Points E, F, G and H lie on the circle and EG = EH.
HF and EG intersect at K.
ET is a tangent to the circle at E.
Angle FET = 47° and angle FEG = 25°.
Find the value of x.

The rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.

To maximize the area of the pen, we need to create a rectangular shape. We can use all 40 cubes to create a rectangular pen with dimensions 5 x 6 x 2.

To build the pen, we can use 10 cubes for the base layer, then add 15 cubes for the second layer, and finally add 15 cubes for the third layer, creating a total of 40 cubes.

The base layer will be a rectangle with dimensions 5 x 6, and we will use 10 cubes to create it. Then we can stack two more layers of cubes on top of the base layer, each layer will have dimensions 5 x 6 and will use 15 cubes.

To prove that this pen has the largest area that can be made with 40 cubes, we can compare it with other possible shapes. For example, if we try to create a cube-shaped pen, we would only be able to create a cube with side length 3, which would have a volume of 27 and therefore could not use all 40 cubes.

Therefore, the rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.

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The mean of Kelly's second data set doesn't change compared to the mean of her original survey because none of the classmates were given math homework.

To determine the change in the means without calculating the mean of either data set, you can compare the number of data points, the range, and any outliers. If the number of data points and the range are the same and there are no outliers, then the means will be the same.

In this case, since none of the classmates had math homework in both surveys, there are no changes in the data set, and the means remain the same. Therefore, there is no change in the mean of Kelly's second data set compared to her original survey.

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The inequality which is used to represent normal "temperature-range" for  "human-body", is (d) |t − 98.6| ≤ 1.8.

The "average-temperature" of body is = 98.6° F, and it can vary by 1.8°F.

The inequality |t − 98.6| ≤ 1.8 indicates that the absolute difference between the body temperature and the average temperature is less than or equal to 1.8° F.

This means that the body temperature t can vary within a range of 1.8° F from the average temperature of 98.6° F.

Which means, the temperature cam range from :

⇒ 98.6-1.8 ≤ t ≤ 98.6+1.8,

⇒ 96.8 ≤ t ≤ 100.4;

Therefore, the correct inequality is (d) |t − 98.6| ≤ 1.8.

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The given question is incomplete, the complete question is

The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.

(a) |t − 1.8| ≥ 98.6

(b) |t − 1.8| ≤ 98.6

(c) |t − 98.6| ≥ 1.8

(d) |t − 98.6| ≤ 1.8

Answer: |t − 98.6| ≤ 1.8

Step-by-step explanation: If takes then takes then takes then takes then takes.

The greatest whole number that rounds to 500 when rounding to the nearest hundred is 550.

When rounding a number to the nearest hundred, you need to look at the digit in the tens place. If that digit is 5 or greater, you round up the hundreds digit; if it is less than 5, you round down the hundreds digit.

For example, let's say we have the number 2,548. The digit in the tens place is 4, which is less than 5, so we round down the hundreds digit (2) to get 2,500.

Now, if we are looking for the greatest whole number that rounds to 500 when rounded to the nearest hundred, we need to find the largest number that has 5 in the tens place and 0 in the ones place. That number is 550. When we round 550 to the nearest hundred, we get 500.

Therefore, the greatest whole number that rounds to 500 when rounded to the nearest hundred is 550.

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(a) Miguel had the greatest spread in training times.

(b) Adam had the least spread in the middle 50% of training times.

(c) Miguel's training times had a greater range, indicating more variability, while Adam's training times were more consistent and tightly grouped.

(a) To determine which person had the greatest spread, we need to compare the range or variability of their training times. By observing the given data, we can see that Adam's training times range from 92 to 106, resulting in a spread of 14. On the other hand, Miguel's training times range from 85 to 105, resulting in a spread of 20. Therefore, Miguel had the greatest spread of training times.

