Martin a une table ronde de 1 ,10m de diamètre il peut ajouter jusqu'à 5 rallonge de 40 cm chacune pour son repas d'anniversaire 10 personne seront présentes autour de cette table En comptant 60 cm par personne quel est le nombre minimal de rallonge qu'il doit installé

This is an exercise in parametric equations, which are a way of representing a curve or surface on the plane or in space using arbitrary values or a constant called a parameter instead of using an independent variable. In the case of circles, the points (x,y) can be expressed from a single variable θ, which is called a parameter. The parametric equations of a circle with radius r ≥ 0 and center (h,k) are given by x = h + rcosθ y = k + rsinθ, where 0 < θ < 2π. The parametric equation of a circle can be expressed from the angle θ of the point through the circle with respect to the x-coordinate axis. The parametric equations of the conics, including the circumference, can be deparameterized to obtain the canonical equation.

The parametric equation of a circle can be expressed from the angle θ of the point through the circle with respect to the x-coordinate axis. The angle can be expressed in radians (θ∈[0,2π]) or sexagesimal degrees (θ∈[0º,360º]). The parametric equation of a circle with center C=(-1,3) and radius r=2 cm is defined by x = -1 + 2cosθ and y = 3 + 2sinθ.

The parametric equations of a curve are expressed from the variable (or parameter) t, such that x = x(t) and y = y(t). Each value of t determines a point (x,y) in the plane. The parametric equations of a circle with radius r ≥ 0 and center (h,k) are given by x = h + rcosθ y = k + rsinθ, where 0 < θ < 2π. The parametric equation of a circle centered at the origin and with radius r is x² + y² = r².

The parametric equations for a curve are not unique. They represent the same circle with center at (0,0) and radius R. The parametric equations of the conics, including the circumference, can be deparameterized to obtain the canonical equation. To go from the parametric to the Cartesian equations, the parameter t must be eliminated. The parametric equations of a point on a circle of radius r at an angle θ are x = rcos(θ) and y = rsin(θ).

cos²(t) + sin²(t) = 1

Multiplying both sides by 25, we get:

25 cos²(t) + 25 sin²(t) = 25

Which is equivalent to:

x² + y² = 25

Therefore, we can write:

x(t) = 5 cos(t), y(t) = 5 sin(t)

This means that for every value of t in the interval 0≤t≤2π, we can get a point on the circle.

The lengths of the legs are 7.7 units and 6.4 units

To determine the lengths of the legs of the triangle, we have that;

We need to know the different trigonometric identities. These identities are expressed as;

From the information given, we have that;

Using the sine identity;

sin θ = opposite/hypotenuse

Substitute the values

sin 40 = x/10

cross multiply the values, we get;

x = 6. 4 units

Using the cosine identity;

cos 40 = y/10

y = 7. 7 units

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The length of the other two legs are 6.4 and 7.6

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Since the hypotenuse is 10, we are going to find the other legs of the right triangle using the trig functions.

sin40 = opp/hyp

0.643 = opp/10

opp = 0.643 × 10

opp = 6.4

Cos 40 = adj/hyp

0.766 = adj/10

adj = 0.766 × 10

adj = 7.6

Therefore the length of other two legs are 6.4 and 7.6

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After considering the given data we conclude that the x-coordinate of the inflection points for the function are x = - 2 and x = 2, which is option A.

To evaluate the x-coordinate of the inflection points for the function f(x) = ln(x² + 4) we need to evaluate the second derivative of the function and find for x when the second derivative equals zero.
The first derivative of f(x) is:
f' * (x) = (2x)/(x² + 4)
The second derivative of f(x) is:
f"(x) = 2(x² + 4)-4x² /(x²+4)² = 8 - 2x²/(x²+4)²
To evaluate the inflection points, we need to find the equation f'' (x) = 0 for x:
8 - 2x²/(x²+4)² = 0
After applying simplification this equation, we get:
8 - 2x² = 0
Evaluating for x, we get:
x = +/- √4) = +/- 2
Therefore, the x-coordinate of the inflection points for the function f(x) = ln(x² + 4)
x = - 2 and x = 2 .
The answer is A. x = - 2 and x = 2.
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The surface area of the rectangular pyramid is approximately 387.6 square yards.

To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.

The area of the base is:

Area of base = length x width

Area of base = 14 yards x 14 yards

Area of base = 196 square yards

To find the area of the four triangular faces, we need to first find the height of each triangle using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs (the two shorter sides) is equal to the square of the hypotenuse (the longest side).

In this case, the hypotenuse is the slant height of the pyramid, which is 12 yards. The legs are half the length and width of the base, which are both 7 yards.

