What are whole numbers integers and rational numbers are the set of whole numbers and their opposites?; What are whole numbers integers and rational numbers?; What are whole numbers and their opposites?; What is a whole number ?

In the picture the correct option is A when the function shown in graph (A) has a constant additive rate of change is -1/4.

Given that,

We have to find which function has an additive change rate that is -1/4 constant throughout time. a line in the coordinate plane with a downward slope. (negative 2, 2) and the line (2, 1).

We know that,

The line goes through the points:

(-2, 2) and (2, 1)

y - 1 = (1-2)/(2+2)[x -2]

y - 1 = (-1/4)[x -2]

y = -x/4 + 1/2 + 1

y = -x/4 + 3/2

The change at a constant additive rate is -1/4.

Therefore, In the picture the correct option is A when the function shown in graph (A) has a constant additive rate of change is -1/4.

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Based on the information, we may conclude that there are  210 options to answer the given question.

Combination refers to choosing all or a portion of a group of objects, regardless of their order of selection.

Consider a group of three characters,

therefore the combination will be,  

nCr = n! / r! ( n - r)!

The number of ways in which this business can purchase them are

35 X 6 =

210 ways

A combination in mathematics is a method of choosing items from a collection where the order of the choices is irrelevant. Consider a group of three numbers, P, Q, and R. The number of ways that we can choose two numbers from each group is thus determined by combination.

It is easy to count the number of combinations in smaller cases, but cases with more groups of elements or sets also have a higher likelihood of a set of combinations. As a result, a formula for calculating the number of items that could be chosen has been developed.

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Answer:

1,229

Step-by-step explanation:

100 + 100 = 200

1,000 + 200 = 1,200

9 + 9 = 18

1,200 + 18 = 1,218

1,218 + 11 = 1,229

On solving the provided question, by the given information we can say that Momentum is a vector quantity.

A physical quantity that only has magnitude is known as a scalar quantity. such as distance, speed, mass, density, etc. However, vector quantities—which include displacement, velocity, acceleration, force, and mass—are physical quantities that have both magnitude and direction.

Momentum is a vector quantity.

It is directed and has a magnitude. According to Isaac Newton's second law of motion, the force pushing a particle has an equal and opposite effect on the time rate at which its momentum changes. Consider Newton's laws of motion.

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Answer:  The top right table

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Given: [tex]\textsf{y = 30 - 3x}[/tex]

Find:  [tex]\textsf{Match the table of values with the equation}[/tex]

Solution: First we must understand what form our equation is in and what each of the numbers represent.  This form is known as the slope intercept form which is formatted as y = mx + b.  Our equation is slightly re-ordered but we can change that by converting it to y = -3x + 30 where m is equal to -3 and b is equal to 30.  Let us know talk about what m and b are.  M is the slope of the equation or also known as the rise/run or the change in y over the change in x.  B is the y-intercept which is basically the value of y when x is equal to 0.  In this case, our b is equal to 30.

Looking at the tables we can see what the value of y when x is equal to 0 for each table.  The only table that matches up stating that y is equal to 30 when x is 0 is the top right table.

You do not have to go any further but if you want to confirm that the slope is as expected we can do the following:  [tex]\frac{y_2\ -\ y_1}{x_2\ -\ x_1}[/tex].

Plug in the values and simplify

Therefore, we can confirm that the slope matches up with the given equation as well.  So, the final answer would be that the top right table would correspond to the equation y = 30 - 3x.

Answer:

----------------------------------------------

Given is the parallelogram.

Properties:

Solve the following:

Answer:

w = 72°

x = 36°

2x = 72°

3x = 108°

y = 72°

z = 108°

Step-by-step explanation:

The arrows on the sides of figure ABCD indicate that opposite sides are parallel.  Therefore, ABCD is a parallelogram.

