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The angles that form a linear pair is 6 and 8.

option C.

Linear pair angles are two adjacent angles formed by two intersecting lines. These two angles are always supplementary, which means that their sum is equal to 180 degrees. In other words, if we add the measure of one angle to the measure of the other angle, we will get a total of 180 degrees.

A linear pair of angles can be easily identified by observing the angles formed when two straight lines intersect each other. For example, if line AB intersects line CD at point E, then the two pairs of adjacent angles formed are:

Each pair of adjacent angles in a linear pair is supplementary, which means that ∠AED + ∠DEB = 180 degrees and ∠CEB + ∠BED = 180 degrees.

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Step-by-step explanation:

3.2  liters    divided by 300 ml / bottle is

3200 ml / 300 ml/bottle = 10 2/3 bottles  

             10 full bottles plus 2/3 of a bottle left over

                        2/3 bottle * 300 ml/bottle = 200 ml left over

Answer:

1/72

Step-by-step explanation:

There are a total of 17 students in the class, and we want to choose one boy from 9 and one girl from 8 without replacement. The total number of ways to choose two students from the class is:

17C2 = (17!)/(2!15!) = (1716)/(21) = 136

To choose a boy and a girl, we can choose the boy in 9 ways and the girl in 8 ways, for a total of 9*8 = 72 ways.

Now, since the brother and sister are both in the class, there is only one way to choose them together. Therefore, the probability of choosing the brother and sister is:

1/72

So the probability is 1/72, written as a fraction in simplest form.

Approximately 40.4 defective items in a sample of 101 items from this manufacturing machine with a 40% defect rate. The correct symbol for this random variable is X.

For this specific question, the random variable can be described as the number of defective items in a sample of 101

items taken from a manufacturing machine with a 40% defect rate. The correct wording for the random variable in this

case is "the number of defective items in a sample of 101 items."

The correct symbol for this random variable is X, which is often used to represent an unknown variable. Therefore, the

random variable can be written as X = the number of defective items in a sample of 101 items.

To find the expected number of defective items in this sample, we can use the formula for the expected value of a

discrete random variable: E(X) = np, where n is the sample size and p is the probability of the event of interest (in this

case, the probability of an item being defective).

Using this formula, we can calculate the expected number of defective items in the sample as:

E(X) = (101)(0.4) = 40.4

Therefore, we would expect to find approximately 40.4 defective items in a sample of 101 items from this manufacturing

machine with a 40% defect rate.

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Answer:

the length of the rectangle is 21 feet.

Step-by-step explanation:

Let's use "w" to represent the width of the rectangle. According to the problem, the length is three times the width, so we can use "3w" to represent the length.

The perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

Substituting the expressions for length and width, we get:

56 = 2(3w + w)

Simplifying the right side, we get:

56 = 2(4w)

56 = 8w

w = 7

So the width of the rectangle is 7 feet. To find the length, we can use the expression we derived earlier:

length = 3w = 3(7) = 21

Therefore, the length of the rectangle is 21 feet.

The coordinates of the image based on the transformation rule (x, y) → (x - 2, y) include the following:

A' (2, -4).

B' (3, -4).

C' (3, -1).

D' (2, -1).

In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

By translating the pre-image of quadrilateral ABCD horizontally right by 4 units, the coordinates of quadrilateral ABCD include the following:

(x, y)                               →                  (x - 2, y)

A (4, -4)                        →                  (4 - 2, -4) = A' (2, -4).

B (5, -4)                        →                  (5 - 2, -4) = B' (3, -4).

C (5, -1)                        →                  (5 - 2, -1) = C' (3, -1).

D (4, -1)                        →                  (4 - 2, -1) = D' (2, -1).

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The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

What is probability?

The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.

The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.

To find the probability of both events occurring together, we multiply the probabilities:

P(blue and even number) = P(blue) x P(even number)

P(blue and even number) = (1/3) x (1/2)

P(blue and even number) = 1/6

Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

What is spinner?

