A map of a park has no scale. The distance between the campground and the entrance station on the map is 2 inches. The actual distance between them is 8 miles. On the map, the distance between the campground and the lake is 12 inch.



What is the actual distance in miles between the campground and the lake?

The equation of the linear function represented by the table below in slope-intercept form is y = -3x + 5

The linear function that will be obtained by using these values of x and y will be a Equation of line.

The slope-intercept form of line looks like this,

y = mx + c

where,

m is the slope.

c is the y intercept,

Firstly, to find the slope we can use any two points,

we will use (1,2) and (2,-1)

Hence, slope m,

m = (-1-2)/(2-1)

m = -3

Putting the value of slope in equation y = mx + c,

y = -3x + c

To fin the value of c,

Using the coordinate (1,2) and putting the values of x and y,

2 = -3 + c

c = 5.

Putting the values of c and m in the equation,

we get,

y = -3x + 5.

The required equation of the line in slope-intercept form is y = -3x + 5

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Answer:

[tex]f(x) = - 2x - 1 \\ h(x) = - x + 5 \\ \\ The \: \: value \: \: of \: \: \: f(6) = ( - 2) \times 6 - 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 13 \\ \\ as \: we \: know ,\: \\➪(hf)(x) = h(f(x)) \\ so \:➪( hf)(6) = h(f(6)) \\ \\ put \: the \: value \: \: of \: f(6) \: we \: \: get \\ \\➪ (hf)(6) \: = h( - 13) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - ( - 13) + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 13 + 5 \\ \: \: \: \: \: \: \: = 18[/tex]

Given that:

- The triangle is isosceles.

- Its base is 49.96 meters.

- Each base angle is 31.43°.

You can draw the triangle. See the picture shown below (it is not drawn the scale):

Notice that the Isosceles Triangle can be divided into two equal Right Triangles. Then, you know that:

Since it is isosceles, the sides AB and AC have equal length.

Then, you can choose one of the equal Right Triangles and use the following Trigonometric Function in order to find the length of each equal side:

In this case, you can set up that:

Therefore, substituting values and solving for AC, you get:

Hence, the answer is:

The length of the two equal sides of the triangle is:

Suppose C's capital = x then

B's capital = 4x (Since B's Capital is four times C's capital)

A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)

A : B : C =6x : 4x : x

= 6 : 4 : 1

B's share = 16500×411

  = 1500 × 4 = 6000.

What is meant by Capital?

A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the wide definition of capital.

While money in and of itself might be considered capital, the term is most frequently used to refer to money that is being used for investments or productive purposes. In general, capital is an essential part of managing firm day-to-day and funding its expansion in the future.

Business capital may be generated via activities or obtained through debt or equity finance. Typical sources of funding are as follows:

individual savings

relatives and friends

Angel backers

financiers for startups (VC)

Corporations

State, municipal, or federal governments

Personal loans

Working or conducting business

getting an IPO to go public

Working capital, equity capital, and debt capital are the three types of capital that firms of all sizes commonly concentrate on when creating budgets. A company in the financial sector names trading capital as the fourth element.

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The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13

From the table given, we have

The balance of the credit card from May 1 - May 5 was 2000 which is 5 days, from may 6- may 10 was 1600, which is again 5 days, from may 11 to may 20 was 1350, the interval is 10 days and 21 to may 31, 11 days the balance was 1550.

The avergae daily balance was

=[tex]\frac{(Balance (number of days))}{Total number of days}[/tex]

= [tex]\frac{2000(5)+1350(10)+1550(11)}{5+5+10+11}[/tex]

=[tex]\frac{48550}{31}[/tex]

=1566.13

So The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13

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what the??????????????

This is a simple question to be solved.

First we need to know the number of vehicles (there are 6 vehicles), and second we need to know the number of cars (there are 4 cars). So the relation between the number of cars and vehicles is ----> 4/6

But we can simplify this relation as follows and represent it in a simple way:

So the final answer is the letter B) 2/3

We need to graph the line:

Notice that there is no restriction on the values of x. So, all the points with y-coordinate 3 belong to that line.

When we graph that line, we obtain:

Thus, this line is a horizontal line (parallel to the x-axis).

To answer this question, we need to expand the original equation, and then simplify to obtain the equivalent expression as follows:

We used the distributive property for -5 (1 + 5).

Then, we have:

Adding like terms:

In summary, therefore, the equivalent expression is:

The determinant of the matrix for the pineapple cake is 4350

The price of a pineapple cake is $30

The determinant of the matrix for the chocolate cake is 5075

The price of a chocolate cake is $35

Basically, what we want to do in this question is to form a set of linear equations then use matrix determinant method to solve for the unknowns in the linear equation.