In a parallelogram:

As adjacent angles sum to 180°:

⇒ m∠A + m∠B = 180°

⇒ 3x + 2x = 180°

⇒ 5x = 180°

⇒ x = 36°

Therefore:

⇒ m∠A = 3(36) = 108°

⇒ m∠B = 2(36) = 72°

As opposite angles are equal:

⇒ y = m∠D = m∠B = 72°

⇒ z = m∠BCD = m∠A = 108°

Angles on a straight line sum to 180°:

⇒ z + w = 180°

⇒ 108° + w = 180°

⇒ w = 72°

The number -84 makes the expression 12(−1.4m+0.4) = 0.2(?m+0.2) equivalent.

To calculate for the unknown number represented by the question mark (?), we first expand the left hand side of the equation and then compare with the expression at the right hand side of the equation.

From the left hand side;

12(−1.4m+0.4) = -16m + 4.8 {by expansion}

12(−1.4m+0.4) = 0.2 × -84m + 0.2 × 0.2 {factor out 0.2 from both terms}

12(−1.4m+0.4) = 0.2(-84m + 0.2) {use bracket}

Therefore, by comparing 0.2(-84m + 0.2) with 0.2(?m+0.2), we observe the unknown number represented by "?" is -84 which makes the expression equivalent for 12(−1.4m+0.4) = 0.2(?m+0.2)

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Possible question

What number makes the expressions 12(−1.4m+0.4) = 0.2(?m+0.2) equivalent?

The 90% confidence interval for the given data is 4.8 ± 2.73.

A confidence interval is a type of interval computation used in statistics that determines the true value of an unknown parameter based on the observed data. The interval estimates the deterministic parameter with a level of confidence that is quantified by the confidence level.

Given, sample mean (x) = 4.8

           z at 90% confidence level = 1.645

           sample standard deviation (s) = 5.25

           sample size (n) = 10

We know that, Confidence interval = x ± (z × s) ÷ √n

                                                           = 4.8 ± (1.645×5.25)/√10

                                                           = 4.8 ± 8.63625/3.1622

                                                           = 4.8 ± 2.73

            ∴ Lower bound = 4.8 - 2.73 = 2.07

       and, Upper bound = 4.8 + 2.73 = 7.53

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The correct option is option C i.e., current students are not included in the sample for the survey.

Current students are not required to participate in this survey because its main objective is to learn about respondents' career histories and starting salaries .

Survey could mean:

Research into humans and statistics.

A statistical survey is a technique for gathering numerical data on constituents of a population.

Type of survey

Cadastral surveyors provide paperwork, diagrams, plats, and maps to prove who owns the land.

Most of Western Canada is divided into one-square-mile pieces using the Dominion Land Survey technique for agricultural and other uses. Identifying and surveying land parcels in the United States using the Public Land Survey System.

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The solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3

Any equation in algebra that can be rearranged in standard form as follows is known as a quadratic equation (from Latin quadratus, which means "square").

[tex]{\displaystyle ax^{2}+bx+c=0\,,}[/tex]

While a, b, and c are known values, x is an unknown value, and vice versa. The assumption is that a > 0; equations with a = 0 are thought to be degenerate because they become linear or even simpler. The terms "quadratic coefficient," "linear coefficient," and "constant or free term" can be used to distinguish the three values that make up the equation's coefficients, respectively.

Given,

4x²-9x-9=0

4x²-12x+3x-9=0

4x(x-3)+3(x-3)=0

(4x+3)(x-3)=0

4x+3=0, x-3=0

4x-3=0

4x=3

x= -3/4

x-3=0

x=3

Therefore, the solution sets for 4x²-9x-9=0 are -3/4, 3

Hence, the solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3

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The sample standard deviations of the data set 2, 3, 5, 6, 7 rounded up to 2 decimal spaces is 2.07.

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. Think about the following data: 2, 1, 3, 2, 4.

The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.

