1. Use integration in cylindrical coordinates in order to compute the vol- ume of: U = {(x,y,z):05:36 - 12 - y}

The total area of the composite figure is 576 square meters

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the individual shapes

So, we have

Surface area = Rectangle + Trapezoid

Using the area formulas, we have

Surface area = 29 * 16 + 1/2 *(14 + 18) * (36 - 29)

Evaluate

Surface area = 576

Hence. the total area of the figure is 576 square meters

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Complete question

Find the area of the polygon.

See attachment

The area of the polygon is ____ square meters.

The volume of the different shapes have been calculated in the space below

Volume of rectangular prism = lwh

where we define the variables as :

l = length

w = width

h = height

then when we multiply, we will have

= 4 x 10 x 6

= 240

Volume of triangular pyramid = 1 / 3 b x h

where b = base

h = height

1 / 3 x 1.5 x 2

= 1

Volume of rectangular pyramid = lwh / 3

= 7.5 x 4.5 x 5 / 3

= 56.25

= 1/2 x b x h x l

= 1/2 x 3 x 8.5 x 7

= 89.25

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The dean of students at a large college is interested in learning about their opinions regarding the percentage of students who are satisfied with their academic experience. This is an important question for the dean to consider, as it can help them identify areas for improvement and ensure that they are meeting the needs of their students.

To gather this information, the dean may choose to conduct a survey or hold focus groups with students to hear their feedback. They may also review data on student retention rates and academic performance to get a sense of how satisfied students are with their experience at the college.

Once the dean has gathered this information, they can use it to make informed decisions about how to improve the academic experience for their students. This may involve investing in new programs or resources to better support students, or making changes to existing programs based on feedback from students.

Ultimately, by taking the time to gather and listen to student opinions about their academic experience, the dean can create a more student-centered learning environment that meets the needs and expectations of their diverse student population.

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The surface area of the composite figure is given as follows:

446 cm².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The figure is this problem is given by the composition of two rectangular prisms, with dimensions given as follows:

Hence the surface area is given as follows:

S = 2 x (5 x 10 + 5 x 7 + 10 x 7) + 2 x (8 x 4 + 8 x 3 + 4 x 3)

S = 446 cm².

The prism is given by the image presented at the end of the answer.

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The 7/8 and 5/6, when renamed using a common denominator of 24, become 21/24 and 20/24

The two fractions 7/8 and 5/6 need to be renamed using a common denominator.

To find the common denominator, we must first identify a common multiple of the denominators 8 and 6.

The smallest common multiple of 8 and 6 is 24. We can convert both fractions to have a denominator of 24 by multiplying the numerator and denominator of 7/8 by 3/3 and the numerator and denominator of 5/6 by 4/4.

This results in 21/24 and 20/24, respectively.  

Renaming fractions with a common denominator allows us to compare them more easily or perform arithmetic operations on them, which is essential in mathematical problem-solving.

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The credit card's effective interest rate for the year is [tex]40.51%.[/tex]%

We can use the following formula:

Effective annual interest rate is calculated as[tex](1 + APR/365)365 - 1.[/tex]

The interest is compounded everyday in this case and the APR is 33.01 percent. When we enter these values into the formula, we obtain:

Effective annual interest rate =[tex](1 + 0.3301/365)^365 - 1[/tex]

Effective annual interest rate =[tex]1.4051 - 1[/tex]

Effective annual interest rate =[tex]1.4051 - 1[/tex]

So the credit card's effective interest rate for the year is[tex]40.51%.[/tex]%

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The mean is 7

The median is the middle value, which is 7.

Mean Absolute Deviation: 2

Step 3: Find the absolute deviation of each value from the mean:

|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|

These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.

Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:

Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2

Step 5: Find the absolute deviation of each value from the median:

|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|

These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.

Therefore, the absolute deviation from the median is 5.

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The area of the base of the prism is,

Area = 5.5 cm²

We have to given that,

This trapezoid-based right prism has a volume of 30 cm³.

We have;

Here we assume

a = 6

b = 5

c = 1

Now we know that

Area = (a + b) c / 2

Area = (6 + 5) 1 /2

Area = 11/2

Area = 5.5 cm²

Thus, The area of the base of the prism is,

Area = 5.5 cm²

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The probability that a marble selected from the jar is green, P(green) = 5/19. The correct option is therefore;

5/19

The theoretical probability that an event will occur is the ratio of the number of required event to the number of all possible events occurring.