(b) To determine which person had the least spread in the middle 50% of training times, we need to compare the interquartile range (IQR). By calculating the IQR, we find that Adam's IQR is 9 (from the 25th to the 75th percentile), whereas Miguel's IQR is 7. Since Adam's IQR is greater, it means Miguel had the least spread in the middle 50% of training times.

(c) The answers to parts (a) and (b) indicate that while Miguel had a greater spread of training times overall, Adam's training times had a greater spread in the middle 50%. This suggests that Adam's training times were more concentrated around the median, while Miguel's training times were more spread out.

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a) All of the training times of Adam had the greatest spread.

(b) The middle 50% of the training times of Adam had the least spread.

(c) The answers to Parts (a) and (b) tell us that Adam's training performance may be more stable within that middle 50%, while Miguel's performance is more variable.

(a) Adam's training times had the greatest spread.

To determine this, we can calculate the range of the data sets. For Adam, the range is 106-92 = 14 seconds, while for Miguel, the range is 105-85 = 20 seconds. However, a better measure of spread is the interquartile range (IQR), which focuses on the middle 50% of the data. For Adam, the IQR is 101-97 = 4 seconds, while for Miguel, the IQR is 96-89 = 7 seconds. In both cases, Miguel's data has a greater spread.

(b) Adam's training times had the least spread for the middle 50% of the data. This is demonstrated by the IQR, as mentioned above. For Adam, the IQR is 4 seconds, while for Miguel, it is 7 seconds.

(c) The answers to Parts 2(a) and 2(b) tell us that while Miguel's overall training times have a greater spread, the middle 50% of Adam's training times are more consistent, with less variation. This suggests that Adam's training performance may be more stable within that middle 50%, while Miguel's performance is more variable.

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A quadratic function should have an exponent of 2, a parabola ending its life by going down should have a leading coefficient sign of negative, and either y = x^2 or y = -x^2 can be a valid equation for a quadratic function, with the choice depending on the direction of the desired parabola.

1. The quadratic should have an exponent of 2, as a quadratic is a polynomial of degree 2.
2. A parabola ending its life by going down should have a leading coefficient sign of negative, as this indicates that the quadratic term has a negative coefficient and the parabola opens downwards.
3. Both equations, y = x^2 and y = -x^2, are valid equations for a quadratic function. The main difference between them is the direction in which the parabola opens. The equation y = x^2 represents a parabola that opens upwards, while y = -x^2 represents a parabola that opens downwards. The choice of which equation to use depends on the specific context and the direction of the desired parabola.

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Answer:

x = 73, y = 88, z = 45

Step-by-step explanation:

40+52+y = 180 (Angle Sum Property)

=> y = 180-40-52

=> y = 88

x + (15 + 40) + 52 = 180 (Angle Sum Property)

=>x = 180 - 52 - 55

=> x = 73

40 + 43 + (52+z)  = 180

=> z = 180 -53 - 40 -43

=> z = 45

Answer:

To make the polynomial 9x^10 + ax^b + 100 a perfect square trinomial, we need to add a constant term to it such that it becomes a square of a binomial.

Let's first write the square of a binomial in general form:

(a + b)^2 = a^2 + 2ab + b^2

If we compare this general form with our polynomial, we can see that the first term, 9x^10, is equal to (3x^5)^2, which means that we can write our polynomial as:

(3x^5)^2 + ax^b + 100 = (3x^5 + c)^2

Expanding the right-hand side of this equation, we get:

(3x^5 + c)^2 = 9x^10 + 6cx^15 + c^2

Comparing the coefficient of x^15 on both sides, we get:

6c = 0

Since c cannot be zero (otherwise we would end up with the original polynomial), this means that we must have:

c = 0

Therefore, we can write our polynomial as:

(3x^5)^2 + ax^b + 100 = (3x^5)^2

Expanding the right-hand side, we get:

(3x^5)^2 = 9x^10

Therefore, we must have:

a = 0

b = 10

So the values of a and b that make the polynomial 9x^10 + ax^b + 100 a perfect square trinomial are a = 0 and b = 10.

It is not possible to use n = 10.

It is not possible to use n = 20.

It is possible to use n = 25.

1. The error probabilities for n = 10 are as follows:

- P-value: It is not possible to use n = 10 because there is no value of x which results in a p-value.
- Beta (0.3): B(0.3) > 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too high.

Therefore, it is not possible to use n = 10.

2. The error probabilities for n = 20 are as follows:

- P-value: It is not possible to use n = 20 because it results in a beta error probability (B(0.3)) < 0.1, which means the probability of incorrectly rejecting the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too low.
- Beta (0.3): B(0.3) > 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too high.

Therefore, it is not possible to use n = 20.

3. The error probabilities for n = 25 are as follows:

- P-value: P(0.3) < 0.1, which means the probability of incorrectly rejecting the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is low enough to proceed with production.
- Beta (0.3): B(0.3) < 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is low enough to proceed with production.

Therefore, it is possible to use n = 25.

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Area of sector = 161.1 square inches

Activity 1:

The radius of the pizza is half of its diameter, which is 16/2 = 8 inches.

The central angle of the sector is 80%, which is 0.8 times 360 degrees = 288 degrees.

To find the area of the sector, we use the formula:

Area of sector = (central angle / 360) x πr^2

Area of sector = (288 / 360) x π x 8^2

Area of sector = (0.8) x π x 64

Area of sector = 161.1 square inches (rounded to the nearest tenth)

Activity 2:

The unit of measurement for the area of the sector is square inches (in²).

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Keegan will have approximately $878.85 in the account after 5 years.

What is Compound interest ?

Compound interest is the interest that is earned not only on the initial amount of money invested (known as the principal), but also on any interest earned on that principal over time. In other words, compound interest is interest on interest.

The compound interest formula is given by:

A = P[tex](1 + r/n)^{nt}[/tex]

where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, Keegan deposited $675, the annual interest rate is 4.8%, the interest is compounded quarterly, and the investment is for 5 years. Therefore, we can plug in these values into the formula to get:

A = 675[tex](1 + 0.048/4)^{20}[/tex]

A = 675[tex](1.012)^{20}[/tex]

A ≈ $878.85

Therefore, Keegan will have approximately $878.85 in the account after 5 years.

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If he water in Earth’s oceans has a volume of about 3.2x10⁸ cubic miles, it would take 3.52x10²⁰ gallon jugs to hold all the water in Earth's oceans.

To calculate how many gallon jugs it would take to hold all the ocean water on Earth, we need to multiply the volume of the water by the conversion factor from cubic miles to gallons.

Given that the water in Earth's oceans has a volume of about 3.2x10⁸ cubic miles and there are about 1.1x10¹² gallons in 1 cubic mile, we can calculate the total number of gallons using the following equation:

Total gallons = (Volume in cubic miles) x (Gallons per cubic mile)

Substituting the given values, we get:

Total gallons = (3.2x10⁸) x (1.1x10¹²) = 3.52x10²⁰

This number is very large and is written in scientific notation to make it more manageable. Scientific notation is a compact way of writing very large or very small numbers using a power of ten. In this case, the number is expressed as a coefficient (3.52) multiplied by 10 raised to the power of 20 (10²⁰).

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In order for a triangle to be acute, the relationship that c² must have with a² + b² is c² < a² + b².

An acute triangle is a triangle in which all three angles are acute angles, which means they are less than 90 degrees. In other words, an acute triangle is a triangle with three acute angles.

To understand why the relationship between c^2 (the square of the longest side) and a^2 + b^2 (the sum of the squares of the other two sides) is important in determining whether a triangle is acute, we need to delve into the concept of the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as c^2 = a^2 + b^2, where c represents the hypotenuse, and a and b represent the other two sides.

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side.

This can be visualized as follows: If we were to draw a right triangle with the shorter sides represented by segments a and b, and the longest side represented by segment c, the acute triangle would be formed by making the length of segment c shorter than the length determined by the Pythagorean theorem. This ensures that the angle opposite to the longest side remains acute.

On the other hand, if c^2 were equal to a^2 + b^2, we would have a right triangle, not an acute triangle. If c^2 were greater than a^2 + b^2, we would have an obtuse triangle since the angle opposite to the longest side would be greater than 90 degrees.

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The answer to the first question is: Burger Quick, because it has a larger median.

The answer to the second question is: Histogram, because it can show the frequency distribution of the continuous variable "number of carbohydrates" and group the data into intervals.

A histogram is a graphical representation of a distribution of numerical data. It consists of a series of bars, where each bar represents a range of values of the data and the height of the bar indicates the frequency or count of data points falling within that range.

In a histogram, the horizontal axis represents the range of values or intervals of the data, called bins, and the vertical axis represents the frequency or count of data points falling within each bin. The bins can be of equal or unequal width depending on the nature of the data.

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The amount of interest earned by Mr. Jones's retirement account over 5 years is $79,025.

Mr. Jones has invested $410,000 in a retirement account that earns 3.85% simple interest per year. Simple interest is calculated by multiplying the principal amount by the annual interest rate and the time period in years.

In this case, the time period is 5 years. Using the formula for simple interest, we can calculate the amount of interest earned on this investment as:

I = P * r * t = $410,000 * 0.0385 * 5 = $79,025

Therefore, the amount of interest earned by Mr. Jones's retirement account over 5 years is $79,025. This means that the total value of his retirement account after 5 years would be $489,025 ($410,000 + $79,025).

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The value of x in the given circle is 18.1 units.

Given is a circle, where two radii are given one chord is given,

We need to find the value of the x which is also the radius,

We know all the radii in a circle are equal,

So, here the radius = 7.9+10.2 = 18.1 units.

Hence the value of x in the given circle is 18.1 units.

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The fraction of her clothes that is left is 1/8.

To solve this problem, we first need to determine the fractions of clothes Christen sells to Maria and Alexandra. Christen sells 5/8 of her clothes to Maria and 1/4 to Alexandra. To find the total fraction of clothes sold, we can add these two fractions:

(5/8) + (1/4)

To add fractions, we need a common denominator. In this case, the least common denominator is 8. We can convert 1/4 to 2/8:

(5/8) + (2/8) = 7/8

Christen sold 7/8 of her clothes to Maria and Alexandra. To find the fraction of clothes left, we subtract this value from the total, which is 1:

1 - (7/8) = 1/8

So, Christen has 1/8 of her clothes left after selling to Maria and Alexandra.

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(a) The value of the constant is 1/24, (b) P(X<=1,Y<=1)  is 5/48 and (c)  P(X + Y <= 1) is also 5/48

(a) The constant C can be found by using the fact that the total probability of the joint density function over the entire space is equal to 1. Therefore, we integrate the joint density function over the region where it is defined and set it equal to 1:

∫∫f(x,y) dA = 1

∫[0,2]∫[0,4] Cx(1+y) dy dx = 1

C∫[0,2]x[(y+(y²)/2)] [0,4] dx = 1

C(24/5) = 1

C = 5/24

(b) To find P(X <= 1, Y <= 1), we integrate the joint density function over the region where X <= 1 and Y <= 1:

P(X<=1,Y<=1) = ∫[0,1]∫[0,1] (5/24) x(1+y) dy dx

= (5/24) ∫[0,1] x(1+(1/2)) dx

= (5/24) [(1/2) + (1/6)]

= 5/48

(c) To find P(X + Y <= 1), we integrate the joint density function over the region where X + Y <= 1:

P(X+Y<=1) = ∫[0,1]∫[0,1-x] (5/24) x(1+y) dy dx

= (5/24) ∫[0,1] x(1+(1-x)/2) dx

= (5/24) [(1/2) - (1/12)]

= 5/48

Therefore, P(X + Y <= 1) = 5/48.

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Answer:

There are 6 goldfish in each of the 3 aquariums at Joe's fish store.