Number of data points (n)=5

Mean (x)= (2+3+5+6+7)/5= 4.6

Here x = 2, 3, 5, 6, 7

(x-x)  = -2.6, -1.6, 0.4, 1.4, 2.4

[tex](x-X)^{2}[/tex] = 6.76, 2.56, 0.16, 1.96, 5.76

∑[tex](x-X)^{2}[/tex] = 17.2

Sample standard deviation :

[tex]\sqrt{\frac{(x-X)^{2}}{n-1} } \\\\\sqrt{\frac{17.2}{4} } \\\\[/tex]

= 2.07

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In January the Net cash flow: ($35,200) , In February Net cash flow: $6,400 and In march Net cash flow: $21,900.

A cash receipt is an official document that is issued to a customer or client when they make a payment in cash. It serves as proof of the payment, and is an important record for both the buyer and the seller. A cash receipt typically contains the date and time of the transaction, the amount of cash received, and a description of the goods or services that were purchased. It is usually signed by both the seller and the buyer.

January
Cash receipts:
Cash sales: $400,000 x 60% = $240,000
Credit sales from November: $260,000 x 20% = $52,000
Credit sales from December: $340,000 x 20% = $68,000
Total cash receipts: $360,000

Cash payments:
Materials: $400,000 x 20% = $80,000
Labor: $400,000 x 50% = $200,000
Selling and administrative: $400,000 x 15% = $60,000
Overhead: $31,000
Depreciation: $10,600
Taxes: $8,600
Dividends: $5,000
Total cash payments: $395,200
Net cash flow: ($35,200)

February
Cash receipts:
Cash sales: $440,000 x 60% = $264,000
Credit sales from December: $340,000 x 20% = $68,000
Credit sales from January: $400,000 x 20% = $80,000
Total cash receipts: $412,000

Cash payments:
Materials: $440,000 x 20% = $88,000
Labor: $440,000 x 50% = $220,000
Selling and administrative: $440,000 x 15% = $66,000
Overhead: $31,000
Depreciation: $10,600
Total cash payments: $405,600
Net cash flow: $6,400

March
Cash receipts:
Cash sales: $410,000 x 60% = $246,000
Credit sales from January: $400,000 x 20% = $80,000
Credit sales from February: $440,000 x 20% = $88,000
Total cash receipts: $414,000

Cash payments:
Materials: $400,000 x 20% = $80,000
Labor: $410,000 x 50% = $205,000
Selling and administrative: $410,000 x 15% = $61,500
Overhead: $31,000
Depreciation: $10,600
Dividends: $5,000
Total cash payments: $392,100
Net cash flow: $21,900

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The two variables to have a negative correlation are x and y.

Negative correlation is the relationship where x grows as y decreases.

Given,

Here, negative correlation is used to describe the relationship between two variables that results in independent variables moving in one direction while dependent variables move in another.

Positive correlation

Positive correlation is when the value of the variable x rises as the value of the variable y rises.

Negative Correlation

Negative correlation is the relationship where x grows as y decreases.

No correlation

No correlation exists between the two variables.

That example, the term "no-correlation" refers to the absence of a connection between two variables.

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The question is improper. Proper question is given below;

What two variables are likely to have a negative correlation

The maclaurin expansion for function eˣ  is 1 + x + x²/2 + x³/6 + x⁴/24 + .....

A function's expansion series, which provides the function's derivatives' sum, is known as a Maclaurin series.

Series [f, x, 0, n] can be used to find a function's Maclaurin series up to order n.

When x = 0, it is a specific example of the Taylor series. The series of Maclaurin is provided by

[tex]f(x) = f(x_0) + f(x_0)(x - x_0) + \frac{f"(x_0)}{2!}(x - x_0)^2 + . . .[/tex]

The formula for maclurin series is :

[tex]f(x) = \sum^{\infty}_{n=0} \frac{f^n (x_0)}{n!} (x-x_0)[/tex]

Where,

f(xo), f’(xo), f’‘(xo)……. are the successive differentials when xo = 0.