A spinner is a device or a toy used to randomly select or generate a value or outcome. It consists of a circular board or disc, often divided into sections of different colors or with different values or symbols, and a pointer or arrow that is spun around the disc to land on a particular section. Spinners are commonly used in games, educational activities, and statistical experiments to create random outcomes or to simulate probability distributions.

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Complete question is: The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

Answer:

Step-by-step explanation:

The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.

The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.
To find the probability of both events occurring together, we multiply the probabilities:

P(blue and even number) = P(blue) x P(even number).

P(blue and even number) = (1/3) x (1/2).

P(blue and even number) = 1/6.

Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

Answer:

b = 8.485

c = 23.995 ≈ 24

Step-by-step explanation:
Part b:

[tex]\sqrt{(10-4)^2+(9-3)^2}[/tex]

√(36 + 36)

= 8.485

Part c:

Base = [tex]\sqrt{(6-2)^2+(1-5)^2}[/tex]

Base = 5.656

Area = Base x Height x 0.5

Area = 5.656 x 8.485 x 0.5

Area = 23.995 ≈ 24

The information makes sense in different scenarios like manufacturing, baking, researching survey, etc.

A sample is a portion of a population that is used to represent the full population in statistics. Researchers frequently utilise samples to draw conclusions about the population since it might be difficult or impossible to collect data from the complete population. In order for the conclusions made from the sample to be applicable to the entire population, it is important to pick a sample that is representative of the wider population. Many techniques, such as cluster sampling, stratified sampling, and random sampling, can be used to choose samples.

The knowledge of biscuit preferences may come in handy in a variety of situations. Here are three potential instances:

A biscuit manufacturer wants to launch a brand-new taste. They may opt to create a chocolate chip or peanut butter flavor as those are the most popular ones based on the preferences data.

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Complete question -

A national sampling of cookie preferences showed that 75% of people like chocolate chip, 50% like peanut butter, and only 3% like coconut. The use of this information makes sense in which of the following scenarios? A. The school cafeteria decides to make 3 coconut cookies for each 100 students who buy lunch, even though it puts them over budget for desserts. B. A national cookie company is thinking of changing the recipe in their peanut butter cookies. C. A national cookie company decides to spend $5 million in advertising to convince people to eat coconut cookies. D. Tom is about to open a small bakery and is using the result of the sampling to decide what kind of cookies to offer.

As a result, the monument's shadow is approximately 28.9 metres long as the monument's height is on the other side .

The length of an object or the separation of two points is a measurement of its size in one dimension. It is an important physical quantity that is employed in many disciplines, including physics, technology, and daily life. Depending on the situation, length is typically expressed in quantities like metres (m), centimetres (cm), feet (ft), inch (in), and miles (mi).

given

Assume that the monument's shadow extends "x" metres in length.

Because we are aware of the monument's height and the sun's elevation angle, we can use the tangent function to get "x":

tan(60) = adjacent/opposite

where the monument's height is on the other side, and the shadow's length is right next to it.

Adding the values we obtain:

tan(60) = 50/x

To solve for "x," we obtain:

x = 50/tan(60) (60)

(Using the value of the tangent of 60 degrees, which is 3 or 1.732) x = 50/1.732

28.9 metres x

As a result, the monument's shadow is approximately 28.9 metres long as the monument's height is on the other side .

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Answer:

$1529

Step-by-step explanation:

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the final amount (balance) in the account

P = the initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = the annual interest rate (as a decimal)

t = the time period (in years)

Plugging in the given values, we get:

A = 1000e^(0.0855)

A = 1000*e^0.425

A = 1000*1.529

A = 1529

Therefore, the balance after 5 years with continuous compounding at 8.5% interest rate is $1529.

The required Jane is approximately 59.28 inches tall.