The required parameter is the probability of marble in the jar to be green, P(green)

The number of each color of marbles in the jar are;

Red = 5, Yellow = 11, Blue = 7, Green = 10, Brown = 5

The total number of marbles in the jar is therefore;
5 + 11 + 7 + 10 + 5 = 38

The probability that a marble in the jar is green, P(green) = 10/38 = 5/19

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I would say she has to walk 17 dogs, im not sure if that's correct though

Let's assume that Lucinda needs to walk "x" more dogs to have at least $80. Then, the amount of money she will earn from walking those "x" dogs can be calculated by multiplying the number of dogs by the amount of money earned per dog, which is $3:

Amount of money earned from walking "x" dogs = $3x

To determine how many more dogs Lucinda needs to walk to have at least $80, we can write the following inequality:

$30 + $3x ≥ $80

Simplifying the inequality, we get:

$3x ≥ $50

Dividing both sides by 3, we get:

x ≥ 16.67

Since we can't walk a fraction of a dog, we need to round up to the nearest whole number. Therefore, Lucinda needs to walk at least 17 more dogs to have at least $80.

First, we need to find the total number of parts in the ratio 1:4:5:

1 + 4 + 5 = 10

This means that the string is divided into 10 equal parts. To find the length of each part, we divide the total length of the string by the number of parts:

80 cm ÷ 10 = 8 cm

Now, we can find the length of the longest piece, which is 5 times the size of each part:

8 cm x 5 = 40 cm

Therefore, the length of the longest piece is 40 cm.

Jamal must charge a monthly rent of 2,000 to earn an 8% annual income on his capital investment.

It is given that Jamal Winchester invested 75,000 in to a property and he expects his annual expenses to be 18,000. Jamal wants to earn 8% annual income on his capital investment. Hence, the monthly rent he must charge is determined as follows.

1. Calculate the desired annual income:

75,000 (capital investment) x 0.08 (8% annual income) = 6,000.

2. Add the annual expenses:

6,000 (desired annual income) + 18,000 (annual expenses) = 24,000.

3. Divide by 12 months to find the monthly rent: 24,000 ÷ 12 = 2,000.

Jamal must charge a monthly rent of 2,000.

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A) Internal goods in mathematics include problem-solving skills, logical thinking, analytical reasoning, and a deep understanding of mathematical concepts.

B) Coercive power, on the other hand, might manifest when individuals impose their methods or beliefs on others, potentially stifling creativity and discouraging alternative perspectives.
C) Teachers affirm their students' dignity as creative human beings in the ways they do mathematics by creating a safe space, encourage exploration and expression, value the learning process, celebrate creativity and originality in problem-solving

A) When you share these goods with others, they multiply in the sense that others also develop these skills, fostering collaboration, and generating new ideas, ultimately contributing to the overall progress in the field of mathematics.
B) Creative power in mathematical settings can be seen when individuals or teams come up with innovative solutions to problems, develop new theories, or find unique ways to apply mathematics to real-world situations.
C) Teachers can affirm their students' dignity as creative human beings in the ways they do mathematics by:
1. Encouraging students to explore multiple solution methods and strategies, allowing them to find the approach that best suits their thinking style.
2. Valuing each student's input, ideas, and questions, creating a safe and supportive environment for them to express their thoughts.
3. Challenging students with open-ended problems that require creativity and critical thinking, emphasizing the importance of understanding concepts over rote memorization.
4. Recognizing and celebrating each student's unique strengths and contributions to the learning process, promoting a growth mindset and a sense of accomplishment.

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Using trigonometry, the length that Ruth has to play in if she plays between her friend's house (point D) and the edge of the lighted area (point C) is 6.72 feet. Option C is the correct answer.

To solve this problem, we need to use trigonometry. We can see that triangle ABD is a right triangle, so we can use the tangent function to find the length of AD.

First, we need to find the length of BD. We can use the right triangle trigonometry again to find it.

tan(27) = BD/AB

BD = AB × tan(27)

BD = 54 × tan(27)

BD ≈ 24.12

Now, we can use the right triangle trigonometry on triangle BCD to find the length of CD.

tan(41) = CD/BD

CD = BD × tan(41)

CD ≈ 18.85

Finally, we can use the Pythagorean theorem on triangle ACD to find the length of AD.

AD² = AC² - CD²

AD² = 20² - 18.85²

AD ≈ 6.72

Therefore, the length that Ruth has to play is approximately 6.72 feet.

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The question is -

Ruth has a street lamp in front of her house, represented by Segment AB The street Lamp is 20 feet tall. Her mom insists that at night she only plays within its light. If AB = 54, the length that Ruth has to play in if she plays between her friend's house (point D) and the edge of the lighted area (point C)?