Maclaurin expansion for the function eˣ

Firstly , We will derivate the function

f(x) = eˣ

=> f'(x) = e⁰ = 1

=>  f''(x) = e⁰ = 1

=> f'''(x) = e⁰ = 1

and so on

Upon evaluation of all derivatives at x = 0, we obtain the value 1.

Moreover, f(0)=1, so we can deduce that the expansion of the Maclaurin Series as

=> eˣ = 1 + x + x²/2 + x³/6 + x⁴/24 + .....

The given question is incomplete , I answered the question in general according to the knowledge

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The community will contain 15,000 people with the gene that causes a triangle on their forehead after 20 days.

The rate of change of n (t) with respect to time is 500 people per day. This means that the equation for n (t) is given by:

n (t) = 5,000 + 500t

where t is the number of days since time t. At time t, n (t) = 5,000, and as time passes, the number of people with the gene that causes a triangle on their forehead increases. After 20 days, n (t) = 5,000 +500*20 = 15,000, meaning that after 20 days, the community will contain 15,000 people with the gene that causes a triangle on their forehead.

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A line segment is a straight line connecting two points. In the case of a triangle, a line segment will always pass through a vertex, which is one of the three points that make up the triangle. A vertex is defined as the point at which two or more lines meet.

The other two points of a triangle are known as the base and apex. The base is the line that connects two vertices and forms the base of the triangle. The apex is the point of the triangle that is opposite the base and is the highest point of the triangle. All three of these points are connected by line segments, and together they form a triangle. Each line segment will always pass through one of the vertices of the triangle, thus forming the sides of the triangle.

Which of the following will always pass through a vertex of a triangle?

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Although part of your question is missing, you might be referring to this full question: If P is the incenter of ΔJKL, find each measure (triangle as attached).

Based on the property of incenter, the measurements of the sides and the angles will be:

JK = 21.2 units

KL = 26.63 units

JL = 28.33 units

m∠K = 36°

By using the property of incenter:

PM = PN = PO = 7 units

∠MJP = ∠OJP = 32°

∠NLP = ∠OLP = 22°

By using the triangle sum theorem,

m∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

m∠NKP = 36°

Then, from ΔJMP,

tan(32°) = MP/MJ

tan(32°) =  7/MJ

MJ =  7/tan(32)°

MJ = 11.20

And from ΔPOL,

tan(22°) = OP/OL

tan(22°) = 7/OL

OL = 17.33

And from ΔKNP,

tan(36°) = NP/KN

tan(36°) = 7/KN

KN = 9.63

Hence, JK = MJ + MK = 21.2 units

KL = LN + KN = 26.63 units

JL = JO + OL = 28.33 units

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The area is:

Explanation:

To find the circle's area, use the formula [tex]\sf{A=\pi r^2}[/tex].

where:

A = area;

π = 3.14 (pi);

r = radius

Diagram:

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 13\ in}\end{picture}[/tex]

Plug in the data:

The correct option is (d) i.e; MD = 3 with s2 = 20 for the difference scores because it generates a repeated-measures study's population mean difference with the widest 90% confidence interval.

Given that,

Which of the following will result in the widest 90% confidence interval for the population mean difference for a repeated-measures research, provided the sample size is kept constant?

MD = 3 with s2 = 20 for the difference scores.

Therefore, the correct choice is MD = 3 with s2 = 20 for the difference scores because it produces the widest 90% confidence interval for the population mean difference for a repeated-measures study.

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The correct option is: A

Statement I is the cause and statement II is the effects.

Since the Government has imported large quantities of sugar as per trade agreement with other countries, the prices of sugar in the domestic market have fallen sharply in the recent months.

The reason behind this statement is:

An increase in supply always leads to a decrease in price.

Supply : Supply is a fundamental economic concept that describes the total amount of a particular good or service available to consumers. Supply can refer to the quantity available at a particular price or the quantity available across the price range displayed on the chart. It is closely related to the demand for goods or services at a particular price. All else being equal, when prices rise, producer supply increases as all firms try to maximize their profits.