Height is a measurement of vertical distance, either in terms of vertical extent (how tall an object or person is) or in terms of vertical position (how high a point is). "The height of that building is 50 meters" or "The height of an airplane in flight is approximately 10,000 meters" are two examples.

Sylvia's height can be represented as:

Sylvia’s height =56[tex]\frac{3}{4}[/tex] inches

Bill is [tex]\frac{1}{3}$[/tex] of 8 inches taller than Sylvia, which means that Bill's height is:

[tex]$\begin{align*}\text{Bill's height} &= \text{Sylvia's height} + \frac{1}{3} \times 8\ \text{inches} \&= 56 \frac{3}{4}\ \text{inches} + \frac{8}{3}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches}\end{align*}[/tex]

Jane is [tex]1 \frac{1}{5}$[/tex] inches taller than Bill, which means that Jane's height is:

[tex]$\begin{align*}\text{Jane's height} &= \text{Bill's height} + 1 \frac{1}{5}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches} + 1 \frac{1}{5}\ \text{inches} \&= 59 \frac{17}{60}\ \text{inches}\end{align*}[/tex]

Therefore, Jane is approximately 59.28 inches tall.

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Answer:

6.00 %

Step-by-step explanation:

Percent = amount donated/total sales × 100 %

              = 429/7150 × 100 %

              = 6.00 %

The store donated 6.00 % of its sales to charity.

The new dimensions of the poster will be 5 in by 6 in.

In mathematics, scaling is the process of adjusting a geometric form or figure's size by a predetermined factor or ratio. With scaling, a shape's dimensions are all multiplied by the same quantity. Depending on whether the scaling factor is more than 1 or less than 1, respectively, scaling can either make the form larger or smaller. In addition to science, engineering, and computer graphics, scaling is frequently utilised in trigonometry, geometry, and other areas of mathematics.

Given that the scale factor = 1/3.

Thus, the new dimensions are:

New length = 15 in x (1/3) = 5 in

New width = 18 in x (1/3) = 6 in

Hence, the new dimensions of the poster will be 5 in by 6 in.

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The expression that is equal to 9 is 10 − (one-fifth x 10) + 1.

Basic mathematical procedures known as arithmetic are used to calculate using numbers. Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations. Finding the sum of two or more numbers is done using addition, finding the difference between two numbers is done using subtraction, finding the product of two or more numbers is done using multiplication, and finding the quotient of two numbers is done using division. There are more operations outside these four, such as square root and exponentiation (increasing a number to a power) (finding the root of a number).

For the given expressions we have:

4 x (one-half x 6) ÷ 3 = 4 x 3 ÷ 3 = 4 --> not equal to 9

6 ÷ (one-fourth x 3 x one and one-fourth) = 6 ÷ (3/4 x 5/4) = 6 ÷ (15/16) = 96/15 --> not equal to 9

8 + (one-third x 6) ÷ 5 = 8 + 2 ÷ 5 = 8.4 --> not equal to 9

10 − (one-fifth x 10) + 1 = 10 - 2 + 1 = 9 --> equal to 9

Hence, the expression that is equal to 9 is 10 − (one-fifth x 10) + 1.

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Answer:

The amplitude of this graph is 4.

mAD is 74 ° .we can get this answer by using properties of chord and also using fact that  the sum of angles in a quadrilateral is 360 degrees

what is properties of chord?

A chord is a straight line segment that joins two points on the circumference of a circle. Here are some properties of chords

1)The length of a chord is less than the diameter of the circle.

2) A chord that passes through the center of the circle is a diameter, which is the longest chord in a circle.

In the given question,

angle CAD = 180 - angle ADC - angle DCA

= 180 - 102 - 62

= 16 degrees

Now, we can use the fact that angles that subtend the same arc are equal. In particular, angles CAD and ABD subtend the same arc AD, so we have:

angle ABD = angle CAD = 16 degrees

Similarly, angles ADB and ACB subtend the same arc AB, so we have:

angle ACB = angle ADB

Now, we can use the fact that the sum of angles in a quadrilateral is 360 degrees. In particular, we have:

angle ABD + angle BAC + angle CAD + angle ACB = 360

Substituting the values we know, we get:

16 + angle BAC + 16 + angle ADB = 360

Simplifying, we get:

angle BAC + angle ADB = 328

But we also know that angle BAC + angle ADB + angle BAD = 180 degrees (since they form a triangle). Substituting the value we just found, we get:

328 + angle BAD = 180

Solving for angle BAD, we get:

angle BAD = 180 - 328 = -148 degrees

Wait, a negative angle? What's going on here? Well, it turns out that angles are usually measured in a counterclockwise direction, so if we go clockwise instead, we can end up with negative angles. In this case, we can think of angle BAD as a clockwise rotation from DB to BA, which is why it's negative.

But we can fix this by adding 360 degrees to angle BAD, which will bring it back into the range of 0 to 360 degrees. So:

angle BAD = -148 + 360 = 212 degrees

Now, we can use the fact that angles that subtend the same arc are equal again. In particular, angles ABD and ACD subtend the same arc AD, so we have:

angle ABD = angle ACD

Substituting the values we know, we get:

16 = angle ACD

Finally, we can use the fact that the sum of angles in a triangle is 180 degrees again. In particular, we have:

angle ADC + angle ACD + angle CDA = 180

Substituting the values we know, we get:

102 + 16 + angle CDA = 180

Simplifying, we get:

angle CDA = 62 degrees

But we also know that angles ACD and ADB subtend the same arc AD, so they're equal. Therefore:

angle ADB = angle ACD = 16 degrees

Now we can use the fact that the sum of angles in a triangle is 180 degrees again to find mAD:

angle ADB + angle ABD + angle BAD = 180

Substituting the values we know, we get:

16 + 16 + 212 = 180

Simplifying, we get:

mAD = (180 - 32) / 2 = 74 degrees

Therefore, mAD is 74 degrees

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Population proportion: The proportion of people aged under 40 who have savings accounts is the population proportion. This can be calculated as follows:Population proportion = (number of savings accounts belonging to people under 40) / (total number of savings accounts).

Population proportion = 4675/13500Population proportion = 0.3463 (rounded to four decimal places)Mean and standard deviation of the sampling distributionFor a given sample size, the mean and standard deviation of the sampling distribution can be calculated as follows:

Mean of sampling distribution = population proportionStandard deviation of sampling distribution = sqrt[(population proportion * (1 - population proportion)) / n]where n is the sample size.For this question, the sample size is not given, so we cannot calculate the mean and standard deviation of the sampling distribution.

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Answer:

- 5 , - 3 , 3

Step-by-step explanation:

to find the first three terms, substitute n = 1, 2, 3 into the explicit formula

[tex]T_{n}[/tex] = 2n² - 4n - 3

T₁ = 2(1)² - 4(1) - 3

    = 2(1) - 4 - 3

    = 2 - 7

    = - 5

T₂ = 2(2)² - 4(2) - 3

    = 2(4) - 8 - 3

    = 8 - 11

    = - 3

T₃ = 2(3)² - 4(3) - 3

    = 2(9) - 12 - 3

    = 18 - 15

    = 3

the first three terms are - 5, - 3 , 3

Below are the three angles listed out in both radians and degrees:

Let us assume that point P is initially at the topmost point of the wheel, and Q is directly to the right of P.

When the wheel rotates counterclockwise, point P moves along a circle with radius 1 foot, centered at the center of the wheel. To end up at position Q, point P needs to move a quarter of the way around the circle, or pi/2 radians. Therefore, one angle that the wheel can rotate is pi/2 radians (or 90 degrees).

Another angle that the wheel can rotate is 5*pi/2 radians (or 450 degrees), which corresponds to rotating the wheel counterclockwise almost all the way around the circle, but stopping just short of completing a full rotation.

A third angle that the wheel can rotate is 9*pi/2 radians (or 810 degrees), which corresponds to rotating the wheel counterclockwise almost twice around the circle, but stopping just short of completing two full rotations.

Therefore, Note that there are a lot of many other angles that the wheel can rotate to end up at position Q, but these three examples give an idea of the possibilities.

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As per the mentioned informations and values provided, the mean from this sample frequency distribution is calculated to be approximately 160.50.

To find the mean from the given sample frequency distribution, we need to first calculate the midpoint for each class interval, then multiply it by the corresponding frequency, sum all of these products, and finally divide by the total frequency.

Using the formula: mean = (sum of midpoint x frequency) / (sum of frequency)

Midpoint for the first interval = (0 + 70) / 2 = 35

Midpoint for the second interval = (70 + 200) / 2 = 135

Midpoint for the third interval = (200 + 500) / 2 = 350

Now we can calculate the sum of midpoint x frequency:

35 x 73 + 135 x 37 + 350 x 182 + 232 x 500 = 84,166

The total frequency is the sum of all frequencies: 73 + 37 + 182 + 232 = 524

Finally, we can calculate the mean:

mean = (sum of midpoint x frequency) / (sum of frequency) = 84,166 / 524 ≈ 160.50

Therefore, the mean from this sample frequency distribution is approximately 160.50.

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The correct option for the quadratic function g are-

Mathematical expressions with a two as the highest power are called quadratic functions. A function or numerical statement of degree two is a quadratic function. This indicates that two is the function's highest power.

The correct option for the given quadratic function g from the graph are-

Correction for the incorrect statements:

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Answer:

C. Approximately 3 hens per square meter

When the pressure is 2.6 g/m² then the depth is 3.9 m.

The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.

Given that

the pressure varies directly with the depth. When the pressure is 320 g/m² the depth is 480 m.

We need to find the depth if the pressure is 2.6 g/m².

So, here we will use the concept of proportionality,

Let the unknown depth be x,

So,

320 / 480 = 2.6 / x

2 / 3 = 2.6 / x

2x = 7.8

x = 3.9

Hence when the pressure is 2.6 g/m² then the depth is 3.9 m.

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complete question:

Pressure varies directly with the depth. When the pressure is 320 grams per square meter the

depth is 480 meters. What is the depth, in meters, when the pressure is 2.6 grams per square

meter? (Round to the nearest tenth)

A 1.7 grams

B 1.9 grams

C 3.7 grams

D 3.9 grams

Answer:

1

Step-by-step explanation:

One to any exponent is just 1 so this fraction simplifies to 1/1 or just simply 1

Answer:

1 or 1 / 1.

Step-by-step explanation:

Square the numbers:

1^22 / 1^7

Any number squared with 1 is always 1:

1 / 1

= 1 or 1 / 1

580.017 is equivalent to 580 tenths and 17 thousandths.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

The number that is equal to 580 tenths and 17 thousandths is 580.017.

To understand this, we need to understand the place value system used in decimal notation. Each digit in a decimal number has a place value that is a power of 10. The rightmost digit represents the ones place, the next digit to the left represents the tens place, and so on.

In the number 580.017, the digit in the ones place is 0, the digit in the tens place is 1, the digit in the hundreds place is 7, the digit in the thousands place is 0, the digit in the ten-thousands place is 8, and the digit in the hundred-thousands place is 5.

Thus, the number 580.017 can be written as the sum of the digits multiplied by their corresponding place values:

580.017 = 5 x 100,000 + 8 x 10,000 + 0 x 1,000 + 0 x 100 + 1 x 0.1 + 7 x 0.01

Simplifying this expression, we get:

580.017 = 500,000 + 80,000 + 0 + 0 + 0.1 + 0.17

580.017 = 580,000 + 0.017

Therefore, 580.017 is equivalent to 580 tenths and 17 thousandths.

