Solve the equation and check your solution: -2(x - 1) = 2 - 2x

Since the expression is the same, we can conclude that the binary operation ⋆ is associative.

To show that the binary operation ⋆ is commutative, we need to demonstrate that a ⋆ b is equal to b ⋆ a for any integers a and b.

Let's start by evaluating a ⋆ b:

a ⋆ b = 2ab + 5.

Now let's evaluate b ⋆ a:

b ⋆ a = 2ba + 5.

By comparing the expressions for a ⋆ b and b ⋆ a, we can see that they are indeed equal:

2ab + 5 = 2ba + 5.

Since the expression is the same, we can conclude that the binary operation ⋆ is commutative.

To show that the binary operation ⋆ is associative, we need to demonstrate that (a ⋆ b) ⋆ c is equal to a ⋆ (b ⋆ c) for any integers a, b, and c.

Let's evaluate (a ⋆ b) ⋆ c:

(a ⋆ b) ⋆ c = (2ab + 5) ⋆ c = 2(2ab + 5)c + 5 = 4abc + 10c + 5.

Now let's evaluate a ⋆ (b ⋆ c):

a ⋆ (b ⋆ c) = a ⋆ (2bc + 5) = 2a(2bc + 5) + 5 = 4abc + 10a + 5.

By comparing the expressions for (a ⋆ b) ⋆ c and a ⋆ (b ⋆ c), we can see that they are indeed equal:

4abc + 10c + 5 = 4abc + 10a + 5.

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In the given  isosceles triangle, the measure of angle G is 74 degrees.

In the given problem, we are dealing with an isosceles triangle where angle G measures 74 degrees. It is mentioned that EF and FG are congruent, indicating that triangle EFG is isosceles.

Since EFG is an isosceles triangle, we can conclude that angles E and G are congruent. Therefore, we can set the measure of angle E equal to the measure of angle G and solve for x.

By setting 4x + 50 (measure of angle E) equal to 14x + 30 (measure of angle G), we have the equation 4x + 50 = 14x + 30.

Solving for x, we find that x = 2.

Now that we have the value of x, we can substitute it into each angle measure to determine their values.

The measure of angle E (mE) is given by 4x + 50, which becomes 4(2) + 50 = 58 degrees.

The measure of angle F (mF) is given by 2x + 60, which becomes 2(2) + 60 = 64 degrees.

Finally, the measure of angle G (mG) is already known to be 74 degrees.

Therefore, the measures of the angles in the isosceles triangle are: mE = 58 degrees, mF = 64 degrees, and mG = 74 degrees.

By understanding the properties of isosceles triangles and utilizing algebraic equations, we can determine the measures of the angles in the given triangle.

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The percentage of the games that Natasha scores between 93 and 142 is given as follows:

96.9%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 115, \sigma = 11[/tex]

The proportion of games with scores between 93 and 142 is the p-value of Z when X = 142 subtracted by the p-value of Z when X = 93, hence:

Z = (142 - 115)/11

Z = 2.45

Z = 2.45 has a p-value of 0.992.

Z = (93 - 115)/11

Z = -2

Z = -2 has a p-value of 0.023.

0.992 - 0.023 = 0.969, hence the percentage is of 96.9%.

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The powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.

Given that, M = {x: x² - 5x + 2x + 8 = 0}

This is a quadratic equation and it can be written in the form of (x - a)(x - b) = 0, where a and b are the roots of the equation.

Substituting x² - 5x + 2x + 8 = 0 in (x - a)(x - b) = 0, we get

(x - a)(x - b) = (x - (-3))(x - 5) = 0

Therefore, the roots of the equation are a = –3 and b = 5.

Now, the powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.

Here,

(1, 2) represents the set containing only the root ‘–3’,

(2, 1) represents the set containing only the root ‘5’,

(2, 4) represents the set containing both the roots

Therefore, the powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.

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The calculated t-value of 1.100 is less than the critical t-value of 2.718, we fail to reject the null hypothesis.

To test the hypothesis that regular physical exercise improves academic achievement, we will conduct a two-sample t-test for independent samples. The null hypothesis is that there is no difference in the mean academic achievement scores between the treatment group (physical exercise) and the control group (no physical exercise).

