8(L x W x H) cubic inches

A three-dimensional object with six faces, including two at the top and bottom and four lateral faces, called a rectangular prism. The prism's faces are all rectangular in shape. There are three sets of identical faces as a result.

We need to know the dimensions of the rectangular prism to solve the problem. Let's assume the dimensions are length = L inches, width = W inches, and height = H inches.

The volume of the rectangular prism is given by V = L x W x H cubic inches.

If the rectangular prism is filled 80 percent with sand, then 20 percent of the volume is empty space. So, the volume of sand in the rectangular prism is 80 percent of the total volume, which can be written as:

0.8 x V = 0.8(L x W x H) cubic inches

Therefore, we need to know the dimensions of the rectangular prism to find the volume of sand.

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The complete question is:

James fills the rectangular prism 80 percent with sand. How many cubic inches of sand are in the rectangular prism?

Answer:

[tex]y=5-2x[/tex]

Step-by-step explanation:

You have to give the equation in the form [tex]y=mx+c[/tex], where m is the gradient and c is the y-intercept (where the line crosses the y-axis).

From the graph, we can see the line crossed the y-axis at (0,5), so the y-intercept is (0,5), which means c is 5.

We can work out the gradient with the two points (2,1) and (1,3) by doing:

[tex]\frac{change in y}{change in x} =\frac{1-3}{2-1}=-2[/tex]
So the gradient of the line, m, is -2.

Thus the equation of the line is [tex]y=5-2x[/tex].

Answer:

The procedure is too tiring but I will arrive at neg107 over 377

The sum of 3/5 and -6/7 is -9/35

To add fractions with different denominators, we first need to find a common denominator. In this case, the common denominator is the least common multiple (LCM) of 5 and 7, which is 35.

Then, we need to convert both fractions to equivalent fractions with the denominator of 35:

3/5 = 21/35 (multiply both the numerator and denominator by 7)

-6/7 = -30/35 (multiply both the numerator and denominator by 5)

Now that both fractions have the same denominator, we can add them by simply adding the numerators and keeping the denominator

21/35 + (-30/35) = (21 - 30) / 35 = -9/35

Therefore, 3/5 +(− 6/7 ​ ) = -9/35.

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The given question is incomplete, the complete question is:

Calculate 3/5 ​ +(− 6/7 ​ )

Answer:

12/5

Step-by-step explanation:

9 x 2/ 5 x 2 + 6/10 =

18/10 + 6/10=

12/5 or 2 2/5

a) The monthly cost for Aiden with 6 slices of pizza would be $30.50

b) The monthly cost for x slices of pizza would be $20 + $1.75x

Since Aiden is a member, he gets a discount of $1.75 per slice of pizza. Therefore, the total cost of 6 slices of pizza would be

Total cost = 6 × $1.75 = $10.50

Since Aiden is paying $20 per month for the membership, the total monthly cost for Aiden would be

Total monthly cost = $20 + $10.50 = $30.50

Now, to find the monthly cost for x slices of pizza, then the linear equation will be,

Total monthly cost = Membership cost + (Number of slices × Price per slice)

Substituting the given values, we get

Total monthly cost = $20 + (x × $1.75)

Simplifying this expression, we get:

Total monthly cost = $20 + $1.75x

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The expression that represents the discounted price of the jacket is 0.7x. This means that the discounted price is 70% of the original price, or equivalently, that the discount reduces the price of the jacket by 30%.

What is original price?

In order to determine the sales price, the value of the discount would be subtracted from the original price.

When an item is offered at a discount, the discounted price is usually calculated by subtracting the discount from the original price. In this case, since the discount is 30%, we can find the amount of the discount by multiplying the original price x by 0.3. This gives us 0.3x, which is the amount of money that is being discounted from the original price. To find the discounted price, we subtract this amount from the original price, which gives us:

x - 0.3x = 0.7x

So, the expression that represents the discounted price of the jacket is 0.7x. This means that the discounted price is 70% of the original price, or equivalently, that the discount reduces the price of the jacket by 30%.

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The exponential function for the new participants is f(x) = 3 * 4^x

Let's start with the initial number of participants who sent selfies on Day 0.

We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.

On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.

We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.

Therefore, we can write an exponential function of the form:

f(x)=a * 4^x

Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.

We know that a = 12 from our earlier calculations.

So, we have

f(x) = 3 * 4^x

Hence, the function is f(x) = 3 * 4^x

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The best answer is (c) understanding others' emotions.

Women tend to have a more empathetic communication style compared to men, and they tend to prioritize relationships and emotions in their interactions. This communication style involves actively listening to others, being supportive, and expressing empathy towards their feelings. Women often seek to connect with others on an emotional level and understand their perspective, rather than simply giving orders or being self-centered.