Options are:

a. 1.7 feet

b. 2.2 feet

c. 6.7 feet

d. 5.9 feet

Luna and her friend Maka decided to make sandwiches using 1/3 of a baguette. To ensure fairness, they agreed to divide the baguette equally between them. They carefully measured the baguette and cut it into two equal parts, ensuring each of them received an equal portion.

Luna and Maka then began assembling their sandwiches. They spread their preferred fillings on their respective portions of the baguette, adding layers of vegetables, meats, and condiments to create delicious sandwiches.

After completing their sandwich preparation, Luna and Maka sat down together to enjoy their culinary creations. They appreciated the taste and quality of their sandwiches, delighted by the shared experience and the equal distribution of the baguette.

As they savored each bite, Luna and Maka cherished their friendship and the simple joy of sharing a meal together. They found contentment in the realization that even the smallest things, like a shared baguette, could strengthen their bond and create lasting memories.

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To find the number when 28 is the geometric mean of 13 and that number, we'll use the formula for the geometric mean: √(a * b) = GM, where a and b are the two numbers, and GM is the geometric mean. In this case, a = 13, GM = 28.

Step 1: Substitute the given values into the formula:
√(13 * b) = 28

Step 2: Square both sides to get rid of the square root:
(√(13 * b))^2 = 28^2
13 * b = 784

Step 3: Divide both sides by 13 to isolate b:
b = 784 / 13
b ≈ 60.31

So, the other number is approximately 60.31 when rounded to the nearest hundredth. In summary, 28 is the geometric mean of 13 and 60.31, as √(13 * 60.31) ≈ 28.

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Answer:

m = -2

Step-by-step explanation:

We Know

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-3,2) (-2,0)

We see the y decrease by 2, and the x increase by 1, so the slope is

m = -2

The area enclosed by the circle is given as 7494.12 m² and the mistake Frank have made is he subtracted the area of the square and the area of 4 semi-circles.

We are given that the figure is made by attaching semicircles to each side of a 54 dash m​-by-54 dash m square. Frank says the area is 1 comma 662.12 m squared.

We have to find the error made by Frank,

Area of the square = Side of the square x Side of the square

In the question; the side of the square given is 54 m and this would also be the diameter of the semicircle attached to each side of a square.

So, the radius of the semicircle = diameter /2  = 54/2 = 27 m

Now, the area of the square = 54 x 54 = 2916 m².

Also, the area of the semi-circle = [tex]\frac{\pi r^2}{2}[/tex] = [tex]\frac{3.14*27^2}{2}[/tex] = 1144.53 m² .

As there are a total of 4 semi-circles attached to the square, so the area of all the 4 semi-circles = 4 x 1144.53  = 4578.12

Now, the total area of the figure = Area of the square + Area of 4 semi-circles

                = 2916 + 4578.12

                = 7494.12 m².

The error made by Frank was that he subtracted the area of the square and the area of 4 semi-circles to find the area of the whole figure as (4578.12  - 2916  = 1662.12 ).

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Complete question:

Frank needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 54 m​-by-54 m square. Frank says the area is 1662.12 meter squared. Find the area enclosed by the figure. Use 3.14 for pi. What error might Frank have​ made?

The greatest number of ride tickets Chase can buy is 17 and spend $30 for total cost of admission.

To solve this problem, we need to use algebraic equations. Let x be the number of ride tickets that Chase can buy. We know that the total amount of money Chase can spend on admission and ride tickets is $30, so we can write:

4.25 + 1.5x = 30

To solve for x, we can isolate the variable by subtracting 4.25 from both sides and then dividing by 1.5:

1.5x = 25.75
x = 17.17

Since Chase can't buy a fractional number of ride tickets, we need to round down to the nearest whole number. Therefore, Chase can buy a maximum of 17 ride tickets with his $30 budget.

To double-check our answer, we can calculate the total cost of admission and 17 ride tickets:

4.25 + 1.5(17) = 29.25

This is less than $30, so it is indeed possible for Chase to buy 17 ride tickets within his budget.

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To compare Ralph's and Frank's t-shirt companies, let's calculate the total cost of buying a certain number of t-shirts from each company.

1. Ralph's t-shirt company:

- Price per t-shirt: $5.00

- Shipping and design fee: $20.00

Total cost for Ralph's t-shirts = (number of t-shirts * $5.00) + $20.00

2. Frank's t-shirt company:

- Price per t-shirt: $10.00

- No additional fees

Total cost for Frank's t-shirts = number of t-shirts * $10.00

Now you can compare the total costs for each company depending on the number of t-shirts you want to buy.

