Find the 8th term of the geometric sequence 7, 28, 112, ...

The required cost of the meal given as a hot dog is of $6 and the hamburger is of $8.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Let's call the cost of a hot dog meal "x" and the cost of a hamburger meal "y".

From Mrs. Hammond's purchase, we know that:

x + 3y = 30   -- - - - - -(1)

From Mr. Weber's purchase, we know that:

3x + 3y = 42 - - - - - -(2)

We can use substitution to solve for one of the variables in terms of the other. If we substitute the first equation into the second equation:

3x + 3y = 42

3x + 3(30 - x)/3 = 42

3x + 30 - x = 42

2x = 12
x = 6

now,
6 + 3y = 30
3y = 24
y = 8

Thus, the required cost of the meal given as a hot dog is of $6 and a hamburger is $8.

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Answer:

#9       (x, y) = (6, 32)

#10      The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same and is $32

Step-by-step explanation:

The legend is missing so by looking at the graph alone we are unable to determine which color line corresponds to which kind of kite(Kites-R-Fun or Windy Kites)

However the associated table will help us determine this

The linear equation for a line is expressed as

y = mx + c

where m = slope of the line and b = y-intercept which is the y-value for the point where the line crosses the y-axis(at x = 0)

Slope m = rise/run = Δy/Δx = (y2 - y1)/(x2 - x1) for any two points (x1, y1) and (x2, y2) on the line

Let's take the two  x values as x1=0 and x2=1 and use the table

For Kites-R Fun
x1 = 0 ==> y1 = 8. This is also the y-intercept, b
We see that the red line corresponds to x = 0, y = 8

x2 = 1 ==> y2 = 12

y2 - y1 = rise = Δy =12 - 8 = 4

x2 -   x1 = Δx = 1 - 0 =1

Slope m = 4/1 = 4

Equation of Kites-R Fun is 4x + 8

For Windy Kites

x1 = 0 ==> y1 = 20
y-intercept = 20 or b = 20

x2 = 1 ==> y2 = 22

Rise = Δy =22 - 20 = 2
Run = Δx = 1 - 0 = 1
Slope = m, b = 20

Equation of blue line is
y = 2x + 20

The two equations are:
y = 4x + 8
y = 2x + 20

Equating right sides:
4x + 8 = 2x + 20

Move 2x to the left side and 8 to the right side:

4x + 2x + 8 - 8 = 2x - 2x + 20 -8

2x = 12

x = 6

For x = 6 the costs are the same

Plugging x = 6into equation y = 4x + 8:
y = 4(6) + 8 = 24 + 8 = 32

So the solution set is
(6, 32)

Looking at the graph we see the two lines intersect at this point
(Heck, we could have avoided all this work and just looked at the graph but I don't expect that was what they intended. You can add this as a side note)

On the second part

For Kites-R-US, each kite costs $4
The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same.

The first four terms are 35, 50, 65, 80.

And the recursive formula:

aₙ = aₙ₋₁ + 15

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

The sequence defined by the explicit formula g(n)=15n + 35

The first term,

g(0) = 0 + 35 = 35.

g(1) = 15 + 35 = 50

g(2) = 30 + 35 = 65

g(3) = 45 + 35 = 80.

The common difference is 15.

The recursive formula:

aₙ = aₙ₋₁ + 15

Therefore, the formula is aₙ = aₙ₋₁ + 15.

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Answer:

3rd quadrant

since the x and the y co-ordinates are negative ,it can only fit in the third since

1st=positive, positive

2nd=negative, positive

3rd=negative, negative

4th=positve, negative

The correct answer is option (C). The answer is round function.

Given that,

Instead of just altering what is presented, Excel changes the amount of decimal places it really keeps.

To find : Something alters the real number of decimal places?

Number is rounded using ROUND function to a given number of digits. You can use the following formula, for instance, to round the value 23.7825 in cell A1 to two decimal places: =ROUND(A1,2) (A1,2) is 23.78 is the output of the function

Therefore, option is the right response (C). Round function is the solution.

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Answer:

II and III only

Step-by-step explanation:

Answer:

The amount budgeted for Auto expenses is $100,000 * 14% = $14,000.

