Rosie bought a car for £4000. 3 years later, she sells it for £1400. What is the percentage loss that Rosie has made?

Yes, it is necessarily  true that W(orthogonal complement) = span(v k+1,......,vn)

Since {v1,....,vn} is an othogonal basis for R^n, each vector in the basis is orthogonal to every other vector in the basis. Therefore, the vectors v1,....,vk are orthogonal to the vectors vk+1,....,vn, and vice versa. This means that any vector in W is orthogonal to any vector in span(vk+1,...,vn). Hence, W and span(vk+1,...,vn) are orthogonal complements of each other.

To show that W(orthogonal complement) = span(vk+1,...,vn), we need to show that any vector in W(orthogonal complement) is also in span(vk+1,...,vn) and vice versa.

et x be a vector in W(orthogonal complement). Then, x is orthogonal to every vector in W, which means x is orthogonal to v1,....,vk. Since {v1,....,vn} is a basis for R^n, any vector in R^n can be written as a linear combination of the basis vectors.

Therefore, we can write x as a linear combination of v k+1,......,vn. This shows that x is in span(vk+1,...,vn).

Conversely, let y be a vector in span(vk+1,...,vn). Then, we can write y as a linear combination of v k+1,......,vn. Since v1,....,vk are orthogonal to v k+1,......,vn, we have y is orthogonal to v1,....,vk. Therefore, y is in W(orthogonal complement).

Hence, W(orthogonal complement) = span(vk+1,...,vn).

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Answer:

Commutative property of addition.

Step-by-step explanation:

The given expression is:

x + y + z = z + y + x

To match the example with the corresponding property, we need to simplify the expression using the commutative property of addition.

According to the commutative property of addition, the order of the terms in an addition expression does not affect its value. That is:

a + b = b + a

Using this property, we can rewrite the given expression as:

x + y + z = x + y + z

we see that both sides of the equation are identical. This means that the expression is true, regardless of the values of x, y, and z.

Therefore, the example "x + y + z = z + y + x" matches with the commutative property of addition.

The last year when the population was more than 250,000 was 2005.

What is the natural logarithm?

The natural logarithm, denoted by ln(x), is a mathematical function that gives the logarithm of a number x with respect to the base e, where e is the mathematical constant approximately equal to 2.71828.

We can start by setting up the equation p = 250, where p represents the population in thousands. Then, we can solve for t, the number of years since 2000:

[tex]250 = 90*(34)^t[/tex]

[tex](34)^t = 250/90[/tex]

[tex](34)^t = 2.777...[/tex]

Taking the natural logarithm of both sides, we get:

t ln(34) = ln(2.777...)

t = ln(2.777...)/ln(34)

t ≈ 4.4

So, the population was more than 250,000 in the year 2000 + 4.4 ≈ 2004.4, which we can round up to 2005.

Therefore, the last year when the population was more than 250,000 was 2005.

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The volume of a sphere with a radius of 3cm is 113.04 cm³, which is approximately equal to 36π cm³. So, the correct option is D).

The formula for calculating the volume of a sphere, V = 4/3πr³, is used to find the amount of space enclosed by a sphere with a given radius. In this case, the sphere has a radius of 3cm. By substituting this value into the formula, we can solve for the volume of the sphere.

V = 4/3πr³

V = 4/3 × 3.14 × 3³ = 113.04 cm³

= approximately 36π cm³

The result is 113.04 cm³, which is approximately equal to 36π cm³. This calculation is important in many applications, such as engineering, physics, and mathematics. The correct answer is D).

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_____The given question is incomplete, the complete question is given below:

What is the volume of sphere r = 3cm? responses A 8π cm³ 8 pi, cm³  B 16π cm³ 16 pi, cm³ C 27π cm³ 27 pi, cm³ D 36π cm³

Therefore, the dimensions of triangle ABC and the angles opposite to these sides are:

a ≈ 6.85 units

b = 13 units

c ≈ 9.39 units

A ≈ 40 degrees

B = 97 degrees

C = 43 degrees

A triangle is a geometrical shape that has three sides and three angles. It is formed by connecting three non-collinear points in a plane with straight line segments. The three sides may have different lengths, and the three angles may have different measures. The sum of the angles in a triangle is always 180 degrees. Triangles are used in many fields of mathematics, as well as in science, engineering, and everyday life. They can be classified by their side lengths and angle measures, and there are various formulas and theorems that apply to triangles.

