Solve equation.
n+2=-11

if £1=1. 62USD then, £650 is equivalent to $1053 in US dollars and £450 is equivalent to $729 in US dollars.

To convert British pounds to US dollars, we can multiply the pound amount by the exchange rate of pounds to dollars.

£650 in USD:

£1 = $1.62, so we can write:

650 x 1.62/1 = 1053

Therefore, £650 is equivalent to $1053 in US dollars.

£450 in USD:

Using the same method, we can calculate the value of £450 in US dollars as follows:

450 x 1.62/1 = $729

Therefore, £450 is equivalent to $729 in US dollars.

The conversion of British pounds to US dollars is a common currency exchange process, as both currencies are widely used in international trade and finance. The exchange rate between the two currencies represents the value of one currency in terms of the other. In this case, the exchange rate of £1 to $1.62 means that one British pound is worth 1.62 US dollars. To convert a certain amount of British pounds to US dollars, we simply multiply the pound amount by the exchange rate. The resulting dollar amount reflects the value of the pounds in the equivalent US dollars. Exchange rates can fluctuate frequently due to various economic and political factors, affecting the value of currencies and international transactions.

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Answer:

15 = 9m

15/9 = 9m/9

m =15/9

=5/3

=1.666667

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

The solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.

To solve the equation 3.3 + 4x = -6.9x + 6.6, we need to isolate the variable x on one side of the equation.

First, let's simplify the equation by combining like terms:

3.3 + 4x = -6.9x + 6.6

Next, let's move the variable terms (4x and -6.9x) to one side and the constant terms (3.3 and 6.6) to the other side:

4x + 6.9x = 6.6 - 3.3

Combine the x terms on the left side:

10.9x = 3.3

Now, divide both sides of the equation by 10.9 to solve for x:

x = 3.3 / 10.9

Using a calculator, we can find the decimal approximation of x:

x ≈ 0.3028

Rounding to the nearest tenth, the solution to the equation is x ≈ 0.3.

In summary, the solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.

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A biased sample is created when a sample is collected with some members not as likely to be chosen as others .

When a sample is collected with some members not as likely to be chosen as others, the resulting sample is biased. Bias in sampling occurs when the sample is not representative of the population being studied, leading to incorrect or misleading conclusions.

For example, if a survey on the popularity of a new product is conducted by asking only a select group of individuals who are already known to be fans of the product, the results may be biased and not accurately reflect the true popularity of the product among the general population.

Bias can occur for many reasons, such as non-random sampling techniques, self-selection bias, or researcher bias. It is important to avoid bias in sampling to ensure the accuracy and validity of research findings.

This can be achieved by using random sampling techniques, increasing sample size, and ensuring that all members of the population have an equal chance of being selected for the sample.

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The variability of the data is very small (close to 0) because all the scores are approximately the same.

The variability of these data can be calculated using the variance formula, which is the average squared difference from the mean. In this case, the mean is 3.8 (the sum of 4, 4, 4, 4, and 3 divided by 5). Therefore, the variance is 0.08 (the sum of the squared differences [4-3.8, 4-3.8, 4-3.8, 4-3.8, 3-3.8] divided by 5). This indicates that the variability of the data is very small (close to 0) because all the scores are approximately the same.

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Three iterations are performed here to solve the system of equations using the Successive Over-Relaxation (SOR) method.

To solve the system of equations using the Successive Over-Relaxation (SOR) method, we need to iterate through the equations until convergence is achieved within the given tolerance.

The system of equations is:

- x + 10y - 2z = 8    (Equation 1)

y - 52 = -4           (Equation 2)

1 + 3x - y = 0        (Equation 3)

We start with the initial guesses:

x₀ = 0

y₀ = 0.9

z₀ = 1.1

Using the SOR method, the iteration formula is:

xₖ⁺¹ = (1 - ω)xₖ + (ω/a₁₁)(b₁ - a₁₂yₖ - a₁₃zₖ)

yₖ⁺¹ = (1 - ω)yₖ + (ω/a₂₂)(b₂ - a₂₁xₖ - a₂₃zₖ)

zₖ⁺¹ = (1 - ω)zₖ + (ω/a₃₃)(b₃ - a₃₁xₖ - a₃₂yₖ)

where ω is the relaxation factor, a₁₁, a₂₂, and a₃₃ are the diagonal elements of the coefficient matrix, b₁, b₂, and b₃ are the right-hand side values, and the subscripts k and k+1 represent the iteration steps.