Before we set up these equations,we need to use variables to represent the fruit prices;

Let p represent the price a of pineapple

Let c represent the price of a chocolate;

So let us proceed to form the linear equations;

The equation for the weekdays sales will be;

The equation for the weekend sales will be;

Now, we have two equations that we need to use the matrix determinant method to solve;

The above is the matrix set up we wil use;

Now, we start by calculating the determinant of 2 * 2 matrix; that would be;

Next is to find the determinant of the pineapple cake matrix;

To find this, what we will do is to substitute the coefficient of p with the total sales value to get a new matrix set;

The matrix for the pineapple cake will be;

Next is to find the determinant of the chocolate cake matrix;

To find this, what we will do is to substitute the coefficient of c with the total sales value to get a new matrix set;

The matrix for the chocolate cake will be;

Finally, we proceed to get the prices for the pineapple and the cake;

To get this, we simply divide the matrix of each by the initial matrix value;

There is a total of 10 students in Cassie's class.

8 students choose Pizza

So, the percentage of the students who picked the pizza is 80%.

[tex]Percentage\%= \frac{Students who picked Pizza}{Total number of students in class} *100[/tex]

[tex]Percentage\%= \frac{8}{10}*100\%[/tex]

                 [tex]=\frac{800}{10}\%[/tex]

                [tex]=80\%[/tex]

And 20% of students picked Burgers.

About Percentage

The Latin adverb "percent" means "by the hundred." The 16th century saw its invention. The abbreviation was later changed to %. Later, the period was eliminated, and the two words were merged to form the term "percent." Brief explanations employ the annotation sign %. Calculate your percentage of marks by comparing your final score to your overall score.

The percentage is a fraction or a ratio in which the value of the whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.

Percentage  Definition:

The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

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2a³ - 3a² - 45a + 50 is the simplified form of the expression ( 2a² + 7a - 10 )( a - 5 ) using FOIL method.

Given the expression in the question;

( 2a² + 7a - 10 )( a - 5 )

To expand ( 2a² + 7a - 10 )( a - 5 ), multiply each term in the first expression by each term in the second expression.

( 2a² + 7a - 10 )( a - 5 )

a( 2a² + 7a - 10 ) -5( 2a² + 7a - 10 )

a×2a² + a×7a + a×-10 -5×2a² -5×7a -5×-10

Multiply a and 2a²

2a³ + a×7a + a×-10 -5×2a² -5×7a -5×-10

Multiply a and 7a

2a³ + 7a² + a×-10 -5×2a² -5×7a -5×-10

Multiply a and -10

2a³ + 7a² - 10a -5×2a² -5×7a -5×-10

Multiply -5 and 2a²

2a³ + 7a² - 10a - 10a² -5×7a -5×-10

Multiply -5 and 7a

2a³ + 7a² - 10a - 10a² - 35a -5×-10

Multiply -5 and -10

2a³ + 7a² - 10a - 10a² - 35a + 50

Collect and add like terms

2a³ + 7a² - 10a² - 10a  - 35a + 50

2a³ - 3a² - 45a + 50

Therefore, the simplified form of the expression is 2a³ - 3a² - 45a + 50.

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The situation describes an exponential growth, which can be expressed using the general formula:

Where

a is the initial value

r is the growth rate, expressed as a decimal value

x is the number of times intervals

y is the final value after x time intervals

For the studied population, the growth rate is 2.5%, to express this number as a decimal value you have to divide it by 100:

The initial value is the current population of the town: a=50000

You can express the equation of exponential growth for this population as follows:

We know that after x years the population will be y=100000, to determine how many years it will take to reach this value you have to equal the equation to 100000 and solve for x:

-Divide both sides of the expression by 50000

-Apply logarithm to both sides of the equal sign:

-Divide both sides by the logarithm of 1.025

After approximately 28 years the population of the town will be 100,000.

Answer:

Step-by-step explanation:

y = -|x|

The graph is facing downwards, meaning it is negative.

Question:

Step 1: Apply the exponent rule but taking ln of both sides

Step 2:Divide both sides by -5

Hence,

The value of x is

Hence,

The final answer is = -0.4003

we have the following

sin of an angle is the same as:

therefore we can create the following right triangle:

we can calculate the adjacent side using the pythagorean theorem

where h is the hypotenuse, a is the adjacent side and b the opposite side to the angle.

thus, the adjacent side is:

Using that value, we can now calculate cos of the angle

which can't be simplify, thus that is the answer for the exact value

The percent tip which Ai mi added to the $9 dinner as required in the task content is; 31%.

