of the 58 employees in a firm, 8 are considered support staff, and 7 of the employees have more than five years of experience. All of the support staff
have less than five years of experience. Consider the two events, J and K.
• Event J: Employee is considered support staff.
• Event K: Employee has more than five years of experience.
How many outcomes are possible for the complement of the union of Events J and K?

Answer:

Since sine of all angles are always less than one, this shows there is no possible way to have an angle C. Thus it is impossible to have a triangle ABC with the given properties of side lengths b=3 inches and c= 5 inches to have angle B =45 degrees.

Step-by-step explanation:

In the attached  drawing, each of the tic-marks are equal and

represent 1 inch each.  The angle B has measure 45.  We can

see by the arc that the line AC, which equals 3 inches, is

not long enough to reach the slanted side of the 45 angle.

Therefore triangle ABC is not possible.  We can also show

by the law of sines that no triangle ABC with the given

properties in possible.

Check the picture below, so that's the triangle hmmmm a bit non-right-triangle or irregular per se, so let's use Heron's formula on this one, so we'll have to first find the length of each side

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ J(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill JK=\sqrt{(~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill JK=\sqrt{( 2)^2 + ( 2)^2} \implies JK=\sqrt{ 8 }\)

\(K(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad L(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill KL=\sqrt{(~~ 3- 0~~)^2 + (~~ -4- 3~~)^2} \\\\\\ ~\hfill KL=\sqrt{( 3)^2 + ( -7)^2} \implies KL=\sqrt{ 58 } \\\\\\ L(\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\qquad J(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill LJ=\sqrt{(~~ -2- 3~~)^2 + (~~ 1- (-4)~~)^2} \\\\\\ ~\hfill LJ=\sqrt{( -5)^2 + (5)^2} \implies LJ=\sqrt{ 50 }\)

now let's use those three lengths for Heron's

\(\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{8}\\ b=\sqrt{58}\\ c=\sqrt{50}\\ s=\frac{\sqrt{8}+\sqrt{58}+\sqrt{50}}{2}\\\\ \qquad \frac{\sqrt{58}+7\sqrt{2}}{2} \end{cases}\)

\(A=\sqrt{\frac{\sqrt{58}+7\sqrt{2}}{2}\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{8} \right)\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{58} \right)\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{50} \right)} \\\\\\ ~\hfill {\Large \begin{array}{llll} A=10 \end{array}}~\hfill\)

Answer:

6907 people on that program must be surveyed if we want mean weight loss as 0.25 lb and standard deviation as 10.6 lb.

Step-by-step explanation:

Given that mean of weight loss in 0.25 lb and standard deviation is 10.6 lb.

For 95% confident level z-score must be 1.96.

That is =1.96

Now required sample size is

Where SE means standard deviation=10.6 lb and mean m=0.25 lb

Hence sample size=

Which we always should round up that is 6907.

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

It should be noted that the ratios are the same if we are talking about the numbers 2 and 5.

It should be noted that from the information, one student describes a ratio by saying There are 5 teachers for every 2 students while another student describes a ratio by saying that there are 2 students for every 5 teachers.

In this case, it should be noted that the ratios are the same if we are talking about the numbers 2 and 5 and its equivalent ratios such as 6 and 15.

In this case, there's no difference.

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The area of the composite figure is 159.9 cm²

From the question, we are to determine the area of the given composite figure

In the given diagram, the area of the composite figure = Area of triangle + Area of rectangle

First, we will calculate the area of the triangle

Area of triangle = 1/2 × base × height

Thus,

Area of the triangle = 1/2 × 16.4 × 5.5

Area of the triangle = 45.1 cm²

Calculating the area of the rectangle

Area of rectangle = Length × Width

Thus,  

Area of the rectangle = 16.4 × 7

Area of the rectangle = 114.8 cm²

Therefore,

The area of the composite figure = 45.1 cm² + 114.8 cm²

The area of the composite figure = 159.9 cm²

Hence, the area is 159.9 cm²

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The hοle needs tο be 39 inches deeper.

A cοnversiοn factοr is a number used tο change οne set οf units tο anοther, by multiplying οr dividing. When a cοnversiοn is necessary, the apprοpriate cοnversiοn factοr tο an equal value must be used. Fοr example, tο cοnvert inches tο feet, the apprοpriate cοnversiοn value is 12 inches equals 1 fοοt.

The current depth οf the hοle is 2 feet 9 inches, which is the same as 2 + 9/12 = 2.75 feet (since there are 12 inches in 1 fοοt).

