On a sunny day, you are standing parallel to the Eiffel tower in Paris. The tower’s shadow is huge compared to your shadow. You are interested to know how long the shadow of the tower is. You decide to measure the shadow cast by you, it is 4ft 6 inches, and you are 6ft tall. Using the information below, calculate the shadow cast by the current height of the Eiffel tower (with the antenna). Use proportions to show your work.

Step-by-step explanation:

You can factor out a '10' from each of the terms

10 ( -6 + 6n^2 + 5 n^3 )        

If you meant    - 60 n + 60 n^2 + 50 n^3

   you can factor out a 10 n

     10n ( -6 + 6n + 5n^2)

Answer:

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Feeling sleepy? Students in a high school statistics class responded to a survey designed by their teacher. One of the survey questions was “How much sleep did you get last night?” Here are the data

Answer:

see below

Step-by-step explanation:

y=mx is the start of a line equation.  The line equation is:

[tex]y=mx+b[/tex]

with m being the slope and b is the y-intercept.

If you have 2 points, let's say (0,1) and (4,0), the slope would be -1/4.

The slope is [tex]\frac{rise}{run}[/tex].  The rise is the number of units going up or down from one point to another.  The run is the number of units going left or right from one point to the other.

In this case, the slope is -1/4 because you go down 1 unit and right 4 units.

The y-intercept is 1 because the y-intercept is when x=0 and is located on the y-axis.

Hope this helps :)

Answer:

t is less than or equal to 10

Step-by-step explanation:

At most means less than or equal to. The boat costs 6 an hour, so, 6t. He has a $8 off coupon, so, 6t-8 is less than or equal to 52. Add 8 on both sides and then divide by 6 to isolate t. t is less than or equal to 10 hours.

t = 18, -18

To solve, we will isolate the variable t.

Given:

      0.5t² = 162

Divide both sides of the equation by 0.5:

      t² = 324

Square root both sides of the equation:

      t = 18, -18

The required solution to the equation [tex]0.5t^2 = 162[/tex] is t = ±18, as of the given condition.

To solve the equation [tex]0.5t^2 = 162[/tex], we need to isolate the variable t.

First, we can start by dividing both sides of the equation by 0.5 to eliminate it on the left side:

[tex]0.5t^2 / 0.5 = 162 / 0.5[/tex]

Simplifying:

[tex]t^2 = 324[/tex]

Next, we take the square root of both sides to solve for t:
[tex]\sqrt(t^2) = \sqrt(324)[/tex]

t = ±18

Therefore, the solution to the equation [tex]0.5t^2 = 162[/tex] is t = ±18.

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In the year 2040, the populations of the two towns will be approximately equal.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To find the year when the populations of the towns will be approximately equal, we need to set the two equations equal to each other and solve for t:

8t² + 2000 = 100t + 3000

8t² - 100t - 1000 = 0

We can simplify this equation by dividing both sides by 4:

2t² - 25t - 250 = 0

Now we can solve for t using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = -25, and c = -250. Plugging in these values, we get:

t = (25 ± √(25² - 4(2)(-250))) / (2(2))

t = (25 ± √(9375)) / 4

t = (25 ± 97.0) / 4

So t = 30.25 or t = -6.25. We can ignore the negative solution since we're looking for a year after 2010. Therefore, the populations of the two towns will be approximately equal in the year:

2010 + 30.25 = 2040.25

So, in the year 2040, the populations of the two towns will be approximately equal.

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The speed of the car traveling is 42.96km/hr, under the condition  if d=0. 05v²+2. 2v.

The distance a car travels is 200. We can perform the formula d = 0.05v² + 2.2v to evaluate the speed of the car.
Staging d = 200 in the above equation, we get:

0.05v² + 2.2v - 200 = 0

Evaluating this quadratic equation gives us two values of v:

v = (-2.2 ± √(2.2² + 4 × 0.05 × 200)) / (2 × 0.05)

v ≈ -44.96 or
v ≈ 42.96

Since speed cannot be negative, we take v ≈ 42.96 as the speed of the car.
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Two possible values for the meteorologist's prediction are  $35.24$ inches and $50.76$ inches.

Let's denote the meteorologist's rainfall prediction by x.

The percent error can be calculated using the formula:

percent error = |(actual value - predicted value) / actual value| x 100%

We can use this formula to set up an equation and solve for x.

Since we want to find two possible values for x, we can use both the positive and negative versions of the percent error:

18.02% = |(43 - x) / 43| x 100% or

-18.02% = |(43 - x) / 43| x 100%

We have to find the values of x

18.02% = |(43 - x) / 43| x 100%

0.1802 = |(43 - x) / 43|

0.1802 x 43 = |43 - x|

7.7566 = |43 - x|

43 - x = 7.7566 or 43 - x = -7.7566

x = 35.2434 or x = 50.7566

Therefore, two possible values for the meteorologist's prediction are  $35.24$ inches and $50.76$ inches.

