For each 7 mm of coloured fabric Gavyn uses to make his curtains, he also uses 1 cm of white
fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.

Given:

Height of Isabelle = 62 inches

Shadow of Isabelle = 93 inches

Shadow of tree = 279 inches

To find:

The height of the tree.

Solution:

Let height of tree be x.

Ratio of height to shadow for Isabelle and tree are

\(\dfrac{\text{Height of Isabelle}}{\text{Shadow of Isabelle}}=\dfrac{62}{93}\)

\(\dfrac{\text{Height of tree}}{\text{Shadow of tree}}=\dfrac{x}{279}\)

The shadow of Isabelle and tree are proportional to their shadows. So, both ratios must be equal.

\(\dfrac{x}{279}=\dfrac{62}{93}\)

Multiply both sides by 279.

\(x=\dfrac{62}{93}\times 279\)

\(x=62\times 3\)

\(x=186\)

Therefore, the height of tree is 186 inches.

Stars to Circles Ratio: 4 to 3

Circles to Stars Ratio: 3 to 4

Answer:

4to 3

Step-by-step explanation:

because I'm smart an I've all ready learned about this I'm 100% for sure

Answer:

25% of the mix is raisins

The distance from the initial point to the corner pocket is 164 cm.

The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45 degrees.

We know that the ball traveled 100cm before ricocheting off the rail and another 120cm into the corner pocket.

We can use the Pythagorean Theorem to find the distance from where the cue initially struck the ball to the corner pocket.

Let x be the distance from the initial point to the corner pocket.

x^2 = 100^2 + 120^2 - 2100120*cos(45^{\circ})

x = \sqrt{28000} = \sqrt{700*40} = \sqrt{28000} = 164.856

Rounded to the nearest centimeter, the distance from the initial point to the corner pocket is 164 cm.

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Answer: Y = 7/8x+ 2.25

Step-by-step explanation:

Answer:

So the answer is v=112 sa=165

Step-by-step explanation:

Try using formulas such as 1

4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4

and

A=12bh

Answer: v=112 sa=165

Step-by-step explanation: I took your points and now I'm running away ._.

Answer:

-0.5

Step-by-step explanation:

i got u lil man

Answer:

I think is 0.5 or 0.9 not sure

Answer:

The volume of the wood used is \(1,116\ cm^3\)

Step-by-step explanation:

The Volume of a Rectangular Cuboid

In a rectangular cuboid, all angles are right, and the opposite faces are equal.

The volume of a cuboid of dimensions a,b,c is:

V=a.b.c

The rectangular box is made of wood with externals dimensions of 25 cm by 20 cm by 15 cm.

The external volume of the box is:

\(V_e=(25)*(20)*(15)=7,500\ cm^3\)

The walls of the box are 0.5 thick each, this means that the internal dimensions are 1 cm less than the external dimensions, including the lid.

Thus the internal volume is:

\(V_i=(24)*(19)*(14)=6,384\ cm^3\)

The volume of the wood used is the difference between the external and the internal volumes:

\(V_w=7,500\ cm^3-6,384\ cm^3=1,116\ cm^3\)

The volume of the wood used is \(\mathbf{1,116\ cm^3}\)

The c has only one number  is c = 81/4 that satisfy the conclusion of rolle's theorem.

The three hypotheses of Rolle's theorem are:

(a) f(x) is continuous on [a,b]

(b) f(x) is differentiable on (a,b)

(c) f(a) = f(b)

i) If you graph f(x), you can see that it is continuous that is no breaks on the interval [0,81]

ii) f(x) is differentiable on (0,81)

f '(x) = 1/(2√x) - 1/9  which exists on the open interval (0,81)

iii) f(0) = f(81) = √81 - 81/9 = 9-9 = 0

Rolle's Conclusion:

f'(c) = 0

f'(c) = 1/(2√c) -1/9 = 0

(9 - 2√c)/(18√c) = 0

√c = 9/2

c = 81/4

There is one number c = 81/4, which satisfies f '(c) = 0.

Therefore the c has only one number  is c = 81/4 that satisfy the conclusion of rolle's theorem.

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Full question:

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)

f(x) =x − 1/9 x, [0, 81].

\(\displaystyle \Large \boldsymbol{} a) \ \underline{x^2-3x}+\underline{2x-6}-\underline{xy+3y}=\\\\\\x(x-3)+2(x-3)-y(x-3)=\boxed{(x-3)(x-y+2)} \\\\\\b) \ mn-mx-n+x=m(n-x)-(n-x) =\boxed{ (m-1)(n-x)}\)

Answer: \(\frac{10}{3}\)

Step-by-step explanation:

7+3(5-4)=10

2+1=3

Therefore, 10/3.

Given:-

\( \: \)

\( \: \)

Solution:-

\( \: \)

put the given values in the equation

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

The domain and range for the following graph, is written below:

Domain (interval notation) : [-4,4)

Range (interval notation): [1,4)

Domain (inequality notation): -4 ≤ x < 4

Range (inequality notation): 1 ≤ x < 4

The collection of values that can be put into a function's domain are called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of values that a function can take on is known as its range. Following the putting of the x value, the function outputs this sequence of values.