Let's calculate the mean and standard deviation for each group:

Treatment group (physical exercise):

mean = (4 + 2.67 + 3.65 + 2.11 + 3.21 + 3.6) / 6 = 3.3833

standard deviation = 0.7589

Control group (no physical exercise):

mean = (3.75 + 2.74 + 3.42 + 1.67 + 3 + 3.25 + 2.65) / 7 = 3.0071

standard deviation = 0.7037

We can now calculate the t-statistic:

t = (3.3833 - 3.0071) / sqrt((0.7589^2 / 6) + (0.7037^2 / 7)) = 1.100

The degrees of freedom for this test are 6 + 7 - 2 = 11 (assuming equal variances).

Using a t-table or a t-distribution calculator with 11 degrees of freedom and a significance level of 0.01, we find that the critical t-value is ±2.718.

Since the calculated t-value of 1.100 is less than the critical t-value of 2.718, we fail to reject the null hypothesis. We do not have enough evidence to conclude that regular physical exercise improves academic achievement.

The p-value for this test can be calculated as the probability of getting a t-value as extreme as 1.100, assuming the null hypothesis is true. Using a t-distribution calculator with 11 degrees of freedom, we find that the p-value is 0.294 (rounded to three decimal places).

Since the test result is not statistically significant (p > 0.01), we do not need to report an effect size using Cohen's d.

This test result could be reported in the literature as follows: "A two-sample t-test for independent samples was conducted to examine the effect of regular physical exercise on academic achievement, while controlling for academic aptitude. Six pairs of college students with similar GPAs were randomly assigned to either a treatment group that attended daily exercise classes or a control group. The mean academic achievement score for the treatment group was 3.3833 with a standard deviation of 0.7589, while the mean academic achievement score for the control group was 3.0071 with a standard deviation of 0.7037. The t-test result was not statistically significant (t(11) = 1.100, p = 0.294), indicating that there is not enough evidence to conclude that regular physical exercise improves academic achievement."

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We can use the formula for the area of a sector to find the area of sector $LMN$

The area of a sector with central angle $\theta$ in a circle with radius $r$ is given by:

$A = \frac{\theta}{360^\circ} \pi r^2$

In this case, we know that $m\angle LMN = 66^\circ$ and $LM = 19$ units, so the radius of circle M is half of the diagonal of the rectangle formed by $LM$ and $MN$. Using the Pythagorean theorem, we can find the length of $MN$:

$MN^2 = LM^2 + LN^2 = LM^2 + LM^2 = 2LM^2$

$MN = \sqrt{2} LM = \sqrt{2} \cdot 19$

So the radius of circle M is $r = \frac{1}{2}MN = \frac{1}{2}\sqrt{2} \cdot 19$

Now we can use the formula for the area of a sector to find the area of sector $LMN$:

$A = \frac{m\angle LMN}{360^\circ} \pi r^2 = \frac{66^\circ}{360^\circ} \pi \left(\frac{1}{2}\sqrt{2} \cdot 19\right)^2 \approx \boxed{90.89}$ square units (rounded to the nearest hundredth).

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To find the area of the floor needed for 6 squirrel monkeys, first calculate the additional area needed for 4 monkeys 4 x 9 = 36 square feet. Add this to the initial area of 36 square feet, to get a total area of 72 square feet. Thus, the floor area for all six monkeys should be 72 square feet.

Let's first find the area of the floor required for the additional 4 monkeys

4 additional monkeys * 9 sq ft per monkey = 36 sq ft

So, to accommodate all 6 monkeys, the total floor area required would be

36 sq ft (original area) + 36 sq ft (additional area) = 72 sq ft

Therefore, the area of the floor for all six monkeys must be 72 square feet.

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A) The amount of interest he will earn in a year is $3,000.

B) The amount he spent on furniture is $600.

Part A: To calculate the interest Alex will earn in one year, use the formula for simple interest:

Interest = Principal × Rate × Time.

In this case, Principal = $30,000, Rate = 10% (0.10), and Time = 1 year. So,

Interest = $30,000 × 0.10 × 1 = $3,000.