Tο find οut hοw much deeper the hοle needs tο be, we need tο subtract the current depth frοm the required depth:

6 feet - 2.75 feet = 3.25 feet

Hοwever, we are asked tο express the answer in inches, sο we need tο cοnvert the 3.25 feet tο inches using the given cοnversiοn factοr:

3.25 feet x 12 inches/1 fοοt = 39 inches

Therefοre, the hοle needs tο be 39 inches deeper.

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Answer:

Playing video games or sumthin

Answer:

Step-by-step explanation:

sec(2a+6)cos (5a+3)=1

\(\frac{cos(5a+3)}{cos(2a+6)} =1\\\)

cos(5a+3)=cos(2a+6)

cos(5a+3)-cos(2a+6)=0

\(-2sin(\frac{5a+3+2a+6)}{2} )sin(\frac{5a+3-2a-6)}{2} )=0\\-2sin(\frac{7a+9}{2} )sin(\frac{3a-3}{2} )=0\\either sin (\frac{7a+9}{2} )=0=sin ~n\pi \\\frac{7a+9}{2} =n~\pi \\7a+9=2n~\pi \\7a=2n~\pi -9\\a=\frac{2n\pi-9 }{7} \\where~n~is~an~integer.\)

or

\(\sin\frac{3a-3}{2} =0=\sin ~n\pi \\3a-3=2n\pi \\3a=2n\pi+3\\a=\frac{2~n\pi+3 }{3}\)

where n is an integer.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line G

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 8 } \implies {\Large \begin{array}{llll} - \cfrac{3 }{ 8 } \end{array}}\)

Answer

The mean will decrease

Step-by-step explanation

An outlier is an observation that lies an abnormal distance from other values in a dataset. In the case of the dataset:

4, 5, 5, 6, 7, 8, 17

the outlier is 17

The mean is calculated as follows:

Then, the mean of the original dataset is:

After 17 is removed from the set, the mean is:

The mean will decrease if the outlier is removed

Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

Answer: 11

Step-by-step explanation:

F(1) = 3(1) + 8

F(1) = 3 + 8

F(1) = 11

You just substitute the x in for 1 and solve from there.

Answer:

\(F^{-1} (x) = 2x + 12\)

Step-by-step explanation:

Let's assume F(x) = y, then

\(y = \frac{1}{2} x - 6\)

Let us solve the equation for x.

\(y + 6 = \frac{1}{2} x\)

\(2y + 12 = x\)

Next, replace y with x and also replace x with F⁻¹(x)

Answer: \(F^{-1} (x) = 2x + 12\)

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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The probability that the water will run out on a given day is  0.0038.

To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:

where;

x = of 380 million gallons,

µ is the mean daily demand of water = 300 million gallons,

σ is the standard deviation = 30 million gallons.

Substituting the given values:

z = (380 - 300) / 30

z = 2.67

Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.

Therefore, the probability that the water will run out on a given day is  0.0038.

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the transformation ABC is not similar to A”B”C”. hence the statement is false.

We say the statement is false because the ratios of the grid squares are not similar.

We notice that the first triangle is up to over 3 and the other triangle is up 4 over 4 so in order for them to be similar the first triangle would have to be up 3 over 3.

A transformation is described as  a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

#complete question:

Please help this is due today and I’m so stressed!I will mark Branliest!!!

Tanya performs two transformations on ABC to form A"B"C" as shown on the coordinate grid below.

True or False:ABC is similar to A”B”C”?

Answer:

18x +0=18x

Step-by-step explanation:

The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.

Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.

By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.

For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.

Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.

Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.

Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.

Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.

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In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

B

Step-by-step explanation:

b because everything must cost less than 80 and

< 80 means the unknown number will be less than 80.

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Add 7 to both sides.

Add −4 and 7 to get 3.

Multiply both sides by 3, the reciprocal of 1/3 . Since 1/3 is >0, the direction of inequality remains the same.

Multiply 3 and 3 to get 9.

Answer:

Option B

Step-by-step explanation:

Refer the the picture for working

Answer:

The answer would be E.

When you solve 25 x 1/5, you get 5.

When you solve 25 ÷ 5, you get 5.

The equivalent expression is 25 ÷ 5.

Option E is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example.

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

25 x 1/5

= 25 x 1/5

= 5 x 5 x 1/5

= 5

Now,

1/25 x 5

= 1/5

1/25 x 1/5

= 1/125

1/25 ÷ 1/5

= 1/25 x 5

= 1/5

5 ÷ 25

= 5/25

= 1/5

25 ÷ 5

= 5

We see that,

25 x 1/5 and 25 ÷ 5 have the same value.

Thus,

The equivalent expression is 25 ÷ 5.