So we have:

h² + 7² = 12²

h² + 49 = 144

h² = 95

h = √95

Now we can find the area of each triangular face using the formula:

Area of triangle = 1/2 x base x height

The base of each triangle is 14 yards, and the height is √95 yards. So we have:

Area of triangle = 1/2 x 14 yards x √95 yards

Area of triangle = 7√95 square yards

There are four triangular faces, so the total area of the four triangular faces is:

Total area of triangular faces = 4 x 7√95 square yards

Total area of triangular faces = 28√95 square yards

Finally, we can find the total surface area by adding the area of the base and the area of the four triangular faces:

Total surface area = Area of base + Total area of triangular faces

Total surface area = 196 square yards + 28√95 square yards

Total surface area ≈ 387.6 square yards (rounded to one decimal place)

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Answer:

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

Find the combination of 2 out of 7:

There are 21 combinations.

The equation that relates the cost of a bouquet to the number of balloons in the bouquet is: Y = 5.75x

The bouquet with 6 balloons, and the cost per balloon is:

34.50 / 6 = 5.75

We can repeat this process for each bouquet to get:

6 balloons: cost per balloon = 5.75

9 balloons: cost per balloon = 3.83

12 balloons: cost per balloon = 3.04

we can write an equation of the form: Y = kx

where Y is the cost of a bouquet,

x is the number of balloons in the bouquet, and

k is a constant that represents the cost per balloon.

To solve for k, we can use any one of the bouquets to get:

34.50 = k(6)

Solving for k, we get:

k = 5.75

Therefore, the equation that relates the cost of a bouquet to the number of balloons in the bouquet is:

Y = 5.75x

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Complete question:

Brenda sells balloon bouquets. She charges the same price for each

balloon in a bouquet. The costs for several bouquets are shown in the

table. Write an equation that relates the cost of a bouquet to the number

of balloons in the bouquet.

Number of balloons,

(x= # of balloons)

6

9

12

(Y=cost)

3

4.50

6

The total cost of the snow thrower on the installment plan is $1,641.60.

To find the total cost of the snow thrower on the installment plan, we will first calculate the down payment and then add the total monthly payments. Here's the step-by-step explanation:
1. Calculate the down payment:
Down payment = 20% of the original price
Down payment = 0.20 * $1,248
Down payment = $249.60
2. Calculate the total of the 12 monthly payments:
Total monthly payments = 12 * $116
Total monthly payments = $1,392
3. Calculate the total cost on the installment plan:
Total cost = Down payment + Total monthly payments
Total cost = $249.60 + $1,392
Total cost = $1,641.60
So, the total cost of the snow thrower on the installment plan is $1,641.60.

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Answer:

[tex]y = 1- |x + 1| [/tex]

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{0 +3}{-2} \implies \cfrac{ 3 }{ -2 } \implies - \cfrac{3}{2}[/tex]

[tex]\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 y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{4}) \implies y +3 = - \cfrac{3}{2} ( x -4) \\\\\\ y+3=- \cfrac{3}{2}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{2}x+3 \end{array}}[/tex]

Answer:

y = -1.5x + 3

Step-by-step explanation:

gradient = (-3 - 0) / (4 - 2) = -3/2 = -1.5.

equation on line through two points is given by

y - y1 = m (x - x1)

where y1 and x1 are the coordinates of the point and m is the gradient.

we can choose either point to use in the equation.

y - 0 = -1.5 (x - 2) = -1.5x + 3

y = -1.5x + 3

Answer:

9 - 5 (x + 4) = 12 (x + 1)

-5x - 11 = 12x + 12

-5x - 11 + 11 = 12x + 12 + 11

-5x = 12x + 23

-5x - 12x = 12x + 23 - 12x

x = -23/17

Answer:

x=−23/17

Step-by-step explanation:

Distribute: 9-5(x+4) = 12(x+1)

= 9+−5x+−20=12x+12

Combine like term 9&-220:

−5x+−11=12x+12

Subtract 12x:

−5x−11−12x=12x+12−12x

=−17x−11=12

Add 11:

−17x−11+11=12+11

=−17x=23

Divide by -17:

−17x/-17=23/-17

x=−23/17

.

Answer:

Step-by-step explanation:

Answer:

6 times with a remainder of 0

how do u not know this

skipped basic math have u?

Answer:

5

Step-by-step explanation:

v - e + f =2

5 - 8 + f = 2

f = 2 - 5 + 8

= 5

The value of y is 3 when x = 25.

When two variables, x, and y, vary inversely, it means that as one variable increases, the other decreases in a proportional manner. In other words, their product is constant.

Mathematically, this relationship can be expressed as:

y = k/x

where k is the constant of proportionality.

To solve the problem, we are given that y = 5 when x = 15, which can be rewritten as:

5 = k/15

To find the value of y when x = 25, we need to first determine the value of k. We can do this by rearranging the equation above to solve for k:

k = 5 x 15 = 75

Now that we know the constant of proportionality, we can use it to find the value of y when x = 25:

y = k/x = 75/25 = 3

Therefore, when x = 25, y = 3. This means that as x increases from 15 to 25, y decreases from 5 to 3, in accordance with the inverse variation relationship between x and y.