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As per the unitary method, there would be approximately 84 deer in a 560 square mile region, based on the assumption that the deer population density is uniform throughout the region.

In this case, we want to find the number of deer in a 560 square mile region, given that there are 15 deer in a circular region with a radius of 10 miles.

The first step is to find the area of the circular region with a radius of 10 miles. We can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Substituting the values, we get:

A = π(10)² = 100π

The area of the circular region is 100π square miles.

Next, we can use a unitary method to find the number of deer in one square mile. We know that there are 15 deer in 100π square miles. To find the number of deer in one square mile, we can divide both sides by 100π:

15 deer ÷ 100π square miles = x deer ÷ 1 square mile

Simplifying this equation, we get:

x = (15 ÷ 100π) deer per square mile

Now, we can use this value of x to find the number of deer in a 560 square mile region. We can multiply x by 560 to get:

x deer per square mile × 560 square miles = 560x deer

Substituting the value of x, we get:

560(15 ÷ 100π) deer = 84 deer (rounded to the nearest whole number)

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Answer:

Step-by-step explanation:

To find the area of the garden covered by the pond, we need to find the area of sector ACB.

First, we need to find the measure of the central angle of sector ACB. The central angle is the same as the angle formed by radii OA and OB.

Since the radius of the garden is 3 meters, we can use the Pythagorean theorem to find the length of the chord AB:

AB² = OA² + OB²

AB² = 3² + 3²

AB² = 18

AB = √18 ≈ 4.24 meters

Now, we can use the formula for the area of a sector:

A = (θ/360)πr²

where θ is the central angle and r is the radius of the circle.

The central angle of sector ACB can be found using the inverse cosine function:

cos(θ/2) = AB/2r

cos(θ/2) = 4.24/(2*3)

cos(θ/2) ≈ 0.707

θ/2 ≈ cos⁻¹(0.707)

θ ≈ 2cos⁻¹(0.707)

θ ≈ 144.1 degrees

Now we can calculate the area of sector ACB:

A = (θ/360)πr²

A = (144.1/360)π(3)²

A ≈ 10.6 square meters

Therefore, the area of the garden covered by the pond is approximately 10.6 square meters.

The expression for the length of the rectangular prism is L = 9x² + 7x - 2

Given data ,

Let the length of the rectangular prism be L

Let the volume of the rectangular prism be V = 36x³ - 28x + 8

Let the height of the prism be H = 3x - 1

Let the width of the prism be W = 4

And , Volume of Rectangle = Length x Width x Height

On simplifying , we get

36x³ - 28x + 8 = L ( 3x - 1 ) ( 4 )

L ( 12x - 4 ) = 36x³ - 28x + 8

By long division , we get

       -----9x² + 7x - 2--------------------------------------

4(3x - 1) | 36x³ - 28x + 8

                  - (36x - 9x)

                       -------------------------------------------------

                           7x - 2

                           - (7x - 2)

                                  ---------------------------------------------

                                          0

Hence , the length of the prism is L = 9x² + 7x - 2

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The volume of the triangular prism whose base = 4.8m , height = 3.2m, length = 9m is 69.12 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the base by the height and the length of the prism. The formula for the volume of a triangular prism is:

V = 1/2 x b x h x l

where b is the length of the base, h is the height of the base, and l is the length of the prism.

In this case, the base of the triangular prism has a length of 4.8m and a height of 3.2m, so the area of the base is:

A = 1/2 x b x h = 1/2 x 4.8m x 3.2m = 7.68m²

The length of the prism is 9m, as given in the problem.

Therefore, the volume of the triangular prism is:

V = A x l = 7.68m² x 9m = 69.12m³

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The equation of the parabola as (y-6)^2 = 12x

Here, we have to solve:

Given an axis equation of y=6, focus at (0,6), and p=-3, this is a horizontal parabola with its vertex at (0,6).

Since p<0, it opens to the left.

The standard equation of a horizontal parabola with vertex (h,k) and distance p is (y-k)^2 = -4p(x-h)

Plugging in the values (h,k)=(0,6) and p=-3,

we get the equation of the parabola as  (y-6)^2 = 12x

Hence, The equation of the parabola as (y-6)^2 = 12x

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The polygon is translated 6 units to the left

Given data ,

A ( 1 , 6 ) , B ( 3 , 2 ) , C ( 7 , 2 ) , D ( 5 , 6 ) transformed to A' ( -5 , 6 ) , B' ( -3 , 2 ) , C' ( 1 , 2 ) , D' ( -1 , 6 )

The given coordinates represent two sets of points, one for the original polygon ABCD and the other for the transformed polygon A' B' C' D'.

Now , we can observe that the x-coordinates of each vertex have changed, while the y-coordinates remain the same. Specifically, the x-coordinates of the original vertices have been decreased by 6 units to obtain the x-coordinates of the transformed vertices.

This indicates that a translation has been applied to the original polygon, shifting it 6 units to the left along the x-axis

Hence , the function is translated 6 units to the left

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Hayden can arrange his 5 trophies on the fireplace in 56 different ways.

The formula for combinations,

which is nCr = n!/r!(n-r)!, where n is the total number of items and r is the number of items being chosen. In this case, n=8 and r=5.
So, we can calculate the number of ways that Hayden can arrange his trophies as follows:
8C5 = 8!/5!(8-5)! = 8!/5!3! = (8x7x6)/(3x2x1) = 56
Therefore, there are 56 ways that Hayden can arrange his 5 trophies on the fireplace.

Hence,  Hayden can arrange his 5 trophies on the fireplace in 56 different ways using the formula for combinations.

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Answer:

The top table shows the sample space for two spins of this spinner.

The thing that will be always true about quadrilateral ABCD is C. m∠A+m∠B=180°

The coordinates of the center of the circle is B. (6, 4)

Based on the fact that opposite angles in an inscribed quadrilateral are always equal, then m∠A+m∠B=180°. As a result, ∠A + ∠C = 180 degrees and likewise for ∠B + ∠D = 180 degrees.

The intersection of the two lines, namely, the perpendicular bisector of AB (passing through midpoint (6, 3.5) with a slope -12/7) and the vertical line whose undefined own slope penetrates the midpoint (6, 0) of AC, is exactly the center of circle, which has its coordinates as (6, 4).

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An expression that is equivalent to (-3)^4/(-3)^2 is(-3)^2

From the question, we have the following parameters that can be used in our computation:

(-3)^4/(-3)^2.

Applying the law of indices, we have

(-3)^4/(-3)^2 = (-3)^(4 - 2)

Evaluate

So, we have

(-3)^4/(-3)^2 = (-3)^2

Hence, the solution is (-3)^2

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The ratio of the volume of the first cube to the volume of the second cube is 1:27. The correct option is (C).

Let's represent the length of the edge of the first cube "n" and the length of the edge of the second cube "3n".

The volume of the first cube is:

V1 = n³

The volume of the second cube is:

V2 = (3n)³ = 27n³

To find the ratio of the volume of the first cube to the volume of the second cube, we divide V1 by V2:

V1/V2 = n³ / (27n³) = 1/27

Therefore, the required ratio is 1:27.

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The correct question is as follows:

One cube has edges n meters long. Another has edges 3n meters long. What is the ratio of the volume of the first cube to the volume of the

second cube?

A 1:3

B. 1:9

C. 1:27

D. 1:6

E. 1:81

Based on the graph of f(x) = x³ with three reference points, the points from f(x) to a point on g(x) = 2(x - 4)³ - 3 include the following:

B. (5, -1)

C. (3, -5)

D. (4, -3)

In Mathematics and Geometry, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

At the ordered pair (5, -1), the function g(x) = 2(x - 4)³ - 3 would be tested with given points as follows;

g(x) = 2(x - 4)³ - 3

-1 = 2(5 - 4)³ - 3

-1 = 2(1) - 3

-1 = -1 (True).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Triangles ΔKLM and ΔXYZ are congruent using the ASA criteria.

Given are two triangles as shown in the image given.

The given triangles are ΔKLM and ΔXYZ.

∠L = ∠Y

KM = XZ

∠M = ∠Z

So, by ASA criteria, the triangles ΔKLM and ΔXYZ are congruent.

Therefore, triangles ΔKLM and ΔXYZ are congruent using the ASA criteria.

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There were 4 speed bumps installed on the road leading into the house development.

What is the formula of speed when time and distance have given?

The formula is speed = distance/time

Here given,

The length of the road is 3/4 miles or 12/16 miles and the distance between each speed bump is 3/16 miles.

Now we want to obtain the number of speed bumps,

So, Number of speed bumps = (Total distance of road) / (Distance between each speed bump)

Number of speed bumps = [tex] \frac{ \frac{12}{16} }{ \frac{3}{16} } [/tex]

Number of speed bumps = [tex] \frac{12}{16} \times \frac{16}{3} [/tex]

Number of speed bumps = 4

Therefore, there were 4 speed bumps installed on the road leading into the house development.

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Answer:

3^(2 + 7 - 8) = 3^1 = 3

Jeremiah will have to pay $69.5 in a month in which he downloaded 50 songs. The Total amount Jeremiah will pay for s songs $7 + $1.25 s

We are given that Jeremiah signed up for a streaming music service that costs $7 per month.

Cost per month = $7

Cost of Offline download = $0.50 per song

Total amount Jeremiah will pay = $7 + $1.25(50)

= 7 + 62.5

= $69.5

Jeremiah will have to pay $69.5 in a month in which he downloaded 50 songs.

Therefore, Total amount Jeremiah will pay for s songs = $7 + $1.25* s

= $7 + $1.25 s

Total amount Jeremiah will pay for s songs = $7 + $1.25 s

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The true statements are (A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

There are 30 people and each person is served soup in a 400 ml bowl, so the total amount of soup needed is 30 × 400 ml = 12,000 ml.

Option A is true

30 bowls of soup hold 30 × 400 ml = 12,000 ml, which is the same as 12 litres (since 1 litre = 1,000 ml).

Option B is true

Since 1 litre = 1,000 ml

Noah can multiply the number of bowls of soup by 1,000 to find the number of litres.

For example, 30 bowls of soup hold 12,000 ml = 12 litres.

Option C is true

If each family member has 2 bowls of soup, then the total amount of soup needed is

30 × 2 × 400 ml

= 24,000 ml, which is 24 litres (since 1 litre = 1,000 ml).

Option D is true.

Noah needs to make 24 litres of soup, and each pot contains 6 litres of soup.

Therefore, he would need to make 24 ÷ 6 = 4 pots of soup to serve each family member 2 bowls of soup.

Option E is false.

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Noah is making soup for a family reunion of 30 people. Each pot he makes contains 6 liters of soup. He uses bowl that 400mL to serve the soup to his family

Select all the true statements

(A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

(E) Noah would need to make 2 pots of soup for each family member to have 2 bowls of soup

The probability of selecting two different colors is 13/15.

The probability of selecting two different colors is determined using the complement rule as follows:

The probability of selecting two marbles of the same color from the first bag is:

P(same color) = P(red and yellow) + P(red and green) + P(red and blue) + P(yellow and green) + P(yellow and blue) + P(green and blue)

P(same color) = 0 + 0 + 0 + 0 + (1/6)(2/5) + (1/6)(2/5)

P(same color) = 2/15

The probability of selecting two marbles of the same color from the second bag is:

P(same color) = P(red and yellow) + P(red and green) + P(red and blue) + P(yellow and green) + P(yellow and blue) + P(green and blue)

P(same color) = 0 + 0 + 0 + 0 + (1/6)(1/3) + (1/6)(1/3)

P(same color)  = 1/9

The probability of selecting two different colors from both bags will be:

P(different colors) = 1 - (2/15) * (1/9)

P(different colors) = 13/15

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Answer:

B

Step-by-step explanation:

1/3(9-6x+12)

    3-2x+4

      1-2x

Answer:

[tex]y=x^{2} -14x+48[/tex]      (when a=1)

[tex]y=2x^{2} -27x+88[/tex]    (when a=2)

The general form of the quadratic functions you asked is :

[tex]y=a(x-5)(x-8)-x+8\\(a\neq 0)[/tex]

Here,

-x+8 is a line that passes two given points.

When you put x=5, you get y=3,

which is a coordinate of one of the given points.

When you put x=8, you get y=0,

which is a coordinate of the other one.

-----------------------------------------------------------------------------------------------------

This is the way I got the form above :

Since what we're looking for is a quadratic function, (let's call it "f(x)")

the equation

f(x)=-x+8

can have at most 2 different real solutions.

You can note that the real solution of the equation above

represents the x coordinate of the intersection point of two graphs:

y=f(x) and y=-x+8.

Again, the equation can have at most 2 different solutions.

And we have 2 different real solutions already given -

(It's a requirement ; we want y=f(x) to contain (5,3) and (8,0))

- which are x=5, x=8.

So these are the only two solutions of the equation.

Since the coefficient of a highest order term

hasn't been decided, we can introduce an unknown 'a' for it.

(i.e. Let 'a' be the coefficient of a highest order term.)

To sum up, an equation

f(x)=-x+8

f(x)+x-8=0

has two different real solutions x=5, x=8,

thus it can be written like this;

a(x-5)(x-8)=0

where a is not zero.

Therefore

f(x)+x-8 = a(x-5)(x-8)

(Because two italic-texted equations have the same meaning)

∴ [tex]f(x)=a(x-5)(x-8)-x+8[/tex][tex]\QED[/tex].