Given:

tol = 0.05       (tolerance)

a₁₁ = 3

a₂₂ = 10

a₃₃ = 5

ω = 0.9

Let's proceed with the calculations using the SOR method:

Iteration 1:

x₁ = (1 - 0.9)(0) + (0.9/3)(8 - 10(0.9) - 2(1.1)) = 0.6

y₁ = (1 - 0.9)(0.9) + (0.9/10)(-4 - 3(0) - 5(1.1)) = 0.833

z₁ = (1 - 0.9)(1.1) + (0.9/5)(1 - 3(0) - 10(0.833)) = 1.035

Iteration 2:

x₂ = (1 - 0.9)(0.6) + (0.9/3)(8 - 10(0.833) - 2(1.035)) = 0.610

y₂ = (1 - 0.9)(0.833) + (0.9/10)(-4 - 3(0.6) - 5(1.035)) = 0.841

z₂ = (1 - 0.9)(1.035) + (0.9/5)(1 - 3(0.6) - 10(0.841)) = 1.012

Iteration 3:

x₃ = (1 - 0.9)(0.610) + (0.9/3)(8 - 10(0.841) - 2(1.012)) = 0.620

y₃ = (1 - 0.9)(0.841) + (0.9/10)(-4 - 3(0.610) - 5(1.012)) = 0.842

z₃ = (1 - 0.9)(

1.012) + (0.9/5)(1 - 3(0.610) - 10(0.842)) = 1.008

Continue these iterations until the solution converges within the given tolerance.

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Answer:

1

Step-by-step explanation:

I am not joking around im actually being serious its 1 here are the steps

27/9+6-8

3+6-8

9-8=1

Domain and Range of the given rational functions are:Given rational function f(x) = 3/(x-1)The denominator of f(x) cannot be zero.x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}

The range of f(x) is all real numbers except zero.Given rational function f(x) = (2x)/(x-4)The denominator of f(x) cannot be zero.x ≠ 4 Therefore the domain of f(x) is {x | x ≠ 4}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x+3)/(5x-5)The denominator of f(x) cannot be zero.5x - 5 ≠ 0x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}The range of f(x) is all real numbers except 1/5.Given rational function f(x) = (2+x)/(2x)The denominator of f(x) cannot be zero.x ≠ 0 Therefore the domain of f(x) is {x | x ≠ 0}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x^2+4x+3)/(x^2-9)For the denominator of f(x) to exist,x ≠ 3, -3

Therefore the domain of f(x) is {x | x ≠ 3, x ≠ -3}The range of f(x) is all real numbers except 1, -1. Function Domain Rangef(x) = 3/(x-1) {x | x ≠ 1} All real numbers except zerof(x) = (2x)/(x-4) {x | x ≠ 4} All real numbers except zerof(x) = (x+3)/(5x-5) {x | x ≠ 1} All real numbers except 1/5f(x) = (2+x)/(2x) {x | x ≠ 0} All real numbers except zerof(x) = (x^2+4x+3)/(x^2-9) {x | x ≠ 3, x ≠ -3} All real numbers except 1, -1

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The following equations will have the same value of x as the one provided:

(B) 18x - 9 = 72; (D) 3(6x - 3) = 72; (E) x = 4.5

A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.

Like 3x + 5 = 15, for instance.

Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.