Step-by-step explanation:

Answer:

16 19/50

Step-by-step explanation:

first make improper fractions of both 3 9/10 and 4 1/5

mutltiply the denomiator (the number on the bottom) by the whole number, add the numerator (the number on the top) and put that number over the denomiator. 3 9/10 = 39/10 and 4 1/5 = 21/5. Multiply the improper fractions. numerator x numerator and write that on the top with a line under it. Multiply the denomiators and write that on the bottom. 39*21= 819. 10*5=50. your number would be 819/50. Then divide 819 by 50. You get 16 19/50

The point that creates a right triangle with the points (3, 6) and (8, -2), which Christopher could place on the graph to create a right triangle is the point (8, 7.25)

A right triangle is a triangle with one ninety degrees (90°) interior angle.

The points on the right triangle Christopher already graphed (3, 6), and (8, -2)

The property of a right triangle is one of the interior angles is 90°, therefore, the legs or two of the sides of a right triangle are perpendicular.

The slope of the line joining the specified two points is found as follows;

Slope = (-2 - 6)/(8 - 3) = -8/5

The slope of the line perpendicular to the line segment Christopher used to join the points (3, 6), and (8, -6) is 5/8

The equation of the perpendicular line is therefore;

y - 6 = (5/8)·(x - 6)

y = (5/8)·(x - 6) + 6 = 5·x/8 + 18/8

y = 5·x/8 + 18/8

When x = 8, we get; y = 5 × 8/8 + 18/8 = 7.25

Therefore, the point (8, 7.25), forms a right triangle with the points (3, 6) and (8, -2)

A point Christopher can place on the graph to create a right triangle is (8, 7.25)

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Answer:

I Don.t really know the answer

A rectangular board is 1300 millimeters long and 800 millimeters wide. Then, the area of the board in square meters is 104 m².

These are the specified parameters:

Length of the board (l) = 1300 mm

Breadth of the board (b) = 800 mm

The area of a rectangular board

A = l × b

  = 1300 mm × 800 mm

  = 1040000 mm²

The area of the board in square meters

To convert mm² to m², divide mm² by 10000.

Therefore

A = 1040000 mm²

  = 1040000 : 10000 m²

  = 104 m²

So, the area of the board in square meters is 104 m².

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The volume of the round metal washer is  94.25 cm cube.

As inferred from the question, the shape of the round metal washer is that of a hollow cylinder with:

outer radius=  8 cm

inner radius =2 cm

thickness = 0.5 cm

we know that the formula for calculating the volume of a hollow  cylinder is as follows:

V = π ( [tex]R^{2}[/tex]-[tex]r^{2}[/tex])h cubic units

[ where R = outer radius, r= inner radius]

Putting the values in the above formula gives:

V=  π ( 8 - 2) X 0.5

-> V=  π (64-4) X 0.5 = 94.25 cm cube

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The central angle corresponds to an arc length of 2 yd and a radius of 7 yd is 0.09 pi

Central angle is the angle subtended by an arc of a circle at the center of a circle. The radius vectors form the arms of the central angle. In other words, it is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle. When these two points are joined they form an arc. Central angle is the angle subtended by this arc at the center of the circle

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle. An excellent illustration of a central angle is a pizza slice. A pie chart is made up of several sectors and is useful for representing various amounts.

Central angle =(s*360)/(2pir)

=we have s=2 yd

radius = 7 yd

angle = 16.5 degree = 0.09 pi

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Answer:

yes

Step-by-step explanation:

because everytime you add 2 for x you add 1.8 for y

that means the difference is constant and the function is linear

The value of x considering the mean is two will be equivalent to 7.

The mean also known as the average is obtained by adding the data and then dividing it by the number of values. Here is an example: 3+6+4 = 13 / 3 = 4.3.

We know the mean is 2, based on this let's calculate the missing number:

The current number of cats: is 0+ 8 + 12 +3 =23 Based on this, the missing number would be 7, which would lead to a total of  8+12+24 = 44 cats divided by a total of 22, which means there are 2 cats per family.

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The correct justification of the equation from 2(y - 5) + 4 = 4 to 2y - 10 + 4 = 4 using distributive property of addition.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

2(y - 5) + 4 = 4

Apply distributive property of addition. Then the equation is written as,

2(y - 5) + 4 = 4

2y - 10 + 4 = 4

Simplify the equation further, then we have

2y - 10 + 4 = 4

2y - 6 = 4

2y = 10

y = 5

The correct justification of the equation from 2(y - 5) + 4 = 4 to 2y - 10 + 4 = 4 using distributive property of addition.

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The solution is,  Rectangle A has the largest area.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

from the given figure we get,

Each square is 1 square unit.

now, Rectangle A has 18 square

Rectangle C has 10 squares

Rectangle B has 8 squares

So, area of Rectangle A is 18 sq. unit

Rectangle C is 10 sq. unit

Rectangle B is 8 sq. unit

i.e. 18>10>8

Hence, Rectangle A has the largest area.

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The student's answer is incorrect; they should have distributed the negative sign to the terms in the second parentheses, then combine like terms: 6b 4r - 2b r = 4b + 3r.

The student's answer is incorrect; they should have distributed the negative sign to the terms in the second parentheses. To correctly simplify the expression, first distribute the negative sign, then combine like terms. Start by distributing the negative sign: 6b 4r - 2b r = 6b 4r + (-2b) (-r). Then, combine like terms: 6b 4r + (-2b) (-r) = 6b + (-2b) + 4r + (-r) = 4b + 3r. This is the correct answer.  It is important to note that when subtracting within parentheses, you must distribute the negative sign to each term. Once the negative sign has been distributed, you can then combine like terms. This method can be used to simplify any expression with parentheses and subtractions.

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The statistical procedure that researchers use to identify underlying components that may exist in test without first proposing a formal model is exploratory factor analysis.

In order to carry out a statistical analysis, we need to collect and review a sample of the data available in the research results for analysis.

While there is no single way to perform interpretive analysis, there are practices that can be replicated in any research if done in a way that is appropriate to the information provided.

These tips will allow us to carry out useful statistical analysis.

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Working alone, Allen can build 1/8 of the fence in 1 hour and working together, Allen and Danny can build 1/X of the fence in 1 hour, where X is their combined rate.

Let's say the total time required to build the fence is T hours.

After 2 hours, Allen has completed 1/8 * 2 = 1/4 of the fence.

So, the remaining work to be done is T - 1/4.

When Allen and Danny work together, their combined rate is X = 1 / (1/8 + 1/16) = 4/7.

The total time taken by them to finish the remaining work is (T - 1/4) / (4/7) = (7/4) * (T - 1/4) = 7T/28 - 7/28.

So, the total time taken to build the fence is 2 + (7T/28 - 7/28) = 2 + 7T/28 = T.

Therefore, T = 2 + 7T/28 = 2 + 7 * (8 hours) / 28 = 2 + 4 hours = 6 hours.

So, Allen and Danny took 6 - 2 = 4 hours to build the fence after working together.

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   ( 0, 7 ) and ( 0,4 ) are  two points of the equation .

What Is an Equation, exactly?

An equation is a mathematical expression with two equal sides and an equal sign in between.

                                  An equation is, for instance, 4 + 6 = 10. 4 + 6 is visible on the equal sign's left side, and 4 + 6 is visible on the equal sign's right side.

    ( 4,0) & ( 0,7 )

Given constraint  is

        7x₁ + 4x₂ ≤ 28

  IF  x₁ = 0

         4x₂  =  28  

          x₂ = 7

        ( 0, 7 )

If x₂  = 0

    7x₁ = = 28

     x₁  = 4

       ( 4 ,0 )

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Sigma notation for the sum is  ∑5ⁿ⁻⁴ (where n = 1 to 5)

Sigma notation is the most easiest way of writing a very large sum of elements of a sequence in a simple manner.

∑ is the symbol that is pronounced as "sigma".

"i" or "n" is called the index of summation

Given sum,

1/125 + 1/25 + 1/5 + 1 + 5

First term a is 1/125

Common ratio r = 1/25/1/125 = 5

Sequence can be written as

aⁿ = a.rⁿ⁻¹

aⁿ = 1/125 . 5ⁿ⁻¹

aⁿ = 5⁻³. 5ⁿ⁻¹

aⁿ = 5ⁿ⁻⁴

Sigma notation can be written as

∑5ⁿ⁻⁴ where n = 1 to 5.