Research has shown that women's communication style can be more effective in building and maintaining relationships, as it fosters trust, mutual respect, and understanding. This style also creates a supportive environment where individuals can express their emotions freely and receive validation for their feelings.

In conclusion, women's communication style involves understanding others' emotions, listening actively, and showing empathy towards their feelings.

This approach promotes positive relationships and creates an environment of mutual respect and trust.

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the actuarial expression for the account balance after the final deposit is made as:[tex]FV = $5000 \times [(1.03^{(n-10)}+1)(1.02)^{(204)}-1]/(0.02) + $5000 \times [(1.03^{10}+1)(1.02)^{(104)}-1]/(0.02)[/tex]The account balance after the final deposit is made is [tex]$62,297.36.[/tex]

The account balance after the final deposit is made, the formula for the future value of an annuity due with a growth rate.

Actuarial expression for the account balance after the final deposit is made:

A be the annual deposit amount, n be the number of deposits, i be the nominal annual interest rate, m be the number of compounding periods per year, and g be the annual growth rate of the deposits.

The formula for the future value of an annuity due with a growth rate is:

[tex]FV = A \times [(1+g)\times (1+i/m)^{((n-1) \times m)+1}] / (i/m)[/tex]

Louis' situation, we have:

[tex]A = $5000[/tex] for the first 10 years, and then [tex]A = $5000 \times 1.03^{(n-10)}[/tex] for the remaining 20 years.

n = 30 years

i = 8% nominal annual interest rate, compounded quarterly, so i = 2% per quarter

m = 4 quarters per year

g = 3% annual growth rate for each deposit after the 10th year

The account balance after the final deposit is made:

The above actuarial expression and substituting n=30, we get:

[tex]FV = $5000 \times [(1.03^{20}+1)(1.02)^{80}-1]/(0.02) + $5000 \times [(1.03^{10}+1)(1.02)^{40}-1]/(0.02)[/tex]

Simplifying this expression gives:

[tex]FV = $5000 \times (1.03^{20} \times 1.02^{80} + 1.03^{10} \times 1.02^{40})[/tex]

Using a calculator, we get:

[tex]FV = $5000 \times (10.4619 + 1.7958)[/tex]

[tex]FV = $62,297.36[/tex]

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For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.

We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%

The percentage of students win a jump rope = 16%

The percentage of students win a t-shirt

= 6%

The winning amount for stuffed toy game = $ 3.60

The winning amount for jump rope game = $1.20

The winning amount for t-shirt game

= $7.90

The remaining students do not win a prize. Now, total number of students play the game at the booth = 150

So, number of students who win stuffed toy = 22% of 150 = 33

Number of students who win jump rope = 16% of 150 = 24

Number of students who win stuffed toy

= 6% of 150 = 9

For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6

= 218.7

Hence required value is $218.70.

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The total length of all 10 ribbons is 35 inches when they are placed end to end.

Inches are a unit of length in the imperial system of measurement, which is primarily used in the United States, the United Kingdom, and some other countries. One inch is equal to 1/12 of a foot or 2.54 centimeters.

The inch is commonly used to measure the length or distance of small objects, such as the size of a computer screen, the length of a pencil, or the height of a person. Inches are also used to measure the dimensions of larger objects, such as the width of a door or the size of a piece of furniture.

If John has 10 ribbons, each measuring 3 ½ inches long, we can find the total length of all the ribbons by multiplying the length of one ribbon by the number of ribbons:

Total length = 10 × 3 ½ inches

To multiply a whole number and a mixed number, we can first convert the mixed number to an improper fraction, then multiply:

Total length = 10 × (7/2) inches

Total length = 35 inches

Therefore, the 10 ribbons, placed end to end, would be 35 inches long.

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Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.

Fractions with a numerator less than the denominator are said to be proper fractions. When the numerator exceeds the denominator, the fraction is said to be inappropriate.

Given data:

fraction of crate brought by friend = 1/2

Total number of ice buckets = 6

Fraction of crate in each bucket = fraction of crate brought by friend / Total number of ice buckets

Fraction of crate in each bucket = (1/2) / 6

Fraction of crate in each bucket =  1 / (2*6)

Fraction of crate in each bucket = 1/12

Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

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The answer is B

The internal angles of a triangle have to be 180

IN ΔABC, m∠A=70° and m∠B=35°.