Part B: Alex spends 20% of the interest on furniture. To calculate this amount, multiply the interest by 20% (0.20): $3,000 × 0.20 = $600.

Therefore, in one year, Alex will earn $3,000 in interest. He will spend $600 on furniture for his new house.

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Howler monkeys are heavier on average than spider monkeys (17.75 lbs vs. 11.25 lbs).

Calculate the mean:

Some of the weights divided by the number of monkeys

Calculate the MAD:

Find the absolute deviation (difference) of each weight from the mean

Calculate the average of these deviations

Mean Howler Monkey = (16+17+18+18+18+20+22+23)/8 = 142/8 = 17.75 lbs

Mean Spider Monkey = (8+10+10+11+11+12+14+14)/8 = 90/8 = 11.25 lbs

Now, we calculate the MAD for each type of monkey:

MAD Howler Monkey=  1.875 lbs

MAD Spider Monkey=  1.5625 lbs

we calculate the means-to-MAD ratio for both types of monkeys:

Howler Monkey: Mean/MAD = 17.75/1.875 = 9.466

Spider Monkey: Mean/MAD = 11.25/1.5625 = 7.2

Inference:

Howler monkeys are heavier on average than spider monkeys (17.75 lbs vs. 11.25 lbs).

The means-to-MAD ratio shows that howler monkeys have more consistent weights (9.466) compared to spider monkeys (7.2), as a higher ratio indicates less variability in weights.

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There are now 260 cows on the farm.

Let's start through calculating the amount of milk produced with the aid of the original cows before any modifications were made.

If every of the unique cows was producing 12.8 liters of milk in keeping with day, and there had been "x" cows, then the entire amount of milk produced by means of the original cows could be:

12.8x liters per day

After the adjustments, the farmer has 60 more cows and all cows produce 15 liters of milk per day. So, the full amount of milk produced with the aid of all cows after the modifications would be:

15(x + 60) liters per day

we're told that the new milk production is 1340 liters more according to day than before the changes. So, we can set up an linear equation:

15(x + 60) = 12.8x + 1340

Simplifying the equation, we get:

15x + 900 = 12.8x + 1340

2.2x = 440

x = 200

therefore, there were at first 200 cows on the farm. After the changes, the full number of cows would be:

x + 60 = 200 + 60 = 260 cows

So, there are now 260 cows on the farm.

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Answer:

C. The product of two irrational numbers is irrational.

Example: √3•√3=3

The given expression x²y − 7xy + xyz is a 3rd degree polynomial.

To classify it by degree and term, let's first determine the degree of each term:

1. x²y: The degree is the sum of the exponents of the variables (x and y). Here, the degree is 2 (from x²) + 1 (from y) = 3.
2. 7xy: The degree is 1 (from x) + 1 (from y) = 2.
3. xyz: The degree is 1 (from x) + 1 (from y) + 1 (from z) = 3.

Now, we can classify the expression:

- Degree: Since the highest degree among the terms is 3, the expression is a 3rd-degree polynomial.
- Term: There are three terms in the expression, so it is a trinomial.

In summary, the given expression, x²y − 7xy + xyz, is a 3rd-degree trinomial.

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David's net worth: 86,329.95

To calculate David's new net worth, we need to add the increase in assets and subtract the decrease in liabilities from his current net worth.

New assets value = 62,784.24 + 2,784.89 = 65,569.13

New liabilities value = David's current net worth - his current assets value

New liabilities value = 45,765.78 - 62,784.24 = -17,018.46

Since his liabilities have decreased by 3,742.36, we need to subtract this value from the new liabilities value:

New liabilities value = -17,018.46 - 3,742.36 = -20,760.82

Now we can calculate his new net worth by subtracting his new liabilities value from his new assets value:

New net worth = 65,569.13 - (-20,760.82) = 86,329.95

Therefore, David's new net worth is 86,329.95.

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The relative frequency for the event of spin a 2 is P = 0.16

Given data ,

Let the total number of times the event occurs = 50

Now , the number of times the spin of 2 occurs = 8 times

So , the relative frequency is given by

Relative Frequency = Subgroup frequency / Total frequency

P = 8 / 50

P = 0.16

Hence , the relative frequency is 0.16

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The complete question is attached below :

If the table shows the results for spinning the spinner 50 times. What is the relative frequency for the event "spin a 2"

Therefore, the distance from both Xavier and David's tents to the ranch is: 151 meters and 159.6 meters.