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Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

The length of the major arc AB is 15.44 units

Given:  line x + 2y = −5 and circle of radius 5 centered at the origin

The equation of a circle of radius r whose center is the origin O (0, 0) is given by x²+y² = r². Thus:

x²+y² = 5²

x²+y² = 25

To find the points where the line intersects the circle, we can substitute the equation of the circle into the equation of the line.

Substituting this into the equation of the line, we have;

x + 2y = -5

x²+y² = 25

Solving for x, we have

x = (-5 ±√(33))/2

Since the circle is centered at the origin, both of these points are on the circle. Thus, the coordinates of the points A and B are

A: (-5 +√(33))/2, (-5 - √(33))/4

B: (-5 - √(33))/2, (5 - √(33))/4

To find the length of the major arc AB, we can use the formula

length = θ/360 × 2πr

where r is the radius of the circle, and θ is the central angle formed by points A and B. The central angle can be found using the formula

θ= 180 - 2cos⁻¹((AB² + r² - AC²)/(2 × AB × r))

where AB is the distance between the points A and B, and AC is the distance between point A and the center of the circle (which is the origin)

We can use the Pythagorean Theorem to find AB and AC:

AB = √(((-5 + √(33))/2 - (-5 - √(33))/2)² + ((-5 - √(33))/4 - (5 - √(33))/4)²)

     = √(66)

AC = √(((-5 + √(33))/2)² + ((-5 - √(33))/4)²)

    = √(25 + 33)/2

    = √(58)/2

Substituting these values into the formula for θ, we have

θ = 180 - 2cos⁻¹((√(66)² + 5² - (√(58)/2)²)/(2 × √(66) ×5))

  = 180 - 2cos⁻¹((66 + 25 - 29)/(20))

  = 180 -2cos⁻¹(62/20)

  = 180 - 2cos⁻¹(3.1)

  = 180 - 2 × 1.43

  = 180 - 2.86

  = 177.14

Finally, substituting this value into the formula for the length of the major arc, we have

length = 2 × π × 5 × (177.14/360)

           = 2  × π  5 ×  (0.4925)

           = 2 ×  3.14 ×  5 ×  (0.4925)

           = 6.28 × 5 ×  (0.4925)

           = 31.4 ×  (0.4925)

           = 15.44 units

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Answer:

The two sides are 15 cm and 9 cm

Step-by-step explanation:

Let x be the longer side and y the shorter side

We are given x : y = 5:3

We can represent this as a fraction:
\(\dfrac{x}{y} = \dfrac{5}{3}\)

Multiplying both sides by y:
\(\dfrac{x}{y} \times y = \dfrac{5}{3} \times y\\\\x = \dfrac{5}{3}y\)

Perimeter of a parallelogram = 2(x + y)

We are given 2(x + y) = 48

Dividing both sides by 2 gives:
2(x + y)/2 = 48/2

x + y = 24

Substituting

\(x = \dfrac{5}{3}y \text{ we get}\\\\\\\dfrac{5}{3}y + y = 24\\\\\)

Multiplying throughout by 3 gest rid of the denominator
\(\dfrac{5}{3}y \cdot 3 + y \cdot 3 = 24 \cdot 3\\\\\\\\\rightarrow 5y + 3y = 72\\\\\rightarrow 8y = 72\\\\\rightarrow y = \dfrac{72}{8} = 9\\\)

Since

\(x = \dfrac{5}{3} y\\\\x = \dfrac{5}{3} \cdot 9\\\\x = 15\\\\\)

Therefore the two sides are 15 cm and 9 cm

Evaluating [log2(3)].[log3(4)].[log4(5)]...[log63(64)] is 6

We can use the property that [log_a(b)]=[log_c(b)/log_c(a)] to simplify the expression. Applying this property repeatedly, we get:

[log2(3)].[log3(4)].[log4(5)]...[log63(64)]

= [log2(3)/log2(2)].[log3(4)/log3(3)].[log4(5)/log4(4)]...[log63(64)/log63(62)]

= [log2(3)/1].[log3(4)/1].[log4(5)/1]...[log63(64)/1]

= log2(3) log3(4) log4(5) ... log63(64)

Now, we can use the identity [log_a(b)log_b(c)log_c(d)...log_y(z)] = log_a(z) to combine the logarithms into a single logarithm with a base of 2:

log2(3) log3(4) log4(5) ... log63(64) = log2(64)

Since 2^6 = 64, we have:

log2(64) = 6

Therefore,  [log2(3)].[log3(4)].[log4(5)]...[log63(64)] evaluates to 6.

learn more about logarithmic terms at:https://brainly.com/question/25710806

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