70°+35°+x=180°

105°+x=180°

x=180°-105°

x=75°

Answer B meets the requirements because in ΔPQR m∠P=70° and m∠R=75°

70°+75°+x=180°

145°+x=180°

x=180°-145°

x=35°

The angles of both triangles measure the same

The surface-area of the given cylinders:

1.Surface area of cylinder with radius(r)=8 cm & Height(h)=22 cm, in terms of π is 480π sq. cm & rounded off to nearest hundresths place is 1508.57 sq. cm

2.Surface area of cylinder with radius(r)=4 m & Height(h)=10 m, in terms of π is 112π sq. m & rounded off to nearest hundresths place is 352.00 sq.m

3.Surface area of cylinder with radius(r)=8 cm & Height(h)=15 cm, in terms of π is 368π sq. cm & rounded off to nearest hundresths place is 1156.57 sq. cm

What is surface-area?

The total surface area of each side of a three-dimensional solid shape or figure represents the surface area of the entire object.The surface area of a three-dimensional object, form, or figure as a whole. By multiplying the area of the base by two, together with the areas of the rectangle—whose dimensions are the circumference times the height—we may determine the cylinder's surface area.

The surface area of cylinder= 2(Area of base) + Area of curved surface

                                              =2πr² + 2πrh

                                              = 2πr(r+h)

1)Surface area of cylinder with dimensions radius(r)=8 cm & Height(h)=22 cm

The surface area of cylinder=2πr(r+h)

                                              =2π(8)(8+22)

                                              =16π(30)

                                               =480π sq. cm{in terms of π}

The surface area of cylinder=480(3.1428)

                                               =1508.57 sq. cm

2)Surface area of cylinder with dimensions radius(r)=4 m & Height(h)=10m

The surface area of cylinder=2πr(r+h)

                                              =2π(4)(4+10)

                                              =8π(14)

                                               =112π sq. m{in terms of π}

The surface area of cylinder=112(3.1428)

                                               =352 sq. m

3)Surface area of cylinder with dimensions radius(r)=8 cm & Height(h)=15 cm

The surface area of cylinder=2πr(r+h)

                                              =2π(8)(8+15)

                                              =16π(23)

                                               =368π sq. cm{in terms of π}

The surface area of cylinder=368(3.1428)

                                               =1156.57 sq. cm

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Therefore , the solution of the given problem of circle comes out to be  it can be inferred from the circle graph that for 165 residents, Walk and Streetcar .

Each aeroplane component creates a circle when viewed from this new angle and at a distance. (center). Its structure is made up of surfaces and wavy regions that contrast with one another. Within the core, it rotates uniformly in every direction as well. The "center" of a circular or restricted double sphere remains constant throughout all ultimate extensions.

Here,

This conclusion may be taken from the circle graph's data, which reveals that 15% of the sample favoured the streetcar and 40% preferred walking.

By combining these two figures, we get a sample preference for walking or using the streetcar of

=> 40% + 15% = 55%.

Since there are 300 residents in the sample,

=> 55% of 300 = 0.55 x 300, or 165 residents.

As a result, it can be inferred from the circle graph that for 165 residents, Walk and Streetcar together represent their favourite mode of transportation.

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So, the recipe calls for 0.5 FL oz of orange juice. We have more than enough orange juice in one can to make the dish because a can has 11 FL oz.

A mathematical method called the unitary method is used to address proportionality-related issues. It is a technique that entails determining the value of a single unit prior to applying that value to determine the value of any quantity of units. Problems involving ratios et proportions are frequently solved using the unitary technique. The unitary approach can be used to determine the price of any quantity of apples, for instance, if 5 vegetables cost $2. We can build up a proportion to determine how much 10 apples would cost: 5 apples x $2 Equals 10 apples x. where 10 apples cost x dollars.

given

We can start by applying the conversion rule that states that 6 teaspoons (tsp) of liquid equal 1 fluid ounce (FL oz). The following is how we can convert 11 FL oz to teaspoons:

6 teaspoons per FL oz times 11 FL oz equals 66 teaspoons.

Thus, an 11 FL oz can of orange juice has 66 teaspoons of orange juice.

We can also figure out how many cans of orange juice are required for the recipe as it calls for 3 tablespoons of orange juice.

[tex]0.5 FL oz = 3 tsp * 6 tsp/FL oz[/tex]

So, the recipe calls for 0.5 FL oz of orange juice. We have more than enough orange juice in one can to make the dish because a can has 11 FL oz.

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Answer:

Step-by-step explanation:

The circumference of a circle is found by the formula 2πr. r is defined as the radius, which is the distance from the middle of the circle to any point on its outer curve. In this case, we are given the radius from the line that is drawn halfway through the circle. We can plug in this value (11) and solve it.

C = 2πr

C = 2π(11)

C = 22π cm

Hope this helps!