An equation is a mathematical statement that shows the equality of two expressions, often separated by an equal sign (=). The expressions on either side of the equal sign can contain variables, constants, and mathematical operations. Equations are used to solve problems, find unknown values, and represent relationships between quantities in various fields such as mathematics, physics, engineering, and economics.

Here,

The distance from Xavier's tent to the ranch is XR = (10.5z + 34) meters.

The distance from David's tent to the ranch is DR = (12.3z + 12.4) meters.

Since David and Xavier want to place their tents at equal distances from the ranch, we can set these two expressions equal to each other and solve for z:

(10.5z + 34) = (12.3z + 12.4)

Simplifying this equation, we get:

1.8z = 21.6

z = 12

Therefore, the distance from both Xavier and David's tents to the ranch is:

XR = (10.5z + 34)

= (10.5 x 12 + 34)

= 151 meters

DR = (12.3z + 12.4)

= (12.3 x 12 + 12.4)

= 159.6 meters

So both tents are 151 meters away from the ranch.

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Part A: The given definition states that an angle is two collinear rays with a common endpoint. Part B : A point is an example of an undefined term.In relation to angles, a point is crucial as it serves as the common endpoint of the two rays that form the angle.

Part A :  The given definition states that an angle is two collinear rays with a common endpoint. However, this definition is incorrect as it contradicts the correct definition of an angle. In the correct definition, an angle is formed by two non-collinear rays with a common endpoint.

An example that contradicts the given definition is when you have two rays, AB and BC, with B being the common endpoint. If they were collinear, they would lie along the same straight line, and thus, no angle would be formed between them. To make the definition accurate, you would need to change it to: "An angle is formed by two non-collinear rays with a common endpoint."

Part B: An undefined term in geometry is a term that cannot be defined using other known geometric terms, but its meaning is generally understood. One example of an undefined term is a point. A point is a basic element in geometry, and it has no size, shape, or dimensions. It is merely a location in space. For instance, when discussing angle ABC, point B is the common endpoint of rays AB and BC.

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The slant height of the given cone is 16.36 cm.

The length from the base to the peak along the "center" of a lateral face of an object (like a frustum or pyramid) is its slant height.

It is, in other words, the height of the triangle that a lateral face is a part of (Kern and Bland 1948, p.

So, calculate the slant height as follows:

614π = πr√h²+r²

614 = 16.2√h²+16.2²

614 = 262.44√h²

614/262.44 = h

2.33

Height = 2.33 cm

Then, slant height formula:

s=√(r² + h²)

s=√(16.2² + 2.33²)

s=√267.8689

s=16.36 cm

Therefore, the slant height of the given cone is 16.36 cm.

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(a) The function rule for Big Wave Waterpark, f(x) = 2.5x + 5. where f(x) is total cost and x is number of slides ridden.

b) The function rule for Coaster City is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden and f(x) is total cost.

c) The function rule for Virtual Reality Lan is, f(x) = 3x + 10, where f(x) is total cost and x is the number reality rides ridden.

(a) Let f(x) = ax +b be the function which represents the total cost of Big Wave Park where x represents the number of taken ride.

We can see that f(2) = 10; f(4) = 15 and f(6) = 20.

Therefore, 2a + b = 10 and 4a + b = 15

So, 2(2a + b) - (4a + b) = 2*10 - 15

4a + 2b - 4a - b = 20 - 15

b = 5

Now, f(6) = 20

6a + b = 20

6a + 5 = 20 [putting the value of 'b']

6a = 20 - 5 = 15

a = 15/6 = 5/2 = 2.5

Hence, the function rule for Big Wave Waterpark is, f(x) = 2.5x + 5.

(b) The function rule for Coaster city is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden.

(c) Let the total cost for Virtual Reality Lan is, f(x) = cx + d, where x is the number reality rides ridden.

From the given graph we can see that, f(10) = 40; f(20) = 70; f(30) = 100.