Utilizing graphs is a useful tool for determining the scope and range of functions. A graph's domain is the entire set of input values shown on the x-axis since the term "domain" refers to the set of potential input values. The various output values are displayed on the y-axis and make up the range.

Domain (interval notation) : [-4,4)

Range (interval notation): [1,4)

Domain (inequality notation): -4 ≤ x < 4

Range (inequality notation): 1 ≤ x < 4

As we know,

Domain is the x-values of a function

Range is the y values of a function

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Okay so here is how it works:

Because 2:3:5 is the ratio 10 is the total because 2+3+5 is 10 right?

You therefore equate 10 to 4000

10=4000

so if 10 is equal to 4000 what about 2,3 or 5?

2/10×4000=800

3/10×4000=1200

5/10×4000=2000

Hope this anwered your question

Answer:

B. 10

Step-by-step explanation:

While doing construction O and P are joined then

OQ = OR

<QOR = 80°

<QPR = <QOR /2 ( INSCRIBED ANGLE IS HALF OF THE CENTRAL ANGLE STANDING ON SAME ARC)

<QPR = 80°/2

<QPR = 40°

SO

< QPO = X

<RPO = 30°

<QPO + <RPO = < QPR

X + 30° = 40°

X = 40° - 30°

X = 10°

hope it helps

Answer:

5+5=10

Step-by-step explanation:

5+5=10

hope this helps. plz mark me as brainliest.

The Lagrange polynomial using the given points and calculate its value at x = 2.5. The expression to find the value of the Lagrange polynomial at x = 2.5.

To construct a Lagrange polynomial that passes through the given points (-2, -1), (0.1, 1.3), (14.5, -5.4), (0.3, 0), and (X, y), we can use the Lagrange interpolation formula.

The formula for the Lagrange polynomial is:

L(x) = Σ [y(i) * L(i)(x)], for i = 0 to n

Where:
- L(x) is the Lagrange polynomial
- y(i) is the y-coordinate of the ith point
- L(i)(x) is the ith Lagrange basis polynomial

The Lagrange basis polynomials are defined as:

L(i)(x) = Π [(x - x(j)) / (x(i) - x(j))], for j ≠ i

Where:
- L(i)(x) is the ith Lagrange basis polynomial
- x(j) is the x-coordinate of the jth point
- x(i) is the x-coordinate of the ith point

Now, let's construct the Lagrange polynomial step by step:

1. Calculate L(0)(x):
L(0)(x) = [(x - 0.1)(x - 14.5)(x - 0.3)(x - X)] / [(-2 - 0.1)(-2 - 14.5)(-2 - 0.3)(-2 - X)]

2. Calculate L(1)(x):
L(1)(x) = [(-2 - 0.1)(-2 - 14.5)(-2 - 0.3)(-2 - X)] / [(0.1 - (-2))(0.1 - 14.5)(0.1 - 0.3)(0.1 - X)]

3. Calculate L(2)(x):
L(2)(x) = [(x + 2)(x - 14.5)(x - 0.3)(x - X)] / [(0.1 + 2)(0.1 - 14.5)(0.1 - 0.3)(0.1 - X)]

4. Calculate L(3)(x):
L(3)(x) = [(x + 2)(x - 0.1)(x - 0.3)(x - X)] / [(14.5 + 2)(14.5 - 0.1)(14.5 - 0.3)(14.5 - X)]

5. Calculate L(4)(x):
L(4)(x) = [(x + 2)(x - 0.1)(x - 14.5)(x - X)] / [(0.3 + 2)(0.3 - 0.1)(0.3 - 14.5)(0.3 - X)]

Now, we can write the Lagrange polynomial as:

L(x) = y(0) * L(0)(x) + y(1) * L(1)(x) + y(2) * L(2)(x) + y(3) * L(3)(x) + y(4) * L(4)(x)

To calculate the value of the Lagrange polynomial at x = 2.5,

substitute x = 2.5 into the Lagrange polynomial equation and evaluate it.

It is important to note that the value of X and y are not provided, so we cannot determine the exact Lagrange polynomial without these values.

However, by following the steps outlined above, you should be able to construct the Lagrange polynomial using the given points and calculate its value at x = 2.5 once the missing values are provided.

Now, evaluate the expression to find the value of the Lagrange polynomial at x = 2.5.

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Answer:

244.92 square inches

Step-by-step explanation:

You just have to fill in the formula with the information they gave you.

They gave you the diameter for base circle so you divide that number in half to get the radius which is what you need for the formula represent as "r".

r=3

h=10

and you know pi is 3.14

so just plug in the numbers.

SA=2x3.14x3^2+2x3.14x3x10

SA=6.28x9+6.28x30

SA=56.52+188.4

SA=244.92

Answer: 6

Step-by-step explanation:

Just some simple ratios

P = Pizza People = Pl

P: Pl

2 : 9

x: 27

We want to find x.