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the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

To find the height h of point P, we can use the sine function, which relates the opposite side of a right triangle (in this case, the height h) to the hypotenuse (in this case, the length of the windmill blade, which is 1.5 feet). The angle between the opposite side and the hypotenuse is the complement of the angle of rotation a, which is π/4 radians minus the angle between the ground and the windmill blade, which is arctan(6/1.5) or approximately 1.3258 radians.

So, the equation for the height h of point P after the windmill blade rotates by an angle of a is: h = 1.5 sin(π/4 - arctan(6/1.5))

Therefore, the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.

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According to the solution we have come to find that, The possible coordinates of point A are (2,-2) and (2,4).

Geometry is a branch of mathematics that deals with the study of spatial relationships and properties of objects. It is concerned with the study of shape, size, position, and relative orientation of objects, as well as their properties such as angles, lines, curves, surfaces, and solids. Geometry is used extensively in various fields, including architecture, engineering, physics, astronomy, and computer graphics. The study of geometry involves using logic and reasoning to analyze and solve problems related to shapes and spatial relationships. It is an important subject that has practical applications in many areas of everyday life.

To find the possible coordinates of point A, we need to use the distance formula and the fact that the x-coordinate of point A is 2.

The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) are the coordinates of point A, (x2, y2) are the coordinates of point B, and d is the distance between the two points.

We know that the distance between point A and point B is 5 units:

5 = √((5 - 2)² + (1 - y1)²)

Squaring both sides:

25 = (5 - 2)²+ (1 - y1)²

Simplifying:

9 = (1 - y1)²

Taking the square root of both sides:

3 = 1 - y1 or 3 = y1 - 1

Solving for y1 in each case:

y1 = -2 or y1 = 4

Therefore, the possible coordinates of point A are (2,-2) and (2,4).

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The rate of change of y when x = 1 is 0.005 unit/sec.

To find the rate of change of y when x = 1 and given that x increases at a rate of 0.02 unit/sec, we'll first find the derivative of the equation y = (2x - 5)/(x + 1) with respect to x, and then multiply it by the rate of change of x (0.02 unit/sec). Differentiate the equation with respect to x:

y = (2x - 5)/(x + 1)

To differentiate this function, we'll use the quotient rule: [tex](u'/v) - (uv')/v^2[/tex], where u = (2x - 5) and v = (x + 1).

u' = derivative of (2x - 5) = 2

v' = derivative of (x + 1) = 1

Now, apply the quotient rule:

dy/dx =[tex](2\times(x + 1) - (2x - 5)\times1) / (x + 1)^2[/tex]

Plug in x = 1:

dy/dx =[tex](2\times(1 + 1) - (2\times1 - 5)\times1) / (1 + 1)^2[/tex]

dy/dx = (4 - 3) / 4

dy/dx = 1/4

Multiply the derivative by the rate of change of x:

The rate of change of x is 0.02 unit/sec, so the rate of change of y when x = 1 is:

Rate of change of y = (dy/dx) × (rate of change of x)

Rate of change of y = (1/4) × 0.02 = 0.005 unit/sec

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[tex]x^4y^2-2x^3y^3\\\\x^2y^2(x^2-2xy)[/tex]

Answer is the second one.

step-by-step explanation:

Part A. We can see that within only for a 0-2 second interval, the height of the water balloon increases from 60ft to approximately 80ft.

Part B. In two intervals, 2-4 seconds to approximately 80 ft and 10-14 seconds to 0 ft.

Part C. Between 4 and 6 seconds, the water balloon height changes from approximately 80ft to 40ft, whereas between 6-8 seconds and 8-10 seconds, the height only changes by 20ft.

Part D. According to the graph, we can suppose that the water balloon was thrown up, and after beginning to fall, at 10 seconds touched the floor, so in 16 seconds kept staying on the floor, at 0ft.  

Hope it helps.

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]