So, 10c + d= 40 ........... (i)

20c + d = 70 ............... (ii)

Solving (i) and (ii) we get,

2(10c + d) - (20c + d) = 2*40 - 70

20c + 2d - 20c - d = 80 - 70

d = 10

So putting the value d = 10 in f(30) = 100 we get,

30c + 10 = 100

30c = 100 - 10 = 90

c = 90/30 = 3

So the function rule is, f(x) = 3x + 10.

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Step-by-step explanation:

First you need to do of bracket

(8+2)

=10

Second you need to do of exponential sign ^

10^3=1000(note this sign is also called cube)

Now,

1000-6

=994

Answer:

994

Step-by-step explanation:

We need to use order of operations to solve this problem.

( 8 + 2 ) ^ 3 - 6

According to PEMDAS, Parenthesis must be resolved first.

So we get:

10 ^ 3 - 6

Secondly, PEMDAS states that Exponents go next

1000 - 6

Finally, we only have one operation left, subtraction, so we can go ahead and do that.

994 is your answer.

I put a lot of thought and effort into my answers, so a brainliest would be much appreciated!

The percent error is 4.76%.

To find the percent error, we first need to calculate the actual error, which is the absolute difference between the estimated points and the actual points:

Actual error = |252 - 240| = 12

Next, we need to calculate the percent error, which is the ratio of the actual error to the estimated value, expressed as a percentage:

Percent error = (actual error / estimated value) x 100%

Percent error = (12 / 252) x 100%

Percent error = 4.76%

Therefore, the percent error is 4.76%.

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Answer is 64.05% probability that if we chose a student at random

To find the probability that a randomly chosen student would not like the school lunches, we need to find the complement of the probability that they do like the school lunches.

The proportion of 9th graders in the sample is 45%, so the proportion of 10th graders is 100% - 45% = 55%.

Of the 9th graders, 31% said they liked the school lunches, so the proportion that did not like them is 100% - 31% = 69%.

Of the 10th graders, 42% said they liked the school lunches, so the proportion that did not like them is 100% - 42% = 58%.

So, the probability that a randomly chosen student would not like the school lunches is:

(0.45 * 0.69) + (0.55 * 0.58) = 0.6405 or 64.05% (rounded to two decimal places).

Therefore, there is a 64.05% probability that if we chose a student at random, they would not like the school lunches.

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Ted spent 67 minutes reading.

First, let's determine how long Jared spent reading:

Jared = Pete - 52 minutes

Jared = 3 hours * 60 minutes/hour - 52 minutes

Jared = 148 minutes

Now we can use the fact that Ted spent 1 hour 21 minutes less than Jared:

Ted = Jared - 1 hour 21 minutes

Ted = 148 minutes - 81 minutes

Ted = 67 minutes

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The solution to this system of equations are x = 7 and y = -3.

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

3y = 26 - 5x               .........equation 1.

6x + 7y = 21               .........equation 2.

Rewriting in standard form, we have:

5x + 3y = 26

6x + 7y = 21

By multiplying equation 1 by 6 and dividing by 5, we have:

6x + 3.6y = 31.2   .........equation 3.

By subtracting equation 3 from equation 2, we have:

3.4y = -10.2

y = -3.

x = (26 - 3y)/5

x = (26 - 3(-3))/5

x = 7

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The median score, which represents the middle value of the dataset, can be identified by the line inside the box.

The IQR is represented by the length of the box in the box plot.

Based on the provided box plot for the sixth grade math test, we can infer the following information about the distribution's center, variability, and spread:

1. Center: The median score, which represents the middle value of the dataset, can be identified by the line inside the box. This value divides the data into two equal halves and helps to understand the central tendency of the scores.

2. Variability: The Interquartile Range (IQR) represents the variability in the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

The IQR is represented by the length of the box in the box plot and indicates how scores are dispersed around the median.

3. Spread: The range of the dataset can be identified by the distance between the minimum and maximum scores, represented by the whiskers in the box plot.

This shows the overall spread of the scores and indicates the extent of variation within the class.

By analyzing these aspects of the box plot, we can better understand the distribution of math test scores in the sixth grade class.