So, the given equation is:

3/5(30x-15)=72

Now, we have:
3/5 * 30x - 3/5 * 15 = 72

18x - 9 = 72

Using common 3 as an example, we have the following on the left side of the equation:

3(6x-3) = 72

6x-3 = 72/3

6x-3 = 24

6x = 24+3

6x = 27

x = 27/6

x = 9/2

x = 4.5

Therefore, the following equations will have the same value of x as the one provided:

(B) 18x - 9 = 72; (D) 3(6x - 3) = 72; (E) x = 4.5

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The area of the regular figure of side length 24 cm is 1496.45 square centimeter.

The given regular figure is a hexagon.

A hexagon is a polygon with six sides and six angles.

It is a two-dimensional shape formed by connecting six straight line segments.

The side length of hexagon is 24 cm..

The formula for the area of a regular hexagon is 3√3/2 a².

Where a is the side length of hexagon.

Area =  3√3/2 a².

Plug in a value as 24:

Area = 3√3/2 ×24²

= 3√3×576/2

=2992.9/2

=1496.45 square centimeter.

Hence, the area of figure is 1496.45 square centimeter.

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Find the area of the regular figure below:​

Answer:

We need to find the value of x where f(x) < g(x), which means we need to set the two functions equal to each other and solve for x:

3^x = 2x + 5

We can't solve this equation algebraically, so we'll need to use trial and error or graphing to find the solution.

Using trial and error, we can substitute different values of x into the equation and see which one makes f(x) less than g(x):

- If x = -1, then f(x) = 3^(-1) = 1/3 and g(x) = 2(-1) + 5 = 3. Therefore, f(x) < g(x) when x = -1.

- If x = 2, then f(x) = 3^2 = 9 and g(x) = 2(2) + 5 = 9. Therefore, f(x) is not less than g(x) when x = 2.

- If x = -3, then f(x) = 3^(-3) = 1/27 and g(x) = 2(-3) + 5 = -1. Therefore, f(x) is not less than g(x) when x = -3.

- If x = -4, then f(x) = 3^(-4) = 1/81 and g(x) = 2(-4) + 5 = -3. Therefore, f(x) is not less than g(x) when x = -4.

Therefore, the solution is x = -1, and the answer is A.

Answer:z=4663/586

Step-by-step explanation:

The diameter of the cups used for a slushy stand uses dome shaped lids is 4 inches.

A slushy stand uses dome shaped lids

Lids resemble the shape of a hemisphere

Volume of lid as 16/3 pi cubic inches

Therefore, volume of hemisphere is 16/3 pi cubic inches as lid resemble shape of hemisphere,

Volume of hemisphere is 2/3πr³

V =  2/3πr³

16/3π = 2/3πr³

8 = r³

r = 2

So the radius of the lids is 2

Diameter  = 2r

d = 2x2

D = 4 inches.

Therefore, the diameter of the cups used of lids is 4 inches.

The area that a hemisphere takes up is referred to as its volume. The volume of a thing determines how much space it takes up. A hemisphere is a half-sphere in three dimensions, such as bowls, headphones, an igloo, domes in buildings, etc.

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Answer:

The relationship between the number of oranges and their price is proportional. so the answer is true

Answer:on the circle

Step-by-step explanation:

Point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a center of the circle at D(-1, 3)

And point G(-10, 1) is on the circle.

We know the standard equation of the circle when a center is given:

\(\rm (x-h)^2+(y-k)^2=r^2\)

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

Here (h, k) ⇒ (-1, 3)

The circle equation becomes:

\(\rm (x+1)^2+(y-3)^2=r^2\)

Put the point on the circle equation to get the radius of the circle:

\(\rm (-10+1)^2+(1-3)^2=r^2\)

\(\rm (-9)^2+(-2)^2= r^2\\\\\rm 81+4 = r^2\\\\ \rm r = \sqrt{85} \ units\)

Equation of circle is:

\(\rm (x+1)^2+(y-3)^2=85\)

Now put the point J(-3, 12 ) in the circle equation:

\(\rm (-3+1)^2+(12-3)^2=85\)

4+ 81 ⇒ 85

It means point J is lying on the circle.

Thus, point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

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These steps are often referred to as the principle of mathematical induction or PMI.