Step-by-step explanation:

To find out how many goldfish are in each aquarium, we can divide the total number of goldfish by the number of aquariums:

Therefore, there are 6 goldfish in each of the 3 aquariums at Joe's fish store.

The parametric equations for the tangent line to curve C at point P are: x = -t y = 6t - 1 z = 8t + 6

To find the parametric equations for the tangent line to curve C at point P, we need to first find the derivative of the curve at P.

Taking the derivative of each component of the curve, we get:

dx/dt = -1

dy/dt = -6t

dz/dt = 8

At point P = (0, -1, 6), t = -1.

Plugging this into the derivative, we get:

dx/dt = -1

dy/dt = 6

dz/dt = 8

So, the tangent vector to curve C at point P is < -1, 6, 8 >.

To get the parametric equations for the tangent line, we can use the point-slope form: r(t) = P + t< -1, 6, 8 > Plugging in the coordinates of point P, we get: r(t) = <0, -1, 6> + t< -1, 6, 8 > Expanding this out, we get: r(t) = <-t, 6t - 1, 8t + 6>

So, the parametric equations for the tangent line to curve C at point P are: x = -t y = 6t - 1 z = 8t + 6

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If the first cube has a volume of 125 cm³ and the second cube has a volume of 343 cm³, the difference in the area of one face of the second cube and the area of one face of the first cube is 24cm². The answer is B. 24 cm².

To find the difference in the area of one face of each cube, we first need to find the side length of each cube. Since the volume of a cube is equal to the side length cubed (V = s³), we can find the side length by taking the cube root of the volume.

For the first cube:
Volume = 125 cm³
Side length = cube root of 125 = 5 cm

For the second cube:
Volume = 343 cm³
Side length = cube root of 343 = 7 cm

Next, we find the area of one face of each cube. The area of one face of a cube is equal to the side length squared (A = s²).

Area of one face of the first cube:
A1 = 5² = 25 cm²

Area of one face of the second cube:
A2 = 7² = 49 cm²

Finally, find the difference in the area of one face of each cube:
Difference = A2 - A1 = 49 cm² - 25 cm² = 24 cm²

The answer is B. 24 cm².

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The height of tank which is 65 cm wide and 85 cm long is 40 cm and when it is 3/4 filled the water height is 30cm.

Mika can follow these steps to find the height of the water:

1. Convert the volume from liters to cubic centimeters: 221 L * 1000 cm³/L = 221,000 cm³
2. Calculate the total volume of the tank: V = lwh (where V is the volume, l is the length, w is the width, and h is the height)
3. Solve for the height of the tank: 221,000 cm³ = 65 cm * 85 cm * h
4. Calculate the height of the tank: h = 221,000 cm³ / (65 cm * 85 cm) ≈ 40 cm
5. Since Mika plans to fill the tank 3/4 full, calculate the height of the water: (3/4) * 40 cm = 30 cm

So, the correct steps are:

- Divide the volume by the length and width to find the height
- Calculate the total volume of the tank
- Find the height of the tank
- Calculate the height of the tank
- Calculate the height of the water when the tank is 3/4 full

The height of the water will be 30 cm.

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An equation representing the statement that 282828 is 121212 less than kkk is kkk = 282828 + 121212.

An equation is a mathematical statement showing that two or more mathematical or algebraic expressions share equality or equivalence.

Equations are represented using the equal symbol (=).

Unlike equations, mathematical expressions do not use the equal symbol.

282828 = kkk - 121212

kkk = 282828 + 121212

Thus, one way of representing the statement that that 282828 is 121212 less than kkk is by forming an equation like kkk = 282828 + 121212.

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(a) The marginal cost function is C'(x) = 5 + 0.16x + 0.0012x².

(b) C'(100) = 21.00. This predicts the approximate cost of the 101st pair of jeans.

(c) The difference between C'(100) and the actual cost of manufacturing the 101st pair of jeans is $20.51.