Here,

We can use the Law of Sines to find the missing measures of the triangle.

Recall that the Law of Sines states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides opposite to the angles A, B, and C, respectively.

Given that b=13 units, and angle B=97 degrees, we can set up the proportion:

13/sin(97) = c/sin(43)

Solving for c, we get:

c = (13*sin(43))/sin(97) ≈ 9.39

Now, to find the remaining angle and side, we can use the fact that the angles of a triangle sum up to 180 degrees. We know that angle C is 43 degrees, so we can find angle A as:

A = 180 - 97 - 43 = 40 degrees

And we can find side a using the Law of Sines:

a/sin(40) = 13/sin(97)

Solving for a, we get:

a = (13*sin(40))/sin(97) ≈ 6.85

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By Pythagorean Theorem, the length of AC  is 21.9feet.

How does the Pythagorean Theorem work and for what purposes?

The Pythagorean Theorem asserts that the square of the hypotenuse equals the sum of the squares of the legs of any right triangle. The formula serves as an illustration of this Theorem.

                         The Pythagorean Theorem can be used to determine the third side's length if you know the lengths of any two of a right triangle's sides.

From the given circle, the triangle ACD is right angle since it is a triangle in a semicircle

Hypotenuse = 26 feet = CD

Base side = AD = 14ft

Length AC

Use the theorem

26² = 14² + AC²

AC² =  676 - 196

AC² = 480

AC = 21.9 feet

Hence the length of AC  is 21.9feet.

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After answering the presented question, we can conclude that equation Therefore, the original price of the motorcycle is Rs 125700.

In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.

Let the original price of the motorcycle be P.

Depreciation per year = 4% of P = 0.04P

Cost of motorcycle after 3 years = P - 3(0.04P) = P - 0.12P = 0.88P

[tex]0.88P = Rs 110592\\P = Rs (110592/0.88)\\P = Rs 125700[/tex]

Therefore, the original price of the motorcycle is Rs 125700.

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For given expression e will be 7/3.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a single value.

Expressions can be simple or complex, and they can involve arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, logarithms, and trigonometric functions.

Now,

We can solve for e by setting the given value of f equal to 49 and then solving for e.

f = 9e²

When f = 49, we have:

49 = 9e²

Dividing both sides by 9, we get:

49/9 = e²

Taking the square root of both sides, we get:

±√(49/9) = ±(7/3) = e

So the solutions for e are e = 7/3 or e = -7/3. However, since e is a measure of distance and cannot be negative, the only valid solution is e = 7/3.

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Correct Question:-

Function f=9e² ,  If f=49 then solve for e.

The point at -6.4 is farthest to the left on the number line" must be true.

The correct answer is A.

We have,

The inequality -2.9 > -4.7 tells us that the point at -2.9 is to the right of the point at -4.7 on the number line.

The points -6.4, -4.7, and -2.9 are on the number line, and we know that -2.9 is to the right of -4.7.

The point at -6.4 must be the farthest to the left on the number line.

So the statement "The point at -6.4 is farthest to the left on the number line" must be true.

Therefore,

The point at -6.4 is farthest to the left on the number line" must be true.

The correct answer is A.

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Answer:

a²=b²+c²

37²=35²+c²

1369=1225+c²

1369-1225=c²

144=c²

√144=√c²

12=c

c=12

Step-by-step explanation:

Use the Pythagoras threom. It's formula is a²=b²+c² where a=37, b=35 and c=?

The correct population parameter for shop at this dealership that will purchase a Peterbilt truck is p that is option C.

