The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m Wide all the way around.What is the area of the running track that goes around the field? Round to the nearest square meter.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ - 32 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies {\Large \begin{array}{llll} y-\stackrel{y_1}{1}=\stackrel{m}{- 32}(x-\stackrel{x_1}{2}) \end{array}}[/tex]

The equivalent composite function of the given one is expressed as; -9x + 5

Function is a type of relation, or rule, that maps one input to specific single output. Composite functions are also known as function of a function.

Given the following functions as;

a(x) = 3x+2 and

b(x) = -3x + 1

To determine the value of a(b(x));

a(b(x)) = a(-3x+1)

a(b(x)) = 3(-3x+1) + 2

a(b(x)) = -9x + 3 + 2

a(b(x)) = -9x + 5

Therefore, This gives the equivalent composite function of the given one.

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First Step: Calculate the mean of the values in X and Y

Second step: we have to find the sum of Squares and sum of products

Third step: find the linear equation

Replace the variable in an equation with to write it in function notation. In function notation, the equation would be stated as follows: f (x) = x + 30000, where is the mileage displayed on the odometer.

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Answer:

Step-by-step explanation:

0.033

Since each input value (domain) leads to only one output value, therefore each relation classifies as a function.

An ordered pair set is known as a relation. Each ordered pair's collection of first components is known as the domain, and its set of second components is known as the range.

A function (f) is a relation that gives each value in the domain a single value from the range.

Its given that - (8,0), (5,7), (9,3), (3,8)

Mapping:

Domain    Range

8          →        0

5          →         7

9          →         3

3          →         8

In other words, classify the relationship as a function if each input value (domain) results in just one output value. Do not classify the connection as a function if any domain produces two or more outputs.

As a result, the relationship given is a function.

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The quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.

According to the question,

We have the following expressions:

[tex]3x^{3} -15x-13[/tex] is divided by (x+2)

First, we  will look at some of the rules of the synthetic division:

We have to make the quotient in such a way that it is same as the term with the highest power in the dividend.

We change signs after solving using one complete term of the quotient.

We have to solve this using the synthetic division method:

x+2 )[tex]3x^{3} -15x-13[/tex]( [tex]3x^{2} -6x-3[/tex]

       [tex]3x^{3} +6x^{2}[/tex]

      _-___-_____

              [tex]-6x^{2} -15x-13[/tex]

              [tex]-6x^{2} -12x[/tex]

             +         +

                _________

                          -3x-13

                          -3x-6

                          +   +

                        _______

                              -7

Hence, the quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.

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The interval of heights calculated by using empirical rule which represents the middle 95% of male heights from this school is between 57 inches and 77 inches.

What is Empirical rule?

Empirical rule has three rule of statement based on the normal distribution and they as as follows:

1) About 68% of the x values lie between 1 standard deviation below and above the mean.

2) About 95% of the x values lie between 2 standard deviations below and above the mean.

3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.

According to the question, let us assume 'x' be a random variable representing the heights of males from this school. With the mean and standard deviation given, then the Empirical Rule number two states that the:

From the information given,

mean = 67 inches

Standard deviation = 5 inches

We want to determine where 95% of x values lies. This is 2 standard deviations from the mean Therefore,

2 standard deviations = 2 × 5 = 10 inches

The heights are

67 - 10 = 57 inches and

67 + 10 = 77 inches

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The area of a triangle is given by

Where b is the base and h is the height of the triangle.

Let us substitute the given values of base and height into the above formula

Therefore, the area of the triangle is 31.5 square units.

The most appropriate choice for maxima and minima of a function will be given by

Rectangle of length 72 feet and breadth 36 feet has largest area

What is maxima and minima?

Maxima of function f(x) is the maximum value of the function and minima of function f(x) is the minimum value of the function.

Here,

Let the length be x feet and breadth be y feet

The farmer has 144 feet of fencing

Three of the sides will require fencing and the fourth wall already exists.

So,

x + y + y =1 44

x + 2y = 144

Area of rectangle(A) = xy [tex]ft^2[/tex]

                               = (144 - 2y)y

                               = [tex]144y - 2y^2[/tex]

[tex]\frac{dA}{dy} = \frac{d}{dy}(144y - 2y^2)[/tex]

     = [tex]144 - 2\times 2y^{2-1}\\144 - 4y[/tex]

For largest area,

[tex]\frac{dA}{dy} = 0[/tex]

[tex]144 - 4y = 0 \\4y = 144\\y = \frac{144}{4}\\y = 36[/tex]

[tex]\frac{d^2A}{dy^2} = \frac{d}{dy}(144 - 4y)\\=0-4\\=-4 < 0[/tex]

Hence area is maximum

For largest area, y = 36 feet

[tex]x = 144 - 2\times 36\\x = 144-72\\[/tex]

[tex]x = 72[/tex] feet

So length of rectangle is 72 feet, breadth of rectangle is 36 feet

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Answer:

  33w² +660w

Step-by-step explanation:

You want the expression for the volume of a cuboid with dimensions in inches of 33, (w+20), and (w).

The volume of a cuboid is the product of its dimensions:

  V = HLW

  V = (33)(w +20)(w) = 33(w² +20w)

  V = 33w² +660w . . . . expression for volume

__

Additional comment

Comparing coefficients, you see ...