(a) To find the marginal cost function, we need to take the derivative of the cost function C(x) with respect to x:

C'(x) = 5 + 0.16x + 0.0012x²

(b) To find C'(100), we substitute x = 100 into the marginal cost function:

C'(100) = 5 + 0.16(100) + 0.0012(100)²
C'(100) = 21.00

This predicts the approximate cost of the 101st pair of jeans, as the marginal cost function tells us the cost of producing one additional unit (pair of jeans) at a given quantity. So, we can use C'(100) to estimate the cost of producing the 101st pair of jeans.

To find the approximate cost of the 100th pair of jeans, we can substitute x = 100 into the cost function C(x):

C(100) = -1700 + 5(100) + 0.08(100)² + 0.0004(100)³
C(100) = $2330

So, the approximate cost of the 100th pair of jeans is $2330.

To find the approximate cost of the 101st pair of jeans, we can add C'(100) to the cost of producing 100 pairs of jeans:

C(100) + C'(100) = $2330 + $21.00
C(101) ≈ $2351

So, the approximate cost of the 101st pair of jeans is $2351.

To find the exact cost of the 99th pair of jeans, we can substitute x = 99 into the cost function C(x):

C(99) = -1700 + 5(99) + 0.08(99)² + 0.0004(99)³
C(99) = $2288.44

So, the exact cost of the 99th pair of jeans is $2288.44.

(c) To find the difference between C'(100) and the actual cost of manufacturing the 101st pair of jeans, we need to subtract the cost of producing 100 pairs of jeans from the cost of producing 101 pairs of jeans:

C(101) - C(100) = [-1700 + 5(101) + 0.08(101)² + 0.0004(101)³] - [-1700 + 5(100) + 0.08(100)² + 0.0004(100)³]
C(101) - C(100) = $20.51

So, the difference between C'(100) and the actual cost of manufacturing the 101st pair of jeans is $20.51.

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The watermelon is hitting the ground at around 10.33 seconds.

To find out when the watermelon hits the ground, we need to look for the time when the height of the watermelon is zero. This is because the watermelon will be on the ground at that point.

The x-intercepts of the function h(t) give us the times when the height is zero. So, we know that the watermelon will hit the ground at t = -0.33 seconds and t = 10.33 seconds.

However, the negative value doesn't make sense in this context, so we can ignore that solution. Therefore, the watermelon is hitting the ground at around 10.33 seconds.

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product rule, chain rule, and sum rule are utilized to assess a subordinate of y = sin(x)cos(x), a subsidiary of y = sin(cos(x)), a subordinate of y = sin(-x), a subsidiary of y = sin(x) + cos(x).

a) subordinate of y = sin(x)cos(x) can be assessed by utilizing the product rule.

[tex]y' = (cos(x))(cos(x)) + (sin(x))(-sin(x)) = cos^2(x) - sin^2(x)[/tex]

b) chain rule is used  to find the derivative of y = sin(cos(x)):

y' = (cos(x))(cos(cos(x)))

c) chain rule is used  to find the derivative of y = sin(-x):

y' = -cos(-x) = -cos(x)

d) derivative of y = sin(x) + cos(x)  can be evaluated by using sum rule

y' = cos(x) - sin(x)

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The red arc or chord in the key of C, or the solution to the provided question based on the circle, is 11.

A chord is a piece of a straight line that connects two points on a circle's circumference. When it crosses the circle at two different locations, it is also occasionally referred to as a secant.

The following formula can be used to determine a chord's length:

chord length = 2*radius*sin(angle/2)

where angle is the central angle that the chord is subtended by, and radius is the radius of the circle. In geometry and trigonometry, chords are frequently used to compute circle properties including area, circumference, and arc length.

Since the circle P ≅ circle C

In circle P the radius of PN =7 and

chord LM = 11 with an angle 104°

And  In circle C  the radius =7 and Circle and chord QR are both making the same angle. P = 104°

So the circle P ≅ circle C

The red arc or chord in C is consequently 11.

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