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To find the length of DK, we can divide the length of DF by 2 as the diagonals of a parallelogram bisect each other.

In parallelogram DEFG, the diagonals DF and EG intersect at point K. If we know the length of DF, we can use the property that the diagonals of a parallelogram bisect each other. This means that DK is equal to half the length of DF. Therefore, to find the length of DK, we can simply divide the length of DF by 2.

Length of DK = Length of DF/2

Hence we can find length of DK by above method.

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the complete questions is:

how would you find the length of dk if you knew the length of df in parallelogram defg? explain.

Answer:

Step-by-step explanation:

Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.

From the problem, we have two equations:

Equation 1: $2a=b+2$

Equation 2: $c=3a$

We can use these equations to solve for $a$, $b$, and $c$.

Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.

Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.

Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.

Thus, the original three-digit number is $abc=824$.

When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.

Therefore, the answer is $\boxed{824}$.

Using the Perpendicular Bisector Theorem, the distance from third base to home plate is 90 feet. This means that all the bases are equidistant from home plate, which is a fundamental property of a baseball diamond.

To find the distance from third base to home plate, we need to use the Perpendicular Bisector Theorem, which states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

First, we draw a baseball diamond with points A, B, C, and D labeled as described in the problem.

Next, we draw the line segment that joins first base (B) and third base (D), and we construct the perpendicular bisector of this segment by drawing a line through the midpoint of BD and perpendicular to BD. Let's label the point where the perpendicular bisector intersects the line that connects home plate (A) and second base (C) as E.

Since E lies on the perpendicular bisector of BD, it is equidistant from B and D. We know that first base (B) is 90 feet from home plate (A), so the distance from home plate to E must also be 90 feet. Therefore, the distance from third base (D) to home plate (A) is also 90 feet.

In conclusion, using the Perpendicular Bisector Theorem, we determined that the distance from third base to home plate is 90 feet.

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Answer:

11.325 %

Step-by-step explanation:

44.50 . . ... .. 100%

0.445. . . . . . . . .1 %

49.54 . . . . . . . .?%

49.54 : 0.445=111.325 %

111.325-100 = 11.325%

Answer:

Step-by-step explanation:

The total amount deducted from her gross income health and disability insurance during each pay period is $72.50.

To calculate the total amount deducted from Asako's gross income for health and disability insurance during each pay period, we need to first determine the cost of each insurance plan after the employer's coverage.

For the $3,500 per year disability insurance plan, Asako's employer covers 90% of the cost, which means Asako is responsible for 10% of the cost.

10% of $3,500 is $350, so Asako's cost for the $3,500 per year disability insurance plan is $350 per year.

For the $1,300 per year disability insurance plan, Asako's employer covers 60% of the cost, which means Asako is responsible for 40% of the cost.

40% of $1,300 is $520, so Asako's cost for the $1,300 per year disability insurance plan is $520 per year.

Since Asako gets paid monthly, we need to divide the annual cost of each insurance plan by 12 to determine the cost per pay period.

For the $3,500 per year disability insurance plan, Asako's cost per pay period is $350 / 12 = $29.17.

For the $1,300 per year disability insurance plan, Asako's cost per pay period is $520 / 12 = $43.33.

Therefore, the total amount deducted from Asako's gross income for health and disability insurance during each pay period is $29.17 + $43.33 = $72.50.

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The mean, median, mode,range, and standard deviation when decreased by 15% becomes $43.96,$31.66,$18.16,$353.47 and $10.12 respectively.

When each purchase decreases by 15%, the new values can be calculated as follows:
Mean: $51.72 * 0.85 = $43.96

It is calculated by adding up all the values and dividing the sum by the number of values.
Median: $37.25 * 0.85 = $31.66

It is calculated by the values from smallest to largest and then selecting the middle value.
Mode: $21.36 * 0.85 = $18.16

It represents the most frequently occurring value in a set of numbers.
Range: $415.85 * 0.85 = $353.47

It represents the difference between the largest and smallest values in a set of numbers.
Standard Deviation: $11.91 * 0.85 = $10.12

It is calculated by taking the square root of the variance.

When each purchase is decreased by 15%, the mean is $43.96, the median is $31.66, the mode is $18.16, the range is $353.47, and the standard deviation is $10.12.

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Answer:

Step-by-step explanation:

The volume of a pyramid can be calculated using the formula:

V = (1/3) * Base Area * Height

To calculate the volume of this pyramid, we need to first find the area of its regular hexagonal base. The formula for the area of a regular hexagon is:

A = (3√3/2) * s^2

where s is the length of one side of the hexagon. Substituting s = 10, we get:

A = (3√3/2) * 10^2 = 259.80 square units (approx)

Now we can use the formula for the volume of a pyramid to find the volume of this pyramid:

V = (1/3) * 259.80 * 12 = 1039.20 cubic units (approx)

Therefore, the approximate volume of the pyramid is 1039.20 cubic units.