It follows from the task content that the percent tip which Ai mi added to the dinner is to be determined by evaluation.

Since the dinner itself costs; $9 and she paid $11.79 after adding tip, it follows that the percent tip is the percentage change in price paid per unit original price as follows;

Percent tip = { ( 11.79 - 9 ) / 9} × 100%

Percent tip = 2.79/9 × 100%

Percent tip = 31%.

Therefore, the percent tip added by Ai mi to the original price of dinner is ; 31%.

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Reflection:

A reflection is a transformation that flips a figure across a line.

Properties of reflection:

• The length remains the same, the angles remain the same.

• This means that the image and the pre-image have the same size and shape only the orientation changes.

• The line segment which connects the corresponding parts of the image and pre-image is perpendicular to the line of reflection.

• The distance from the line of reflection of the corresponding parts of the image and pre-image is the same.

Following is an example of a reflection

This is called a horizontal reflection since the image and the pre-image is flipped across the x-axis. The line of reflection is the vertical line.

The system has no solutions

Here, we want to solve the system of linear equations

As we can see, the exact expression is what we have on the left side of both equations

The only different thing is what we have on the right hand side

What this mean is that no values of x and y can satisfy both equations

With that in mind, we have it that the system of equations has no solutions

The total amount (in dollars) saved using both plans combined is T = 50 + 101.1N.

Based on the information, the function = 50+20.55N.

where N is the number of weeks she has been saving.

For the second function, this is illustrated as:

function B = 80.55 N.

Therefore, the total of the plans combined will be:

T = 50 + 20.55N + 80.55N

T = 50 + 101.1N

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A square is a quadrilateral with four equal straight sides and four right angles.

In this sense since the diagonals of a square bisect each other and meet at 90° and are congruent, we can conclude it is enough justification to prove that CDEF is a square

The smallest whole number is 750,000, while the largest whole number is 849,999.

Consider the facts offered.

We must determine the smallest whole integer that, when rounded to the nearest hundred thousands, equals 800,000

Rounding a numerical rule

If the number on the right side of the rounding digit is 0, 1, 2, 3, 4, there is no need to modify the rounding digit and replace the remainder of the digit on the right with 0.

If the number on the right side of the rounding digit is 5, 6, 7, 8, 9, the rounding digit rounds up by one number and replaces the remainder of the digit on the right with 0.

Consider the number 800,000 for a moment.

Because we want the smallest number possible, the number at the hundred thousand place should be 7.

As a result, the smallest whole number is 750,000.

We now want the largest whole number that rounds to 800,000

Similarly, the biggest whole number must be bigger than 800,000 We don't want to raise the number at the hundred thousand place, hence the best ten thousand place option is 4. Put 9 at the rest locations to get the highest number.

As a result, the biggest whole number is 849,999.

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Given:

The coordinates of C, the midpoint of AB, (X, Y)=(1, 5).

The coordinates of A, (x1, y1)=(3, 2).

Let the coordinates of B be (x2, y2).

The midpoint formula is given by,

Hence,

Substitute the known values in equation (1) and solve for x2.

Hence, x2=-1.

Substitute the known values in equation (2) and solve for y2.

Therefore, the coordinates of point B is (x2,y2)=(-1, 8).

To determine the arc length of the shaded area you have to use the following formula:

"θ" represents the measure of the central angle, in degrees

"r" represents the radius of the circle

We know that the arc measure is 126º, the central angle has the same measure as the intercepted arc, then its measure is also θ=126º

The radius of the circle is r=15cm

Generally, one should not write down values such as this directly from a calculator. √2 is an irrational number, which means that instead of writing it as a terminating decimal, it is best to write it in its exact form (√2) to ensure accuracy for further calculations.

Given the function below;

The x-intercept is the point where f(x) = 0 as shown:

The x-intercept of the graph will be at (5.66, 0) and (-5.66, 0)

The y-intercept occurs at the. point where x = 0 to have:

The y-intercept is (0, 4)

The equivalent graphis as shown below

The graph shows that the function has a maxmum point at (0, 4) with no minimum point.

Using it's concept, the probabilities are given as follows:

1. Red then white: 7/26.

2. Both red: 5/26.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For item 1, we have that:

Hence the probability is:

6/13 x 7/12 = 7/26.

For item 2, we have that:

Hence the probability is:

6/13 x 5/12 = 5/26.

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