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This box plot shows scores on a recent math test in a sixth grade class. Identify at least three things that you can infer from the box plot about the distribution’s center, variability, and spread.

The slope of this graph is equal to 25.

In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided above, we can reasonably infer and logically deduce that Alyssa made $200 for every 8 hour shift she works as a personal trainer. Additionally, the amount of money Alyssa earned would be plotted on the y-axis while the number of hours she work would be plotted on the x-axis of a graph;

Slope (m) = 200/8

Slope (m) = 25.

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There are 9 different outcomes in the sample space when selecting one fruit from each basket.

Using an organized list, we can represent all the possible outcomes in the sample space for the two baskets of fruit:

1. Red Apple, Orange
2. Red Apple, Lemon
3. Red Apple, Peach
4. Yellow Apple, Orange
5. Yellow Apple, Lemon
6. Yellow Apple, Peach
7. Green Apple, Orange
8. Green Apple, Lemon
9. Green Apple, Peach

In total, there are 9 different outcomes in the sample space when selecting one fruit from each basket.

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The measure of minor arc MPQ in a circle with central angle <MQP measuring 44 degrees is 316 degrees.

To find the measure of minor arc MPQ, we need to first find the measure of central angle <MNQ that intercepts this arc. Since minor arc MPQ and minor arc MP are adjacent, their sum equals the measure of minor arc MPNQ,

<MPQ+arc MP = <MPNQ

Substituting the measure of minor arc MP as 44 degrees, we get,

ZMPQ+ 44 360

Solving for MPQ, we get,

ZMPQ = 360-44

<MPQ = 316 degrees

Therefore, the measure of minor arc MPQ is 316 degrees.

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(A) There is only one term in the expression:[tex]-112y^2.[/tex]

(B) There are four terms in the expression[tex]: 7x^2, 5y, -9xy, and 3.[/tex]

In A option, There is only one term within the algebraic expression [tex]-112y^2.[/tex]A term is a single numerical or variable expression this is separated from other expressions through addition or subtraction.

In B option, There are 4 terms within the algebraic expression[tex]7x^2 + 5y - 9xy +[/tex] 3. A time period is a single numerical or variable expression that is separated from other expressions through addition or subtraction.

In this situation, the primary term is[tex]7x^2[/tex], the second time period is 5y, the 0.33 time period is -9xy, and the fourth term is 3.

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The expression in terms of π that represents the area of the shaded part of ⊙R is 3πR²/4, obtained by subtracting the area of the smaller circle from the larger circle.

To find the area of circle of the shaded part of ⊙R, we need to subtract the area of the smaller circle from the area of the larger circle.

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

Let the radius of the larger circle be R and the radius of the smaller circle be r. Then the area of the shaded part can be expressed as:

A(shaded) = A(large circle) - A(small circle)

= πR² - πr²

We can simplify this expression further by noticing that the radius of the smaller circle is half the radius of the larger circle, so r = R/2. Substituting this into the equation gives:

A(shaded) = πR² - π(R/2)²

= πR² - πR²/4

= 3πR²/4

Therefore, the area of the shaded part of ⊙R can be expressed as 3πR²/4. This expression represents the difference in the area between the larger and smaller circles, which gives us the area of the shaded region.

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The expression in terms of π that represents the area of the shaded part of ⊙R is 3πR²/4, obtained by subtracting the area of the smaller circle from the larger circle.

To find the area of circle of the shaded part of ⊙R, we need to subtract the area of the smaller circle from the area of the larger circle.

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

Let the radius of the larger circle be R and the radius of the smaller circle be r. Then the area of the shaded part can be expressed as:

A(shaded) = A(large circle) - A(small circle)

= πR² - πr²

We can simplify this expression further by noticing that the radius of the smaller circle is half the radius of the larger circle, so r = R/2. Substituting this into the equation gives:

A(shaded) = πR² - π(R/2)²

= πR² - πR²/4

= 3πR²/4

Therefore, the area of the shaded part of ⊙R can be expressed as 3πR²/4. This expression represents the difference in the area between the larger and smaller circles, which gives us the area of the shaded region.

Learn more about area of circle

brainly.com/question/28642423

#SPJ11