Okay, here we have this:

Considering the provided equation, we are going to solve the system using an augmented matrix and Gauss-Jordan Elimination. So we obtain the following:

Finally we obtain that the solution to the system is:

A pancakes require 3.5 cups of milk and 1 cup of flour, or a ratio of 3.5:1 or a fraction of

(3.5) / (1)

If you have 4.6 cups of milk you need x cups of flour

Set up a ratio of

The linear regression equation is y = 15430.5034 + 301.2586x .

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x + y=7 and x - y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage. There are three steps in the substitution technique: For each variable, solve a single equation. Solve the other equation by substituting (plugging in) this expression. Find the corresponding variable by substituting the value back into the original equation.

∑x = 56

∑ y = 109453.5

∑ x² = 760

∑ x × y = 1093064.7

Substitute the upper values

6a + 56b = 109453.5

56a + 760b = 1093064.7

Solve the above 2 equations

a = 15430.5034

b = 301.2586

Now substitute the values in y = a + bx

y = 15430.5034 + 301.2586x

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Answer: The answer is -1

Answer:

62

Step-by-step explanation:

x + 87 and 2x are linear pair angles.

Sum of linear pair angles is 180,

x + 87 + 2x = 180

x + 2x + 87 = 180

3x + 87 = 180

3x = 180 - 87

3x = 93

x = 93 / 3

x = 31

2x

= 2 * 31

= 62

Answer:

-1.12 or -28?/25 or -1 3/25

Step-by-step explanation:

The given situation represents a random sample because, in statistics, a simple random sampling refers to the subset of individuals chosen from a larger set called population, where the sample is chosen randomly.

In this case, the dialed number are a random event, so it can be called a simple random sample.

Let's call X the ounces of water and Y the ounces of the salt solution.

Of she

The value for a number that is 1000 more than 3,872 will be 4,872

In the given question, it is stated that we have to find out the value of the expression given. The expression states that we have to find out a number that is 1000 more than 3872.

This can easily be done. To find out the value for a number that is 1000 greater than 3872, we just need to add the value to the number i.e. we need to add 1000 to 3872. Let the new number be 'x'.

So, by solving this condition, we get

=> x = 3872 + 1000

=> x = 4872

Here we get x = 4872.

Hence, 1000 more than 3,872 will be 4,872.

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The amount of tax owed is  $ 6,960.

It is given in the question that:-

Vacant land value = $ 24,000

Tax percentage = 18 %

Tax per hundred dollars = $ 11

We have to find the tax owed.

Tax = (18/100)*24000 = $ 4,320

Tax per hundred for $ 24000 land = 11*(24000/100) = $ 2,640

Hence, total tax owed = $ 4,320 +  $ 2,640 = $ 6,960

Percentage

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

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Answer:

y=2/3x+4

Step-by-step explanation:

The time taken to screen-print a batch of 14 shirts are 42 minutes

In the above question, it is given that,

Lizz does screen-printing and she screen-prints a batch of T-shirts

The time taken in initial set-up to screen print the first t-shirt is = 15 minutes

After that,

The time taken in screen printing further t-shirts of the batch is = 3 minutes

We need to find the time taken to screen-print a batch of 14 shirts = 3 x 14 = 42 minutes

Hence, the time taken to screen-print a batch of 14 shirts are 42 minutes

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Answer:?=12x

Step-by-step explanation: 6(2x+4)=?+24, 6 x 2x= 12x. 6 x 4= 24, 24 is already in the equation, so 12x is our missing number.

If two shapes are similar to each other, they have the same shape, but not necessarily the same size.

All circles are similar to each other. All points on the circumference of any circle are equidistant from its center.

The ratio of the radii of the pair of circles will give the scale factor.

The correct option is the SECOND OPTION.

Clearly, we can see that x+2 is a factor of the given polynomial.

The value for the A³ matrix will be [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]

In the given question, it is stated that A is a given matrix. We have to find out the values of A³. This can be done by product of A*A*A. The product should follow the properties of the Matrix. First, we will find out the value of A². So calculating, we get:

=> [tex]A^{2} = \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]

=> [tex]A^{2} = \left[\begin{array}{ccc}-25+0 &1 -1\\0+0&0 + 1\end{array}\right][/tex]

=> [tex]A^{2} = \left[\begin{array}{ccc}-25 &0\\0&1\end{array}\right][/tex]

Now we will calculate the value of A³. We can calculate the value of A³ by using the values of A² because we know that A³ = A².A. So, after calculating we get:

=> [tex]A^{3} = \left[\begin{array}{ccc}-25&0\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]

=> [tex]A^{3} = \left[\begin{array}{ccc}75+0&0 + 0\\0+0&0+1\end{array}\right][/tex]

=> [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]

Hence we get value for [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]

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Answer:

the value of x is 32 degree

Step-by-step explanation:

100 + 68 +x = 180

168 +x=180

x= 180- 168

x= 32 degree

To do this, this equation must be taken to the form

So,

Then a positive slope of 2/5 tells you that for every 2 units on the y-axis there are 5 units on the x-axis. And 3 tells you that the line intercepts the y-axis at 3.

EXPLANATION

Since the line segment is 7 units long, we can apply the following relationship:

(x_1+ 7 , y_1) = (x_2 , y_2)

The coordinate of the endpoint is as follows:

We can get to this point by applying the distance formula as follows:

Applying the square power to both sides:

Subtracting numbers:

Now, if the x_2 coordinate is -3, the value of y_2 will be as follows:

Subtracting -4 to both sides:

Applying the square root to both sides:

Adding +4 to both sides:

In conclusion, the equation to get the coordinate from a given point is,