Increase in Supply:

If the demand does not change, there is an inverse relationship between the supply and price of goods and services. When the supply of goods and services increases at the same demand, prices tend to fall resulting in lower equilibrium prices and higher equilibrium quantities of goods and services. When the supply of goods and services decreases for the same demand, prices tend to rise towards higher equilibrium prices and smaller quantities of goods and services.

Since the supply of sugar increases as government has over imported, the price of sugar decreases in domestic market.

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The surface area is 131 square units.

The surface area of a solid object is a measure of the total area that the surface of the object occupies

An upward point normal to the plane 33x−19y+z=1,0≤x,y≤1  is  is

N=<33,−19,1>

Therefore F⋅N=33y−19z+x

Since the plane is defined by the equation z=1+19y-33x

the dot product becomes 33x−(33y−19z+x)+x=628x-328y-19

The limits of integration are given as 0≤x≤1,  0≤y≤1

Therefore the surface integral becomes

∫ ∫S F⋅dS= [tex]\int\limits^1_0 \int\limits^1_0{(628x-328y-19)dy} \, dx[/tex]

=[tex]\int\limits^1_0{(628x-183)} \, dx[/tex]

=314x²-183x|₀¹

=131

Hence, the surface area is 131 square units.

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[tex]\fbox{x=56}[/tex]

Simplify:

[tex]x-14=42[/tex]

Add 14 to both sides:

[tex]x-14+14=42+14[/tex]

[tex]x=56[/tex]

The compound inequality of amount of money is 176.4 < f < 352.8

What is compound inequality?

A compound difference (or combined difference ) is 2 or a lot of inequalities joined along with or or and.

Main Body:

Given,

A construction worker earns an average bi-weekly net pay of $1,764.00.

and, the worker can spend if the monthly budget for food is between 10% and 20%.

To find the which compound inequality correctly shows the amount of money?

Now, According to the question:

Total earning is $1,764.00

Amount can be spent on food is :

0.1× 1764.00 < f < 0.2 ×1764.00

176.4 < f < 352.8

Hence, The compound inequality of amount of money is 176.4 < f < 352.8

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The mean score is 6.48. If we were to give this quiz to more and more students, the mean score for these students would approach 6.48.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

To find the mean score, we need to calculate the expected value of the score. The expected value is calculated by multiplying the score by its probability and summing over all possible scores.

The expected value is:

(5 * 0.06) + (6 * 0.18) + (7 * 0.37) + (8 * 0.22) + (9 * 0.11) + (10 * 0.06) = 6.48

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The correct location of the point is (d) between Quadrant II and Quadrant III.

We must choose the response that accurately describes the position of the point whose coordinates have a negative abscissa and a zero ordinate.

Any point with a negative abscissa and a zero ordinate on the XY plane in two dimensions can be represented as

Where a > 0, (x, y) = (-a, 0).

Let's plot (-1, 0), (-2, 0), (-3, 0), etc. on the coordinate plane as an example. The corresponding figure illustrates this.

The figure shows that every point of the type (-a, 0) is located on the X-axis' negative side.

The location of the negative X-axis between Quadrants II and III is known. As a result, the supplied point is situated between Quadrants II and III.

the appropriate answer is (d).

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The expression represents the difference between the two temperatures is  d = 9°C  + 2°C

The difference between two number a and b is d = a - b

Since Lauren woke up one morning and saw frost on the windows. It was -2°C outside. Later in the day, the frost melted. At 3 p.m. it was 9°C outside.