1) Factorial - Numbers arranged in a specific order.

2) 0! - An array of numbers.

3) Sigma - A symbol for a sum.

4) Addition series - A series whose terms are formed by addition.

5) Combinations - 1.

6) Geometric series - A series whose terms are formed by multiplication.

7) ! - Permutation.

8) Sequence - A set of elements that does not consider order.

9) Pascal's triangle - A study of likelihoods.

10) Probability - A sum of numbers in a specific order.

11) Arithmetic series - A set of elements in a specific ord

1. Factorial: A product of all positive integers up to a given number (n!). For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

2. Array of numbers 0!: 0! is defined to be 1. This is a convention to simplify mathematical expressions and formulas.

3. Sigma (Σ): A symbol used to represent the sum of a series of numbers, typically written as Σ(expression) with specified lower and upper limits.

4. Series: A sequence of terms formed by adding the terms of a sequence. An example of an addition series is 1 + 2 + 3 + 4 + 5.

5. Combinations: The number of ways to choose a specific subset of items from a larger set without regard to the order in which they are chosen.

6. Geometric Series: A series whose terms are formed by multiplying each term by a constant factor. For example, 1, 2, 4, 8, 16 is a geometric series with a constant factor of 2.

7. Permutation: An arrangement of elements from a set where the order of the elements matters.

8. Sequence: A set of elements that does not consider order. It is a list of numbers or objects arranged according to a specific rule.

9. Pascal's Triangle: A triangular array of numbers in which the first and last number in each row is 1, and each of the other numbers is the sum of the two numbers above it. Pascal's Triangle is used to study the likelihoods and combinatorics.

10. Probability: A measure of the likelihood that a particular event will occur. It is the sum of the probabilities of all possible outcomes in a specific order, expressed as a number between 0 and 1.

11. Arithmetic Series: A set of elements in a specific order where each term is formed by adding a constant difference to the preceding term. For example, 2, 5, 8, 11, 14 is an arithmetic series with a constant difference of 3.

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The solution to the equations obtained using inverse trigonometric function values are;

1. x ≈ 0.65

4. x ≈ 0.95

Trigonometric functions indicates the relationships between the angles in a right triangle and two of the sides of the triangle. Trigonometric functions are periodic functions.

The value of x is obtained from the inverse trigonometric function of the output value of the trigonometric function, as follows;

The inverse function for sine is arcsine

The inverse function for cosine is arccosine

The inverse function for the tangent of an angle is arctangent

1. sin(x) = 0.6051

Therefore; x = arcsine(0.6051) ≈ 0.65 radians

The value of x in the interval [0·π, 2·π] is x ≈ 0.65

4. tan(x) = 1.3972

Therefore, x = arctan(1.3972) ≈ 0.95

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The example describes learned behavior in a living thing is give by Most humans begin to speak when they are one or two years old, option B.

Living creatures include bacteria, fungus, algae, protozoans, plants, and animals. Organisms are another word for living things. Because living things behave differently from nonliving things, scientists can distinguish between the two. On Earth, there are around 1.5 million different species of living organisms, according to scientists.

With the use of their own energy, all living things can move. Plants remain stationary, yet they move their leaves to catch the sunshine. Additionally sensitive or perceptive are living things. Simplest living forms just have a feeling of warmth and cold or can only feel when they are touched.

Chemicals are ingested and expelled by living beings. Carbon dioxide is exhaled and oxygen is inhaled by animals. Through their leaves, green plants absorb carbon dioxide and exhale oxygen. All living things require the vitamins and energy that food provides. Green plants use sunlight to produce their own sustenance. For energy, animals consume both vegetation and other creatures. Waste is also released by organisms.

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Most humans begin to speak when they are one or two years old. This example describes learned behavior in a living thing, as humans learn to speak by observing and imitating the speech of others around them.

Babies first begin to discriminate between distinct sounds, such as vowels and consonants, by listening to the speech of those around them.

The sounds they have heard are then repeated by them. They gradually begin to blend the sounds to create words.

Eventually, when babies hear more spoken language, they start to comprehend the meanings of the words and can utilise them appropriately.

As their vocabulary and linguistic knowledge increase, they become more fluent speakers and are able to communicate effectively. Language acquisition is a difficult process that takes many years of exposure and practise to master.

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