In statistics, a population parameter characterises an individual or population. A population parameter describes the distribution of all values within a group and is a fixed but unknowable property. The parameters used in other sorts of maths should not be confused with this. These are the parameters of a mathematical function that never change. An indicator of the population is not a statistic. This information only applies to a portion of a certain demographic. You can determine the genuine population value with the aid of a well-designed research.

Statistics and parameters share many similarities. Both express a characteristic of the group, such as the fact that 20% of M&Ms are red. Yet, the fundamental distinction is in who and what they are describing. The entire population is referred to by parameters. The part or sample that was examined in a study is referred to as the statistic.

You might count the quantity of red M&Ms in the aforementioned example's various packs. Your statistic will be provided by this. If your study was well-designed, the statistic you obtain should precisely reflect the population parameter.

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Complete question:

A recent flyer claimed that 2 out of every 9 trucks sold at a local dealership are manufactured by Peterbilt. Find a 95% confidence interval for those who shop at this dealership that will purchase a Peterbilt truck. Identify the correct population parameter.

μ

х

р

p^

[tex]\mu_1 - \mu_2[/tex]

Xi – X2

î

Pi – P2

The volume of the cylinder is 785.40 cm³.

What is the formula for the volume of a cylinder?

[tex]V = π {r}^{2} h[/tex]

Where r is the radius of the cylinder and h is the height of the cylinder.

Since d is the diameter of the cylinder, we can find the radius by dividing d by 2.

Now, radius [tex]r = \frac{d}{2} = \frac{10}{2} = 5[/tex]

So, the volume of the cylinder is

[tex]V = π {r}^{2} h \\ = π {5}^{2} \times 10\\ = π×25×20 = 250π[/tex]

We know π = 3.14

So, V = 250×3.14

Using a calculator, we can approximate this to the nearest hundredth of a unit:

V ≈ 785.40

Therefore, the exact volume of the cylinder is 250π and its approximate value to the nearest hundredth of a unit is 785.40 cm³.

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In the given figure of Rhombus, Angle ∠BAD is 0°. In summary: angle ∠ABC = 135°

angle ∠ADC = 135°

angle ∠BAD = 0°

What is rhombus?

A rhombus is a quadrilateral (four-sided) geometric shape with equal-length sides. Since it has two sets of opposite equal acute angles and opposite equal obtuse angles, it is also known as a diamond form. In other words, the opposite angles and the neighbouring sides of a rhombus are congruent. A rhombus has two equal-length diagonals that are right angles to one another. A rhombus's area is equal to the product of its diagonal lengths.

by the question.

In a rhombus, opposite angles are equal, so we know that:

angle ∠ABC = angle ∠ADC (opposite angles of rhombus)

angle ∠BCD = angle ∠BAD (opposite angles of rhombus)

We are given that angle ∠ADC is 135°. Therefore, angle ∠ABC is also 135°.

To find angle ∠BAD, we can use the fact that the angles of a quadrilateral sum to 360°. Since we know three of the angles (∠ABC, ∠BCD, and ∠ADC), we can find the fourth angle (∠BAD) by subtracting their sum from 360°:

∠BAD = 360° - (∠ABC + ∠BCD + ∠ADC)

= 360° - (135° + 90° + 135°)

= 360° - 360°

= 0°

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If three cards are drawn randomly for a standard card deck, then the probability that all three are different suits is 0.3976.

We know that the total number of cards in a standard deck is = 52 cards;

So, the probability of drawing 3 cards from a standard deck is =

⇒ ⁵²C₃ = 22100 ,

We know that each suit in a standard deck has 13 cards,

So, the probability of selecting 3 cards from a standard deck is :

⇒ 4(¹³C₁ × ¹³C₁ × ¹³C₁);

The probability that all three are different suits;

⇒ 4(¹³C₁ × ¹³C₁ × ¹³C₁)/22100,

⇒ 169/425,

⇒ 0.3976.

Therefore, the required probability is 0.3976.

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Answer:

Answer:

sin(θ)  =  -6/10  =  -0.60 and tan(θ)  =  -6/8  =  -0.75.