The steps for mathematical induction are:

Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.

Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.

Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.

Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.

These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.

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The point that preserves the function is option  A(-3,-8).

What do you mean by function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given question,

We have four option for the answer.

Note: if f is a function then each number of the domain has an unique image.

Since (regarding the table) the image of 9 is 6 then the answer D is wrong

The same apply on answers B and C .

Therefore, the right answer is A(-3,-8).

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To find the slope of the line passing through points (3,6) and (4,7), we use the formula for slope: slope = (y2 - y1) / (x2 - x1). By substituting the coordinates of the two points into the formula, we can calculate the slope. The corresponding change in y, or the change in the y-coordinate, is the difference between the y-values of the two points. Finally, to find an equation of the line passing through a specific point with a given slope, we can use the point-slope form of the equation and substitute the values into the formula.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

For points (3,6) and (4,7), we can substitute the values into the

formula:

slope = (7 - 6) / (4 - 3) = 1/1 = 1

The corresponding change in y is the difference between the y-values of the two points:

Change in y = 7 - 6 = 1

To find an equation of the line passing through a point and with a given slope, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

If we have the point (6,5) and a slope of 1, we can substitute the values into the equation:

y - 5 = 1(x - 6)

y - 5 = x - 6

y = x - 1

So, the equation of the line passing through the point (6,5) and with a slope of 1 is y = x - 1.

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Step-by-step explanation:

Given

Function is  \(y=0.18x+0.15\)

where,

\(y=\text{Percent of the battery remaining}\\x=\text{time in hours}\)

Comparing the given function with the standard slope-intercept form of the equation \(y=mx+c\)

Here, before plugging into the laptop, the percentage of battery is

\(y=0.18\times 0+0.15\\y=0.15\ \text{or}\ 15\%\)

The slope of the given function is \(0.18\) i.e. in one hour it charges 18% of battery.

Answer:

35 ways

Step-by-step explanation:

Seven juniors to choose three from

  7 C 3 = 7! / ( 4! 3!) = 35

Yes, the person needs to stop for petrol. The car can travel distance 25 miles per litre, so it has 4 litres left in the tank. 90 miles divided by 25 miles per litre is 3.6, so the person needs approximately 4 litres of petrol in order to complete the journey.

1. Calculate how many litres the car can hold - 12 litres

2. Calculate how many miles the car can travel with one litre of petrol - 25 miles

3. Calculate how many litres of petrol left in the tank - 1/4 of 12 litres = 3 litres

4. Calculate how many miles the car can travel with 3 litres of petrol - 3 x 25 miles = 75 miles

5. Calculate how many miles the person is away from Islamabad - 90 miles distance

6. Calculate how many litres of petrol the person needs to complete the journey - 90 miles divided by 25 miles per litre = 3.6 litres

7. The person needs to stop for petrol – Yes

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The complete statements are:

The complete question is added as an attachment

The roots are given as:

x = 0 second

and

x = 9.8 seconds

x = 0 implies that the height of the arrow was 0 meters above his bow after 0 seconds

x = 9.8 implies that  it takes approximately 9.8 seconds for the arrow to return to the height of the bow.

The x-value of the vertex is

x = (0 + 9.8)/2

Evaluate

x = 4.9

Approximate

x = 5

This means that the vertex is approximately 5 seconds

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Answer:

\( m = \frac{y2 - y1}{x2 - x1} \)

therefore: m=6

a)The distribution of \(X_{1} +X_{2}+X_{3}\) is a normal distribution with mean μ = 180 and variance σ² = 36.(b)P( \(X_{1} +X_{2}+X_{3}\) > 185) ≈ P(Z > 5/6).(c) The distribution of Y - X is a normal distribution with mean μ = 5 and variance σ² = 27.(d)P(Y - X > 8) ≈ P(Z > 1.732)

(a) The sum of independent normal random variables follows a normal distribution. In this case, X1, X2, and X3 are independent normal random variables with a common mean μ1 = 60 and a common variance σ1² = 12. Therefore, the distribution of \(X_{1} +X_{2}+X_{3}\) is also a normal distribution with the following parameters:

Mean: μ = μ1 + μ1 + μ1 = 60 + 60 + 60 = 180

Variance: σ² = σ1² + σ1² + σ1² = 12 + 12 + 12 = 36

So, the distribution of \(X_{1} +X_{2}+X_{3}\) is a normal distribution with mean μ = 180 and variance σ² = 36.