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Answer:

356.89$

Step-by-step explanation:

259.9 + 62.99 = 322.98, 8.25% + 2.25 = 10.5 tax rate... So 322.98 + 10.5% = 356.89$

Answer: A = 470 in²

Step-by-step explanation:

          If the given prism is a rectangular prism, we can use the given formula to solve for the surface area of a rectangular prism.

A = 2((8 in)(15 in) + (5 in)(15 in) + (5 in)(8 in))

A = 2(120 in² + 75 in² + 40 in²)

A = 2(235 in²)

A = 470 in²

The plane traveled approximately 15,806 feet from point A to point B.

tan(angle) = opposite side / adjacent side

Let x be the horizontal distance from Qasim to point A and y be the horizontal distance from Qasim to point B. Then:

tan(16°) = 7200 / x

tan(38°) = 7200 / y

We can solve for x and y:

x = 7200 / tan(16°)

y = 7200 / tan(38°)

Now, we can calculate x and y:

x ≈ 7200 / 0.2878

= 25016.6 feet

y = 7200 / 0.7813

= 9210.7 feet

Finally, to find the distance the plane traveled from point A to point B, we take the difference between y and x:

distance = y - x

= 9210.7 - 25016.6

= -15805.9 feet

we take the absolute value:

distance = 15806 feet (rounded to the nearest foot)

approximately 15,806 feet from point A to point B.

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The value x, y and z from the given matrix are -3.65, -4.5 and 2.2 respectively.

From the given matrix,

[tex]\left[\begin{array}{ccc}-2&6&-7\\2&-7&-3\\6&-4&-6\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-47\\22\\-10\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-2x+6y-7z\\2x-7y-z\\6x-4y-6z\end{array}\right] =\left[\begin{array}{ccc}-47\\22\\-10\end{array}\right][/tex]

-2x+6y-7z=-47  -------(i)

2x-7y-z=22 ---------(ii)

6x-4y-6z=-10 ---------(iii)

Add equation (i) and (ii), we get

-2x+6y-7z+2x-7y-z=-47+22

-y-8z=-27 ---------(iv)

Multiply equation (ii) by 3, we get

6x-21y-3z=66  ---------(v)

Subtract equation (iii) from (v), we get

6x-21y-3z-(6x-4y-6z)=66-(-10)

6x-21y-3z-6x+4y+6z=76

-17y+3z=76  ---------(vi)

Multiply equation (iv) by 17, we get

-17y-136z=-216  ---------(vii)

Subtract equation (vi) from (vii), we get

-17y-136z-(-17y+3z)=-216-76

-133z=-292

z=-292/(-133)

z=2.2

Substitute z=2.2 in equation (vii), we get

-17y-136(2.2)=-216

-17y-292.6=-216

-17y=-216+292.6

-17y=76.6

y=-4.5

Substitute y=-4.5 and z=2.2 in equation (ii), we get

2x-7y-z=22

2x-7(-4.5)-2.2=22

2x+31.5-2.2=22

2x+29.3=22

2x=22-29.3

2x=-7.3

x= -7.3/2

x= -3.65

Therefore, the value x, y and z from the given matrix are -3.65, -4.5 and 2.2 respectively.

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The capacity of the bottle is 16 ounces

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

A water bottle is 3/4 full.

When half of the water is drained, we have

Remainder = 1/2 * 3/4x

Evaluate

Remainder = 3/8x

Where x is the capacity of the bottle

We understand that 6 ounces of water remain in the bottle.

This means that

3/8x = 6

So, we have

x = 8 * 6/3

Evaluate

x = 16

Hence. the capacity of the bottle is 16 ounces

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Answer:

h = 5t²+ 25t

from projectiles

h = u²sin²∆ / 2g

taking the angle to be ∆

and range is u²sin2∆/g

Therefore integrate the equation h= 5t²+25t

R = 5t³/3 + 25t²/2 + t

Answer:

49 [tex]ft^{2}[/tex]

Step-by-step explanation:

a = 1/2 (bh)

a = 1/2(7x14)

a = 49

Helping in the name of Jesus.

The measure of 5 is 110°.

Given, Lines n and p are parallel to each other and have transversal t.

To find: The value of angle 5.

Therefore, the sum of these angles will be 180

Angle 4 = angle 5

Now, they are alternate interior angles.

Therefore,

angle 5 = 110

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The chances that, at least, one of the dinosaur toys in Franklin's set is a T.rex is 57%.

We can use the complement rule to find the probability that none of the dinosaur toys in Franklin's set is a T. rex, and then subtract this from 1 to get the probability that at least one of the toys is a T. rex.