Step-by-step explanation:

Since  cos(θ) = adjacent / hypotenuse  in a right triangle andsince cos(θ) = 0.8  =  8/10   --->   adjacent = 8  and  hypotenuse  =  10.Using the Pythagorean Theorem, opposite = +6  or  -6, depending upon the quadrant.Since tan(θ) < 0, the triangle is found in either the second quadrant or the fourth quadrant.Since cos(θ) > 0, the triangle is found in either the first quadrant or the fourth quadrant.Therefore, it must be in the fourth quadrant.In the fourth quadrant, sin(θ) < 0, making the opposite side -6.--->   sin(θ)  =  -6/10  =  -0.60.--->   tan(θ)  =  -6/8  =  -0.75.

Answer:it’s wrong if so then 5 would’ve been in c’s place

Step-by-step explanation:

Performing an elementary row operation on a matrix does not change its determinant.

An elementary row operation is a transformation of a matrix that involves interchanging two rows, multiplying a row by a nonzero scalar, or adding a scalar multiple of one row to another row.

Let A be a matrix and let B be the matrix obtained from A by performing an elementary row operation. We want to show that det(A) = det(B).

If the row operation involves interchanging two rows, then the determinant of the resulting matrix is the negative of the determinant of the original matrix.

If the row operation involves multiplying a row by a nonzero scalar, then the determinant of the resulting matrix is the scalar multiplied by the determinant of the original matrix.

If the row operation involves adding a scalar multiple of one row to another row, then the determinant of the resulting matrix is the same as the determinant of the original matrix.

In any case, the determinant of the matrix is preserved under elementary row operations. Therefore, performing an elementary row operation on a matrix does not change its determinant.

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The probability that the first white ball drawn in powerball will not be an 18 is 0.985.

Concept used:

Probability of an event = number of favorable outcomes / total number of outcomes.

We have 69 balls, out of which 1 is an 18. Thus, there are 68 balls that are not 18.

Therefore, the probability of the first white ball drawn in powerball will not be an 18 is given by,

P(event)= number of favorable outcomes / total number of outcomes= 68/69 = 0.985 (approx)

Thus, the required probability that the first white ball drawn in powerball will not be an 18 is 0.985, rounded to three decimal places.

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Answer:

3.606

Step-by-step explanation:

ur solving for x

:)

Solving the proportion, the smallest amount of this green paint that he must throw away so that, using the rest of his green paint and some extra blue and/or yellow paint, he could make 4.08 liters of paint of the correct shade of green is    5 liters.

Let's assume the amount of green paint to be thrown away is x liters. Since, 5 liters of green paint (the correct shade of green) is required then the proportion can be expressed as

2 liters of blue paint: 3 liters of yellow pain

The sum of blue and yellow paint is 5 - x liters

Then,0.4 = 2/5 + a/(5 - x)

where,  "a" is the amount of blue paint to be added to the 3 liters of yellow paint

0.4(5 - x) = 2 + 5a-2 = 2.6x - 5a

0.6 = 2.6x - 5a

Since the least amount of green paint should be thrown away to make the correct shade of green paint, the minimum value of x should be found.

0.6 = 2.6x - 5a

0.6 + 5a = 2.6x

5a = 2.6x - 0.6a = (2.6/5)x - 0.12a = 0.52 - 0.12a

To minimize the value of x, a should be maximized. The maximum value of a is 2 (two liters) since there are only 3 liters of yellow paint.

Using a=2 (two liters), the value of x is:

a = (2.6/5)x - 0.12a = (2.6/5)x - 0.12 (2)2 = (2.6/5)x - 0.24x = 5(2 + 0.24)/2.6x = 4.08

Therefore, he could make 5 liters of paint of the correct shade of green is 4.08 liters.