(b) To find P(\(X_{1} +X_{2}+X_{3}\) > 185), we need to calculate the probability that the sum of X1, X2, and X3 exceeds 185. Since X1, X2, and X3 are normally distributed with a mean of 180 and a variance of 36, we can standardize the variable using the Z-score formula.

Z = (X - μ) / σ

Z = (185 - 180) / √36 = 5 / 6

Now, we need to find the probability that Z is greater than 5/6. We can look up this probability in the standard normal distribution table or use statistical software to find the corresponding value.

P(\(X_{1} +X_{2}+X_{3}\) > 185) ≈ P(Z > 5/6)

(c) The difference of independent normal random variables follows a normal distribution. In this case, Y - X is the difference between Y (with mean μ2 = 65 and variance σ2² = 15) and X (with mean μ1 = 60 and variance σ1² = 12).

The mean of Y - X is μ2 - μ1 = 65 - 60 = 5.

The variance of Y - X is σ2² + σ1² = 15 + 12 = 27.

Therefore, the distribution of Y - X is a normal distribution with mean μ = 5 and variance σ² = 27.

(d) To find P(Y - X > 8), we need to calculate the probability that the difference between Y and X exceeds 8. Since Y - X is normally distributed with a mean of 5 and a variance of 27, we can standardize the variable using the Z-score formula.

Z = (Y - X - μ) / σ

Z = (8 - 5) / √27 ≈ 1.732

Now, we need to find the probability that Z is greater than 1.732. We can look up this probability in the standard normal distribution table or use statistical software to find the corresponding value.

P(Y - X > 8) ≈ P(Z > 1.732)

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Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x_1 - x_2})^{2} + ({y_1 - y_2})^{2} } \\\)

From the question the points are

F(6, 9) and G(4, 14)

The distance between them is

\( |FG| = \sqrt{ ({6 - 4})^{2} + ({9 - 14})^{2} } \\ = \sqrt{( { - 2})^{2} + ({ - 5})^{2} } \\ = \sqrt{4 + 25} \\ = \sqrt{29} \: \: \: \: \: \: \: \: \\ = 5.3851...\)

We have the final answer as

Hope this helps you

Using the properties of Isosceles Triangle we get that When the line containing the vertex of an isosceles triangle is drawn from the vertex angle perpendicular to the base, it bisects the vertex angle and the base.

Based on the length of the sides of the triangle, there are three types of equilateral triangles . , isosceles triangle, unequal triangle. An isosceles triangle is a triangle with two sides of equal length and corresponding angles are equal.

Statement : -

Let ABC be an isosceles triangle such that AB=AC.

Let AD be the bisector of ∠A.

we have to prove:- BD=DC

Proof :-

In △ABD&△ACD

AB=AC(∵△ABC is an isosceles triangle)

∠BAD=∠CAD(∵AD is the bisector of ∠A)

AD=AD (Common)

By S.A.S.(side angle side)

△ABD≅△ACD

By corresponding parts of congruent triangles-

⇒BD=DC

Hence proved that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.

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Complete question:

Prove that if a line containing a vertex of an isosceles triangle is perpendicular drawn from the vertex angle to the base bisect the vertex angle and the base.

Answer:

2.H

Step-by-step explanation:

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Answer:

When a shape is transformed by rigid transformation, the sides lengths and angles remain unchanged.

Rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.

Assume two sides of a triangle are:

And the angle between the two sides is:

When the triangle is transformed by a rigid transformation (such as translation, rotation or reflection), the corresponding side lengths and angle would be:

Notice that the sides and angles do not change.

Hence, rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.

Step-by-step explanation: