The sale price of a trampoline before tax is $300 the sales tax is 4% find the sales tax in the total price of the trampoline

Answer:

12Pi

Step-by-step explanation:

circumference of a circle can be worked out as Pi x diameter

Diameter = 2 x radius, therefore here d = 12 and circumference = 12 Pi

The circumference of the circle is C = 12π meters

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r = 6 meters

Now , circumference of circle = 2πr

On simplifying , we get

C = 2π ( 6 )

C = 12π meters

Hence , the circumference is 12π meters

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Answer:

2x² + 2x + 3

Step-by-step explanation:

x = 3 is a zero of both the numerator and the denominator, so the denominator will factor completely into the numerator with no remainder.  Using grouping to factor:

(2x³ − 4x² − 3x − 9) / (x − 3)

(2x³ − 4x² − 6x + 3x − 9) / (x − 3)

(2x (x² − 2x − 3) + 3x − 9) / (x − 3)

(2x (x − 3) (x + 1) + 3 (x − 3)) / (x − 3)

2x (x + 1) + 3

2x² + 2x + 3

To use long division instead, see image.

Answer:

C) –|x| + 3

I got the answer correct!!!

Answer:

The valid value of x is x=-2

Step-by-step explanation:

we know that

The sum of the interior angles of any quadrilateral must be equal to 360 degrees

so

[tex](7x^{2}-24x)+100+(24-46x)+(3x^{2}+56)=360[/tex]

solve for x

Combine like terms

[tex]10x^{2}-70x+180=360[/tex]

[tex]10x^{2}-70x-180=0[/tex]

Divide by 10 both sides

[tex]x^{2}-7x-18=0[/tex]

The formula to solve a quadratic equation of the form

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

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-7x-18=0[/tex]

so

[tex]a=1\\b=-7\\c=-18[/tex]

substitute in the formula

[tex]x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(1)(-18)}} {2(1)}[/tex]

[tex]x=\frac{7(+/-)\sqrt{121}} {2}[/tex]

[tex]x=\frac{7(+/-)11} {2}[/tex]

[tex]x=\frac{7(+)11} {2}=9[/tex]

[tex]x=\frac{7(-)11} {2}=-2[/tex]

Remember that

The measure of the interior angle cannot be a negative number

For x=9

we have that the measure of one interior angle of quadrilateral  is

[tex]24-46x[/tex]

substitute the value of x

[tex]24-46(9)=-390\°[/tex]

therefore

The value of x=9 cannot be a solution

For x=-2

The measure of the interior angles are

[tex](7(-2)^{2}-24(-2))=76\°\\100\°\\(3(-2)^{2}+56)=68\°\\24-46(-2)=116\°[/tex]

therefore

The valid value of x is x=-2

Answer: y+3 = 4( x + 1)

Step-by-step explanation:

The equation in point slope form is given as :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) , where m is the slope

slope = 4

point given : (-1,-3)

Using the formula :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

and substituting the value , we have

y - (-3) = 4 (x -{-1} )

y+3 = 4( x + 1)

Three other ordered pairs with θ between −360° and 360° that name the same point as (−3, 330°) are (−3, 30°), (−3, 690°), and (−3, -30°).

Given the ordered pair (−3, 330°), we can find three other ordered pairs that name the same point by adding or subtracting 360° from the given angle:

These three ordered pairs have angles between −360° and 360° and represent the same point as the given ordered pair.

Answer:

There was 62.23% change in radius as the ion formed.

Step-by-step explanation:

Given

Radius of Aluminium [tex](Al)[/tex] atom  = 143 pm

Radius of Aluminium [tex](Al^{3+})[/tex] atom  = 54 pm

Change is the radius =  Radius of Aluminium [tex](Al)[/tex] atom - Radius of Aluminium [tex](Al^{3+})[/tex] atom = 143 -54 = 89

Now to find % Change is the radius we will divide Change is the radius by Radius of Aluminium [tex](Al)[/tex] atom and multiply by 100 we get

% Change is the radius = [tex]\frac{\textrm{Change is the radius}}{\textrm{Radius of Aluminium (Al) atom}} \times 100 = \frac{89}{143}\times100= 62.23\%[/tex]

Hence there was 62.23% change in radius as the ion formed.

Answer:

(A) y+2=3(x-1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=3(x-1)

y+2=3(x-1)

Answer:

Nick gave 3 marbles to each of his 4 friends.

Step-by-step explanation:

Given:

Total Number of Marbles = 12

Number of Friends = 4

Let the number of marbles to be divided in each friend be x

Solution:

To find the number of marbles to be divided in each friend we have to divide Total Number of Marbles by  Number of Friends.

Hence number of marbles to be divided in each friend x = [tex]\frac{\textrm{Total Number of Marbles}}{\textrm{Number of friends}}= \frac{12}{4}=3[/tex]

Hence we can say that Nick gave 3 marbles to each of his 4 friends.

Answer:

r = 0.93

Step-by-step explanation:

The correlation coefficient gives us the "strongness" of two variables associated.

This is the value "r".

It is positive if there is strong relationship (one goes up, another goes up and vice versa)

It is negative, if one goes up and another goes down (inverse relationship)

First of all, from the scatter points, we see that as x increases, y also tend to increase. And if we were to draw a line of best fit that goes through max points, we would see the line slopes UPWARD (means as x increases, y also increase).

Thus, the value of "r" will be positive. So we can eliminate first and second choice. Now remains the other two choices

0.64

0.93

The closer the value to 1, the more that line is slopier, and less that value from 1, the line will be less "slopy".

A perfect one would be a line with slope 1, as 1 unit increase in x, the y increases 1 unit as well.

So, if we were to draw a line, we would see that it will be very close to a value of 1. The value of 0.64 can be eliminated because the points are not much "relaxed" as it should be for 0.64.

So, the correct choice is the 4th choice, r = 0.93

Answer:

4b = 8

Step-by-step explanation:

Given 12b = 24

This is written as (4 X 3)b = 24

⇒ 4b X 3 = 24

Dividing by 3 throughout, we have

4b = [tex]$ \frac{24}{3} $[/tex] = 8.

Therefore, the value of 4b is 8.

A 100% increase means a value doubles, a 100% decrease means it drops to zero, and 100% error indicates complete inaccuracy. For increases and decreases, the percentage is calculated based on the ratio of change to the original amount multiplied by 100%. Percent error compares the experimental value with the accepted value to judge accuracy.

An example of a 100% increase would be if you have $50, and this amount doubles to $100. Here the final amount is 100% more than the original, as the increase ($50) is equal to the original value ($50). The formula used is % increase = (Amount of increase/original amount) x 100%. So, % increase = ($50/$50) x 100% = 100%.

A 100% decrease implies that something diminishes completely to zero. For instance, if you have 10 apples and all of them are taken away, the percent decrease is 100% since the decrease (10 apples) equals the original quantity (10 apples). The calculation would be % decrease = (Decrease/original amount) x 100%, which results in % decrease = (10/10) x 100% = 100%.

100% error in a measurement means the measurement is completely inaccurate. For example, if the accepted value of a length is 30 cm and the experimental measurement is 60 cm, then the percent error is calculated as: % error = (Absolute value of (Experimental value - Accepted value)/Accepted value) x 100%, which in this case is % error = (|60 cm - 30 cm|/30 cm) x 100% = 100%. This represents a complete deviation from the actual value.

Answer:

120 50 pound bags

Step-by-step explanation:

first you see how much 50 pounds is to one ton which one 50 pound bag is equal to .025 tons

then you multiply .025 by 120 to get 3 (tons)

that shows that the answer is correct

Answer:

Step-by-step explanation:

[tex]-\dfrac{2}{3}u=-4\qquad\text{change the signs}\\\\\dfrac{2}{3}u=4\qquad\text{multiply both sides by}\ \dfrac{3}{2}\\\\\dfrac{3\!\!\!\!\diagup^1}{2\!\!\!\!\diagup_1}\cdot\dfrac{2\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}u=4\!\!\!\!\diagup^2\cdot\dfrac{3}{2\!\!\!\!\diagup_1}\\\\u=(2)(3)\\\\u=6[/tex]

Answer:

See above graph

Step-by-step explanation:

In between those whole numbers, each mark represents ⅕ [or 0,2], therefore you move one-fifth block to the right of 20 with an open circle, then shade everything to the left.

≥, ≤ → Solid Circle [●]

>, < → Blank Circle [○]

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To graph the solution of the inequality, p < 20.2, one must draw a number line. Mark a point on the number line at 20.2 and shade or draw an arrow pointing to the left of this mark. Ensure to use an open circle at 20.2 to show that it itself is not part of the solution.

To graph the solution of the inequality p < 20.2 on a number line, you need to take the following steps:

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If the line is parallel to y=2x, the line must have the same slope.

So, the slope of your line is 2.

Now we need to find the y intercept. We should use the point given.

y=mx+b

-3=2(-4)+b

b=5

Equation: y=2x+5

Answer:

55/18

Step-by-step explanation:

f(x) = 2/3*12 +3

= 1/18 +3

=55/18

The value of f (12) will be;

⇒ f (12) = 11

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is,

⇒ f (x) = 2/3x + 3

Now,

Since, The function is,

⇒ f (x) = 2/3x + 3

Substitute x = 12 in above equation, we get;

⇒ f (x) = 2/3x + 3

⇒ f (12) = 2/3 × 12 + 3

⇒ f (12) = 2 × 4 + 3

⇒ f (12) = 11

Thus, The value of f (12) will be;

⇒ f (12) = 11

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The rectangle can be divided into  6 ways as, 1 × 56 or 56 × 1,  2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

Darren has a piece of wood that is 7 in by 8 in

The area of the rectangle can be given by,

[tex]Area = Length\times width[/tex]

Area = 7 × 8

Area = 56

You can now divide the length and width as shown below,

Rectangle =   1 × 56 or 56 × 1

Rectangle =   2 × 28 or 28 × 2

Rectangle =   4 × 14 or 14 × 4

Therefore, the rectangle can be divided into  6 ways as   1 × 56 or 56 × 1,  2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.

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Answer:

21 miles

Step-by-step explanation:

Jeff drove [tex]=\dfrac{1}{2}[/tex] of the trip

Jason Joe drove [tex]=\dfrac{1}{4}[/tex] of the trip

Together Jeff and Jason Joe drove [tex]=\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}[/tex] of the trip

All trip [tex]=1[/tex]

Remaining trip [tex]=1-\dfrac{3}{4}=\dfrac{4}{4}-\dfrac{3}{4}=\dfrac{1}{4}[/tex]

Susan and Sharon divided the rest of the drive equally, so

Susan drove = Sharon drove [tex]=\dfrac{1}{4}:2=\dfrac{1}{4}\cdot \dfrac{1}{2}=\dfrac{1}{8}[/tex] of the trip.

The entire trip was 168 miles, then

Sharon drove [tex]=\dfrac{1}{8}\cdot 168=21\ miles[/tex]

Answer:

The student council from each box of candy will make the profit of $23.50.

Step-by-step explanation:

Given:

Each box of candy costs $50. Profit of 47% from each candy.

Now, to get the amount of how much profit from each box:

Amount of profit (A) = Profit% of cost of candy of each box

A = 47% of $50

[tex]A=\frac{47}{100}\times 50[/tex]

[tex]A=0.47\times 50[/tex]

[tex]A=23.50[/tex]

Amount of profit = $23.50

Therefore, the student council from each box of candy will make the profit of $23.50.

Answer:

x equals plus or minus square root of 5 minus 1

Step-by-step explanation:

we have

[tex]x^{2} +2x=4[/tex]

Divide by 2 the coefficient of the x-term

[tex]2/2=1[/tex]

squared the number

[tex]1^2=1[/tex]

Adds both sides

[tex]x^{2} +2x+1=4+1[/tex]

[tex]x^{2} +2x+1=5[/tex]

Rewrite as perfect squares

[tex](x+1)^{2}=5[/tex]

take the square root both sides

[tex]x+1=(+/-)\sqrt{5}[/tex]

[tex]x=(+/-)\sqrt{5}-1[/tex]

therefore

x equals plus or minus square root of 5 minus 1

Answer - B. x = ± [tex]\sqrt{5[/tex] - 1

Answer:

Step-by-step explanation:

if y = 1/2x - 1 is the function

y = 1/2(-4) - 1

y = -2 - 1

y = -3

(-4, -3)

y = 1/2(2) -1

y = 1 - 1

y = 0

(2, 0)

y = 1/2(6) - 1

y = 3 - 1

y = 2

(6, 2)

the pictures should be in order

Answer:

[tex]\displaystyle 2 = f(6), 0 = f(2), -3 = f(-4)[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{2}[6] - 1 = 3 - 1 = 2 \\ \\ \frac{1}{2}[2] = 1 - 1 = 0 \\ \\ \frac{1}{2}[-4] - 1 = -2 - 1 = -3[/tex]

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To find the product of 7 and 28 using place value and the distributive property, rewrite the product as 7(20 + 8). Distribute the 7 to both terms inside the parentheses and then add the resulting products.

To find the product of 7 and 28 using place value and the distributive property, we can rewrite the product as 7(20 + 8). This is because 28 can be decomposed into 20 + 8.

Using the distributive property, we can distribute the 7 to both terms inside the parentheses: 7(20) + 7(8).

The product of 7 and 20 is 140 and the product of 7 and 8 is 56. Therefore, the final product is 140 + 56 = 196.

The functions f and g that adds up to h(x) are:

f(x) = -2x+3 and g(x) = 7x-9

Step-by-step explanation:

Required output is:

h(x) = 5x-6

In order to find the required f and g functions we will see that which of the two functions add up to h(x)

In order to make our work easier we can see the functions f and g whose coefficients of  add up to 5x

Then we can select from the functions that produce h(x)

So,

Pair 1 whose coefficients of x add up to 5 is:

f(x) = -2x+6 and g(x) = 7x-9

Adding both functions

[tex](f+g)(x) = -2x+6+7x-9\\= 5x-3[/tex]

Pair 2 that adds up to 5x

f(x) = 8x+9 and g(x) = -3x-3

Adding both functions:

[tex](f+g)(x) = 8x+9-3x-3\\= 8x-3x+9-3\\=5x+6[/tex]

Pair 3 is:

f(x) = -2x+3 and g(x) = 7x-9

Adding both functions

[tex](f+g)(x) = -2x+3+7x-9\\= -2x+7x+3-9\\=5x-6[/tex]

Hence,

The functions f and g that adds up to h(x) are:

f(x) = -2x+3 and g(x) = 7x-9

Keywords: Functions, Sum of functions

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The correct answer is A

Answer: B. 239 Square Feet

Step-by-step explanation:

Let y be the size of a kitchen that costs $3,824.00.

