A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is 4 mph what is the speed of the flying carpet

[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]

Given:

m∠D = 130 degrees

m∠B = (3x - 1.5) degrees

Let's solve for the value of x.

A parallelogram is a quadilateral that has equal opposite angles and equal opposite sides.

Since a parallelogram has equal opposite angles, measure of angle D and measure of angle B are equal.

Thus, we have the equation:

m∠B = m∠D

(3x - 1.5) = 130

Solve for x.

Remove the parentheses:

3x - 1.5 = 130

Add 1.5 to both sides:

3x - 1.5 + 1.5 = 130 + 1.5

3x + 0 = 131.5

3x = 131.5

Divide both sides by 3:

Therefore, the value of x rounded to the nearest whole number 44

ANSWER:

44

For the first sequence

Let a1 = 2

2, 9, 16, 23, ...

Recursive Formula

Explicit Formula

For the second sequence

Let a1 = 2

2, 14, 98, 686, ...

Recursive Formula

Explicit Formula

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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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

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

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:

10% profit

Step-by-step explanation:

since the item was sold for more than it cost, this is a profit

percent profit = [tex]\frac{P}{C}[/tex] × 100%

profit P = SP - CP = Rs 220 - Rs 200 = Rs 20 , then

% profit = [tex]\frac{20}{200}[/tex] × 100% = 0.1 × 100% = 10%

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.

Answer:

Step-by-step explanation:

0.033

The inequality equation is 3c + 2.25b <=15 which represents the possible values of cupcakes and brownies that can be purchased by Aisha with the given amount of money.

Cost of each cupcake = $3

Cost of each brownie = $2.25

Total money available with Aisha to spend on cupcakes and brownies = $15

Let c represent the number of cupcakes purchased by Aisha and b represent the number of brownies purchased by Aisha

Formulating the inequality equation we get the following:

Cost of each cupcake*Number of cupcakes purchased + Cost of each brownie*Number of brownies purchased <= Total money available with Aisha

3c + 2.25b <=15

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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.

We have the fraction 6/10

For finding the equivalent number, we divide 6 by 10:

6 / 10 = 0.6

0.6 is the equivalent number

We have 6 in the numerator and 10 in the denominator, if we calculate any mathematical operation to both, we will find the equivalent fractions.

Let's see two examples:

1. Let's divide by 2:

6 divided by 2 is 3; and 10 divided by 2 is 5. Then our new equivalent fraction is

2. Let's multiply by 3:

6 multiplied by 3 is 18; 10 multiplied by 3 is 30. Then a second equivalent fraction is:

We can calculate additional equivalent fractions, using the same operation for both: numerator and denominator.

For calculating the equivalent fraction in hundreds, we will use the initial decimal equivalent we calculated at the beginning: 0.6

0.6 = 6/10 and we multiply it by 10 numerator and denominator

6 * 10 = 60 and 10 * 10 = 100. Then the fraction is 60/100

20 divided by 10 is 2 and 100 divided by 10 is 10, so the equivalent fraction is 2/10

This case is exactly the same than the previous we solved:

?/10 = 120/100

As you can see the first fraction is notated in tens and the second is notated in hundreds. Therefore, if you divide 120 between 10, what is the result?

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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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 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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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.

Answer: The answer is -1

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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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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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.

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

Of she

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,

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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The expression which correctly represents the amount of candy sold each year per type at Cassandra's Candy corner is; 2x2 – 4x + 54.

It follows from the task content that the expression which shows the amount of candy sold each year per type is to be determined.

Since, the function, C (x) = 4x³ + 16x² + 60x + 648 represents the total amount of candy sold while, T(x) = 2x + 12 represents the amounts of types of candy.

Therefore, the amount of candy sold each year per type is; C(x) ÷ T(x).

Hence, the result of the polynomial division as in the attached image is; 2x² - 4x + 54.

Ultimately, the amount of candy sold each year per candy is represented by the expression; 2x² - 4x + 54.

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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.

The angle BOC has a measure of 50 degrees

From the question, the given parameters about the angles are:

The above parameters implies that

AOC = AOB + BOC

Next, we substitute the angle measurements in the above equation

So, we have

142 = 9x + 20 + 7x - 6

Evaluate the like terms

So, we have the following equation

142 = 16x + 14

Evaluate the like terms again

So, we have the following equation

16x = 128

Divide both sides by 16

x = 8

Substitute x = 8 in BOC = 7x - 6

BOC = 7 x 8 - 6

Evaluate

BOC = 50

Hence, the measure of the angle is 50 degrees

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The angle BOC has a measure of 50 degrees

An angle is formed when two straight lines or rays meet at a common endpoint

If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142

We need to find BOC

We have AOC = AOB + BOC

142=9x + 20+7x-6

142=16x+14

Subtract 14 from both sides

142-14=16x

128=16x

Divide both sides by 16.

8=x

Now put x value in BOC = 7x - 6

BOC = 7x - 6

=7(8)-6

=56-6

BOC=50

Hence If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142 then BOC=50.

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