To find the expression that represents the difference between the two temperatures, we know that the difference is d = a - b where

Given that

Substituting the values of the variables into the difference equation, we have that

d = a - b

d = 9°C  - (-2°C)

d = 9°C  + 2°C

So, the difference is d = 9°C  + 2°C

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The equation of tangent plane to the given parametric surface [tex]r(u,v) = u.cos(v)i + u.sin(v)j + vk[/tex] is [tex]\frac{\sqrt3}{2}x - \frac{5}{2}y + 5z = \frac{5\pi}{3}[/tex] .

The given parametric surface is

[tex]r(u,v) = u.cos(v)i + u.sin(v)j + vk[/tex]

The tangent vectors are

⇒ [tex]r_u = \frac{dx}{du} i+ \frac{dy}{du}j + \frac{dz}{du}k[/tex]

⇒ [tex]r_u =[/tex] [tex]r(u,v) = cos(v)i + sin(v)j + 0k[/tex]

⇒ [tex]r_v = \frac{dx}{dv} i+ \frac{dy}{dv} j+ \frac{dz}{dv} k[/tex]

⇒ [tex]r_v =[/tex]  [tex]r(u,v) = -u.sin(v)i + u.cos(v)j + 1k[/tex]

The normal vector to the tangent plane is

[tex]r_u r_v = \left[\begin{array}{ccc}i&j&k\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right][/tex]

⇒ [tex]r_u r_v =[/tex] [tex]sin(v)i - cos(v)j + u.k[/tex]

When u = 5, v = [tex]\frac{\pi }{3}[/tex], the normal vector becomes

⇒  [tex]sin(\frac{\pi}{3})i - cos( \frac{\pi}{3})j + k[/tex]

⇒ [tex]\frac{\sqrt{3} }{2}i - \frac{1}{2} j + k[/tex]

The point on the surface corresponding to the u = 5 & v= [tex]\frac{\pi}{3}[/tex] is

[tex]r(5, \frac{\pi}{3}) = (5)cos(\frac{\pi}{3})i + (5)sin(\frac{\pi}{3})j + (\frac{\pi}{3})k\\r(5, \frac{\pi}{3}) = \frac{5}{2}i + \frac{5\sqrt3}{2}j + \frac{\pi}{3}k[/tex]

If a is the position vector of a point on the plane & n is a vector normal to the plane, then the equation of the plane is

⇒ (r - a).n = 0

⇒ [tex](x - \frac{5}{2}) . ( \frac{5\sqrt3}{2}) + (y - \frac{5\sqrt3}{2}).(- \frac{5}{2}) + (z - \frac{\pi}{3}).(5) = 0[/tex]

⇒  [tex]\frac{\sqrt3}{2}x - \frac{5}{2}y + 5z = \frac{5\pi}{3}[/tex]

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Answer:

[tex]6g=900[/tex]

Step-by-step explanation:

The number of calories in one bar multiplied by six is the number of calories in six bars. This is given to be equal to 900.

The dimensions of the rectangle of maximum area are the length of 12√3 units and width of 4 units

Given that the ellipse has the equation: x²/144 + y²/16 = 1

Make x the subject:

x²/144 + y²/16 = 1

(x²+9y²)/144 = 1

x² + 9y² =144

x² = 144-9y²

x = √(144-9y²)

The  rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Thus, the rectangle has a length and width of 2x and 2y respectively

The area of a rectangle inscribed inside an ellipse is given by:

Area (A) = 4xy

A = 4(√(144-9y²))y

A = 4y√(144-9y²)

A = 4√(144y²-9y⁴)

The maximum area of the rectangle is at dA/dy = 0  

dA/dy = 4[144-18³y/ (√(144y²-9y⁴))]

4[144-18y³/ (√(144y²-9y⁴))] = 0

144-18y³= 0

18y³ = 144

y³ = 144/18

y³ = 8

y = ∛8

y = 2

x = √(144-9y²)

x = √(144 - 9(2)²)

x = √108

x = 6√3

Thus, the dimensions are the length = 2x = 2×(6√3) = 12√3 units, the width = 2y = 2×2 = 4 units

Learn more about rectangle inscribed in ellipse on:

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