Hence, Sum expressed as Sigma notation ∑5ⁿ⁻⁴ (where n = 1 to 5).

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The volume of the solid is approximately 807.08 cubic units.

To determine the volume of the solid, we can use the method of cylindrical shells.

Imagine taking a slice of the solid parallel to the base, with the cross-sectional area being a square of side length x (where x is a function of the height). The volume of this slice is the product of the square area and the height. The height of the slice is equal to the difference in the radii of two consecutive circular cross sections.

The radius of the larger circular cross-section can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the radius) is equal to the sum of the squares of the other two sides (the height and half the side length of the square). Thus, we have:

r² = x² + (15-x)²

Solving for x, we get:

x = 15 * √(1 - (r/15)²)

The volume of the slice is then given by:

V = x² * (15 - x)

To find the total volume of the solid, we integrate this expression with respect to r from 0 to 15. The result is approximately 807.08 cubic units.

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Line segment is a a measurable part of a line that consists of two points, called endpoints.

a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that measurable part of a line that consists of two points, called endpoints is a line segment.

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

Hence, line segment is a a measurable part of a line that consists of two points, called endpoints.

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The total gallons of water made use of in the park after the new ride is installed is,

⇒ 21.0049 × 10⁶ gallons of water

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

A water park has pools, slides, and rides that, in total, make use of

2.1 × 10⁷ gallons of water.

And, They plan to add a ride that would make use of an additional 4.9 × 10³ gallons of water.

Hence, The total gallons of water made use of in the park after the new ride is installed is,

⇒ 2.1 × 10⁷ + 4.9 × 10³

⇒ 21000 × 10³ + 4.9 × 10³

⇒ (21,000 + 4.9) × 10³

⇒ 21,004.9 × 10³

⇒ 21.0049 × 10⁶ gallons of water

Thus, The total gallons of water made use of in the park after the new ride is installed is,

⇒ 21.0049 × 10⁶ gallons of water

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The surface area of the rectangle prism is 52.05 in²

The total surface area of a prism is the sum of the areas of its lateral faces and its two bases.

The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.

l = 7.2 in

b = 1 1/2 = 3/2

h = 1 3/4 = 7/4

SA = 2( 7.2×1.5+ 7.2 × 1.75 + 1.75×1.5)

SA = 2( 10.8 + 12.6 + 2.625)

SA = 2 ( 26.025)

SA = 52.05 in²

therefore the surface area of the rectangle prism is 52.05 in²

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Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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If Logan has given out a total of 6.65 in nickels and dimes , then the number of dimes he has given out is  38 .

Let the number of nickels that Logan gave out be = n , and

the number of dimes that Logan gave out be =  d ;

From the information , we know that Logan gave out 50% more nickels than dimes,

that means ; n = d + 0.5d = 1.5d   ...equation(1) ;

We also know that the total amount given out in nickels and dimes is $6.65, and each nickel is worth of  $0.05 and each dime is worth of  $0.10,

So ,  n×0.05 + d×0.10 = 6.65 ;

Substituting the expression for n from the first equation into the second:

⇒ (1.5d)×0.05 + d×0.10 = 6.65 ;

Expanding and solving for d ;

we get ;

⇒ 0.075d + 0.10d = 6.65 ;

⇒ 0.175d = 6.65 ;

⇒ d = 6.65/0.175 = 38 ;

Therefore ,  Logan gave out 38 dimes.

The given question is incomplete , the complete question is

Logan works as a cashier. Today, he has given out 50% more nickels than dimes. if he has given out a total of 6.65 in nickels and dimes, How many dimes has he given out ?

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The features of the circle in this problem are given as follows:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The center for this circle has the coordinates given as follows:

(2,-1).

The radius is the distance of any point on the circumference of the circle from the center, hence, tracing a horizontal line at y = -1, we have that:

r = 7 - 2

r = 5.

Hence the equation is given as follows:

(x - 2)² + (y + 1)² = 25.

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