Since 27/9 is equal to 3, we multiply 2 by 3 as well!

2x3=6, our desired amount.

The vector perpendicular to a plane determined by two vectors A and B can be found by taking their cross product. The unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.

A x B = (-2i+4j+0k) x (i+j-k)
= (-4k + 2i + 6j)

To find a unit vector perpendicular to the plane, we need to normalize this vector by dividing it by its magnitude:

|A x B| = sqrt((-4)^2 + 2^2 + 6^2) = sqrt(56)

So, a unit vector perpendicular to the plane determined by A and B is:

(-4k + 2i + 6j) / sqrt(56)

which simplifies to:

(-2i + 3j - k) / sqrt(14)

Therefore, the answer is (-2i + 3j - k).

To find a vector perpendicular to the plane determined by vectors A and B, you need to calculate the cross product of A and B.

A = -2i + 4j
B = i + j - k

Step 1: Calculate the cross product (C) of vectors A and B:
C = (A_y * B_z - A_z * B_y)i - (A_x * B_z - A_z * B_x)j + (A_x * B_y - A_y * B_x)k

Step 2: Plug in the values of A and B:
C = (4 * (-1) - 0 * 1)i - (-2 * (-1) - 0 * 1)j + (-2 * 1 - 4 * 1)k

Step 3: Simplify the expression:
C = -4i + 2j - 6k

Step 4: Find the magnitude of C:
|C| = √((-4)^2 + 2^2 + (-6)^2) = √(16 + 4 + 36) = √56

Step 5: Divide each component of C by its magnitude to find the unit vector:
Unit vector = (-4/√56)i + (2/√56)j + (-6/√56)k

So, the unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.

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Answer:

Step-by-step explanation:

(2n -3)(2n+1) = 4n^2 + 2n - 6n - 3 = 4n^2 - 4n -3

Answer:

Answe(–8, 8) and (2, 2) & (–2, 1) and (3, –2)

Step-by-step explanation:

The lifting force if the speed is 220 miles per hour is F' = 708.53 N.

The force of light, or simply light, is the sum of all forces on an object that cause the object to move perpendicular to the direction of flow.

The most common type of lift is the wing lift. But there are many other common uses, such as propellers on airplanes and ships, rotors on helicopters, fan blades, sails on sailboats, and wind turbines.

We have,

The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. It, means that,

\(F=kAv^{2}\)

Where

k is constant

If, A = 190 Ft², v = 220 mph, F = 950 pounds

Now, find k first from the above data. So,

    \(k=\frac{F}{Av^{2} }\)

⇒ \(k=\frac{950}{190* (220)^2}\)

⇒ k = 0.0001033

It is required to find the lifting force on the wing if the plane slows down to 190 miles per hour.

Let F' is a new force. So,

    F' = 0.0001033 × 190 × (190)²

⇒ F' = 708.53 pounds.

So, the lifting force is 708.53 pounds if the plane slows down to 190 miles per hour.

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An area of mathematics that studies how competing parties interact is known as "game theory."

Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.

Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.

The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.

Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.

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Answer: (A) -24x1/4  (B) Negative multiplied by a positive equals a negative

Step-by-step explanation:

The question says below sea level, so the whole number is negative. we don't need city A its a distraction so city C is multiple by city D. why do we multiply because the word of means multiple there for the expression is

write the product into one single fraction

-24x1

   4        canceled the 4 in the fraction -24x1

                                                                      4

-6x1    any expression divided by one remains the same -6x1

  1

solution

x1=0

If a is an integer, when is a/b always equal to an integer

= b<1

The natural cubic splinecan be represented by three cubic polynomials:

S1(x) = 2 + 2(x - 1) + 0.5\((x - 1)^{3}\).  S2(x) = 8 - 2(x - 3) - 0.5\((x - 3)^{3}\).  S3(x) = 4 + 1(x - 5) + 0.5\((x - 5)^{3}\)

we need to find a set of cubic polynomials that interpolate the given data points while satisfying certain conditions.

First, we divide the interval [1, 7] into three subintervals: [1, 3], [3, 5], and [5, 7].

Next, for each subinterval, we determine a cubic polynomial that passes through the corresponding data points. We define S1(x) for the interval [1, 3], S2(x) for [3, 5], and S3(x) for [5, 7].

To ensure smoothness, we require the first and second derivatives of adjacent polynomials to be equal at the shared data points. This results in a system of equations that can be solved to determine the coefficients of the cubic polynomials.

Finally, to achieve a natural spline, we impose the condition that the second derivatives at the endpoints (1 and 7) are zero.

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The inequality which describes the domain is 0 ≤ x ≤ 5

From the question, we have

Size of tank = 3 gallons

Rate = 0.6 gallons per hour

The highest number of time is calculated as

Time = Size of tank/Rate

         = 3/0.6 =5

The domain is then represented as 0  ≤ x ≤ Time

This gives 0 ≤ x ≤ 5

Domain:

The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The domain is indicated by the fact that the fraction's denominator is not equal to zero and by the fact that the digit under the square root bracket is positive.

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