Given : The price of tiling a room varies directly as the size of the room.

Equation of direct variation between x and y : [tex]\dfrac{x_1}{x_2}=\dfrac{y_1}{y_2}[/tex]

If the tiling costs 4,224.00 for 264 square feet , to find the  size of a kitchen that costs $3,824.00.

We put [tex]x_1= 4224 \ \ ; \ y_1=264\ ; \x_2=3824\ ; \ y_2=y[/tex] , we get

[tex]\dfrac{4224}{3824}=\dfrac{264}{y}\\\\\Rightarrow\ y=\dfrac{264\times3824}{4224}=239[/tex]

Hence, the size of a kitchen that costs $3,824.00 is 239 Square Feet

The correct answer is B. 239 Square Feet

How much money did he have

Answer:

His profit would be $37 of the money he got back.

Step-by-step explanation:

Answer:

I'd say C.60but because of the half units its possibly B. but definitely not A or D.

Step-by-step explanation:

Because the short sides are approximately 6 units long and the long sides are 10 units long. You multiply it to find the area and you get 60.

hope this helps

The area of the graph rectangle is 60 sq. units.

The correct option is D) 60 sq. units.

The area of a rectangle is expressed as:

Area = length × width

First, we use the distance formula to find the length and width of the rectangle.

[tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

From the graph, the length is between the points (-1,1) and (8,-2):

Hence;

[tex]Length = \sqrt{(8-(-1))^2 + (-2 - 1)^2}\\\\Length = \sqrt{(8+1)^2 + (-2 - 1)^2}\\\\Length = \sqrt{(9)^2 + (-3)^2}\\\\Length = \sqrt{81 + 9}\\\\Length = \sqrt{90}\\\\Length = 3\sqrt{10}[/tex]

Next, we find the width which is between the points (-1,1) and (-3,-5):

[tex]Width = \sqrt{(-3 - (-1))^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-3 + 1)^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-2)^2 + (-6)^2}\\\\Width = \sqrt{4 + 36}\\\\Width = \sqrt{40}\\\\Width = 2\sqrt{10}[/tex]

Now, plug the values for the length and width into the above formula and solve for the area:

Area = length × width

Area = 3√10 × 2√10

Area = 3 × 2 × 10

Area = 60 sq. units

Therefore, the area measures 60 sq. units.

Option D) 60 sq. units is the correct answer.

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Answer:

Left box: Outlier in this data set is (57,132)

Right box: because the finish time looks faster than expected for the age.

Step-by-step explanation:

As per the given table shows the [tex]age[/tex] and [tex]finish \ time[/tex] of [tex]10[/tex] runners.

It is clear that people of age around [tex]35[/tex] are finishing at around [tex]142 \ minutes[/tex]

and person with older age takes longer to finish.

One person of age [tex]57[/tex] finishes in [tex]175 \ minutes[/tex] , that looks as expected.

Another person of same age [tex](57)[/tex] finishes it too fast which is unexpected.

Therefore [tex](57,132)[/tex] is an outlier, because it looks a faster finish as per expected.

Answer:

The left box = (57 , 132)

The right box= The finished time is expected for the age.

Step-by-step explanation:  

Answer:

c then b

Step-by-step explanation:

2 - The elevation at Point E is 50 feet, marked by a contour line, 3 - Point F is at 70 feet elevation, illustrating the informative nature of topographic maps.

On Map 1, Point E is situated at an elevation of 50 feet, as it lies directly on the contour line representing this specific elevation. Contour lines on a topographic map connect points of equal elevation, allowing us to visualize the three-dimensional terrain on a two-dimensional surface.

In this context, every point on the contour line labeled "50 feet" shares the same elevation—50 feet above a reference point, typically sea level. Moving to Point F on Map 1, it is positioned on the contour line corresponding to an elevation of 70 feet.

This indicates that Point F is situated 70 feet above the same reference point. Topographic maps are invaluable tools for understanding the landscape's elevation variations, aiding hikers, geologists, and cartographers in navigating and representing the Earth's surface features accurately.

The contour lines on such maps provide a detailed depiction of the elevation changes, and by closely following them, one can trace the undulations of the terrain.

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