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Answer:

Median = 4.5

Step-by-step explanation:

4 and 5 are central numbers.

then:

(4+5)/2 = 4.5

Answer:

4.5

Step-by-step explanation:

if you add the two middle number 4+5=9

then i. you divide 9by2 you'll get the median

We can conclude after answering the provided question that In order to slope make at least $225.00 in sales, we must solve for m:

[tex]s = 75m + 1500 225 = 75m + 1500\s75m = -1275\sm = -17[/tex]

Slope is the downward movement of a near - constant basis in mathematics. It is a test of how much the y-value of an activity appears to vary when the x-value changes. The curve of a line is ordinarily indicated by the letter m and can be determined using the equation: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) are any 2 things on the line. A line's slope can be positive, negative, zero, or unknown. A positive slope indicates that the line moves up from left to right, whereas a decreasing trend indicates that the line descends from left to right.

a. Because the relationship between the two variables is proportional, the function that connects the sales (s) and the number of muffins (m) is a linear function. The slope of the line can be calculated by dividing the change in sales by the change in the number of muffins:

slope = (2400 - 1800) / (12 - 4) = 600 / 8 = 75

The equation line is as follows:

s = 75m + b

To find the y-intercept (b), we can substitute one of the data points:

[tex]1800 = 75(4) + b\sb = 1800 - 300\sb = 1500[/tex]

As a result, the function that connects sales and the number of muffins is:

s = 75m + 1500

b. In order to make at least $225.00 in sales, we must solve for m:

[tex]s = 75m + 1500 225 = 75m + 1500\s75m = -1275\sm = -17[/tex]

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Step-by-step explanation:

There are a total of 6 sides

two  are 3 x 6     m^2

two are   3x 5      m^2

two are   6 x 5     m^2  

Area = 2 ( 3x6    +   3x5    +  6x5)   = 126 m^2

____________________

hopes it's helps

Answer:

To find the maximum gas mileage, we need to find the vertex of the parabola representing the gas mileage function.

The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c is given by -b/2a.

In this case, the gas mileage function is m(x) = -0.026x^2 + 2.593x - 35.023, so a = -0.026 and b = 2.593.

The x-coordinate of the vertex is therefore:

x = -b/2a = -2.593/(2*(-0.026)) = 49.9 (rounded to one decimal place)

This means that the maximum gas mileage occurs at a speed of 49.9 mph.

To find the maximum gas mileage, we can substitute x = 49.9 into the gas mileage function:

m(49.9) = -0.026(49.9)^2 + 2.593(49.9) - 35.023 ≈ 36.1 mpg

Therefore, the maximum gas mileage is approximately 36.1 mpg.

Step-by-step explanation:

Answer:

C- 80 degrees Celsius

Step-by-step explanation:

If you followed the formula by subtracting 176 by 32 you would get 144 multiplied by 5/9 = 80 degrees

The volume of the pyramid is approximately 2.4 cubic centimeters.

The formula for the volume of a pyramid is given by

V = (1/3) × base area × height

Since the base of the pyramid is a square and the perimeter is 4.7 cm, each side of the square has a length of

s = perimeter/4 = 4.7/4 = 1.175 cm

The base area of the pyramid is

A = s² = 1.175² = 1.3806 cm²

Therefore, the volume of the pyramid is

V = (1/3) × 1.3806 × 4.7 = 2.4457 cm³

Rounding this to the nearest tenth of a cubic centimeter, we get

V ≈ 2.4 cm³

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The probability that 4 prefers A, 1 prefer B and 5 will have no preference = 0.0024

Here, in a certain town, 40% of the eligible voters prefer candidate a,

⇒ P(A) = 40%

⇒ P(A) = 0.4

10% prefer candidate b,

⇒ P(B) = 10%

⇒ P(B) = 0.1

and the remaining 50% have no preference.

⇒ P(T) = 50%

⇒ P(T) = 0.5

Also, the sample size = 10

So, the probability that 4 prefers A, 1 prefer B and 5 will have no preference would be:

P = ⁵C₄ (0.4)⁴ × ⁶C₁ (0.1) × (0.5)⁵

P = 0.0024

Therefore, the required probability is 0.0024

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