The probability that a given toy is not a T. rex is 90%, or 0.9.

Since there are 8 toys in the set, the probability that none of them are T. rex is:

0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.43

So the probability that at least one of the toys is a T. rex is:

1 - 0.43 = 0.57, or 57%

In other words, it is 57% likely that at least one of the dinosaur toys in Franklin's set is a T. rex.

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A. The initial size of the culture is 222.11

B. The doubling period is approximately 13.53 minutes.

C. The population after 100 minutes is 5807.76

D . The population will reach 13000 after approximately 44.59 minutes.

Use the formula for exponential growth:

N = N0 × eʳᵗ

where N is the population size at time t, N0 is the initial population size, r is the growth rate, and t is the time elapsed.

Using the given data:

At t=10, N=500

500 = N0 × eʳ×¹⁰

At t=30, N=1500

1500 = N0 × eʳ׳⁰

To solve for N0 and r, we can divide the second equation by the first:

¹⁵⁰⁰/₅₀₀ = eʳ׳⁰ / eʳ×¹⁰

3 = eʳ× ²⁰

Taking the natural logarithm of both sides:

ln(3) = r × 20

r = ln³/₂₀

r ≈ 0.0513 (rounded to 4 decimal places)

Now we can use N = N0 × eʳᵗ to answer the remaining questions:

- The initial size of the culture is:

N0 = N / eʳᵗ = 500 / ₑ(0.0513×10) ≈ 222.11 (rounded to 2 decimal places)

- The doubling period is the time it takes for the population to double. Find this by setting N = 2N0 and solving for t:

2N0 = N0 × eʳᵗ

2 = eʳᵗ

ln(2) = rt

t = ln²/ᵣ

t ≈ 13.53 (rounded to 2 decimal places)

So the doubling period is approximately 13.53 minutes.

- The population after 100 minutes is:

N = N0 × eʳᵗ = 222.11 × ₑ(0.0513×100) ≈ 5807.76 (rounded to 2 decimal places)

- To find when the population reaches 13000, we can solve N = 13000 for t:

13000 = N0 × eʳᵗ

13000 = 222.11 × ₑ(0.0513t)

58.56 = ₑ(0.0513t)

ln(58.56) = 0.0513t

t ≈ 44.59 (rounded to 2 decimal places)

So the population will reach 13000 after approximately 44.59 minutes.

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The equivalent value of the fraction is A = 533 / 99

Given data ,

To find equivalent fractions for the repeating decimal 5.38383838..., we can use the concept of converting a repeating decimal to a fraction.

Let's denote the repeating decimal as x: x = 5.38383838...

Step 1:

Multiply x by a power of 10 to eliminate the repeating part.

100x = 538.38383838...

Step 2:

Subtract x from the product obtained in Step 1 to eliminate the repeating part.

100x - x = 538.38383838... - 5.38383838...

99x = 533

Step 3:

Solve for x by dividing both sides by 99.

x = 533 / 99

Hence , the fraction is A = 533 / 99

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The Equivalent measurements of a given quantity can be useful in a variety of situations, such as when you need to convert between different units of volume

2 1/2 gallons is equal to various measurements depending on the context, but here are a few common conversions:

- 10 pints: There are 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 2 x 4 + 2 = 10 pints.

- 20 cups: There are 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 2 x 4 x 2 + 2 = 20 cups.

- 640 fluid ounces: There are 8 fluid ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 4 x 2 x 2 x 8 x 2.5 = 640 fluid ounces.

Knowing the equivalent measurements of a given quantity can be useful in a variety of situations, such as when you need to convert between different units of volume, or when you need to mix ingredients in a recipe.

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You'll need to build Excel formulas using =SUM() function on specified cells in order to calculate total assets, total liabilities, revenue, and expenses. To calculate net income, subtract total expense from total revenue. Calculate Equity by summing common stock, retained earnings, and net income, then subtracting dividends. Finally, sum total liabilities and total equity.

To answer these questions, you are required to have Excel skills and basic understanding of business accounting principles. Let's break it down per section:

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Answer: D. Parallelogram

Step-by-step explanation: Step 1. Input all the points on a graph, there's not really much to it, sorry if I didn't help but the answer is D

Answer:

8/27

Step-by-step explanation:

There are a total of 27 students in the class, and 8 of them are accounting majors. Therefore, the probability of the first student selected being an accounting major is 8/27.

After the first student is selected, there will be 26 students remaining, out of which 6 are art majors. Therefore, the probability of the second student selected being an art major, given that the first student was an accounting major, is 6/26.

To find the probability of both events occurring together, we need to multiply the individual probabilities:

P(accounting major first) * P(art major second | accounting major first)

= (8/27) * (6/26)

= 48/702

= 8/117