what is the f-1(x) ?

The pattern of the sequence is "add increasing multiples of 9 starting with 1."

To find the pattern in the sequence 10, 11, 21, 32, follow these steps:
1. Identify the differences between consecutive terms:
  11 - 10 = 1
  21 - 11 = 10
  32 - 21 = 11
2. Notice that the differences are increasing by 9 (10 - 1 = 9 and 11 - 10 = 1).
3. Based on this observation, the pattern can be described as adding a value that increases by 9 each time:
  10 + 1 = 11
  11 + 10 = 21
  21 + 11 = 32

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____________________

hopes it's helps

Answer:

66 ways in the triple rooms, 28 ways in the double rooms

Step-by-step explanation:

In total: 8 people;

There are 2 triple rooms, so 3 people can live in one triple room:

In the first triple room:

8×7×6 = 336 / 3×2×1 = 56 ways (we have to divide the number of ways by the factorial, because the order of people doesn't matter)

In the second triple room:

5×4×3 = 60 / 3×2×1 = 10 ways (since we can't choose the same people from the first triple room)

In total: 56+10 = 66 ways

Now, double rooms:

Ir the first double room:

8×7 = 56 / 2×1 = 28 ways

In the second double room:

6×5 = 30 / 2×1 = 15 ways

In total: 28+15 = 43 ways

I don't know if I got this right, though...

Answer:

A right angle turns through a circle, or off, which is equal to 90 degrees.

A circle is a shape that has no edges or corners.

It is a closed shape that is formed by a curve that is equidistant from a fixed point, known as the center.

A degree is a unit of measurement that is used to Bangles.

It is equal to of a circle, and there are 360 degrees in a circle.

A right angle is an angle that measures 90 degrees.

It is formed when two lines or rays meet at a point and create a square corner.

When a right angle turns through a circle, it covers one-quarter of the circle, which is equal to 90 degrees.

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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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Using elimination method to solve the system of linear equations, the workout plans lasts for 3/2 and 1 hours respectively

Let's assume that a session of Plan A lasts for x hours and a session of Plan B lasts for y hours. We need to find the values of x and y.

From the given information, we can set up the following system of equations:

[tex]2x + 5y &= 8 \\8x + 3y &= 15[/tex]

We can solve this system by using the method of elimination. Multiplying the first equation by 8 and the second equation by 2, we get:

[tex]16x + 40y &= 64 \\16x + 6y &= 30[/tex]

Subtracting the second equation from the first, we get:

[tex]34y &= 34 \\y &= 1[/tex]

Substituting this value of y into the first equation, we get:

[tex]2x + 5(1) &= 8 \\2x &= 3 \\x &= \frac{3}{2}[/tex]

Therefore, a session of Plan A lasts for 3/2 hours, and a session of Plan B lasts for 1 hour.

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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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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:

3.606

Step-by-step explanation:

ur solving for x

:)

The  boxes of chocolate should choco lovers produce= $11

A number is a numerical unit of measurement and labeling in mathematics.

The natural numbers 1, 2, 3, 4, and so on are the first examples.

Number words are a linguistic way to express numbers.

Most commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five.

Basic numerals are frequently grouped in a numeral system, which is an ordered manner to represent any number, because only a small number of symbols can be learned.

The most widely used number system is the Hindu-Arabic number system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."

Hence, The  boxes of chocolate should choco lovers produce= $11

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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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The match would be given as

[tex]\left[\begin{array}{ccc}18\\-24\\\end{array}\right]=[/tex][tex]A=3\left[\begin{array}{ccc}6\\-8\\\end{array}\right][/tex]  

[tex]\left[\begin{array}{ccc}-24\\36\\\end{array}\right]=[/tex][tex]D=3\left[\begin{array}{ccc}-8\\12\\\end{array}\right][/tex]

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are used extensively in various branches of mathematics such as linear algebra, calculus, and statistics, as well as in fields such as physics, engineering, and computer science.

1. [tex]A=3\left[\begin{array}{ccc}6\\-8\\\end{array}\right] =\\[/tex]

We are to multiply the values that are in the matrix by 3. This is a 1 x 2 matrix

3 * 6 = 18, 3 * -8 = -24

Hence we would have

[tex]\left[\begin{array}{ccc}18\\-24\\\end{array}\right][/tex]

2. [tex]D=3\left[\begin{array}{ccc}-8\\12\\\end{array}\right] =[/tex]

we will multiply as:

3 * -8 = -24

3 * 12 = 36

Hence [tex]\left[\begin{array}{ccc}-24\\36\\\end{array}\right][/tex]

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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:

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 length of the segment RK using the centroid theorem is: 10.2

The centroid is defined as the Centre point of the object. This is the point in which the three medians of the triangle intersect. It can also be defined as the point of intersection of all the three medians.

The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.

The parameter given is that:

D K = 3.4

Thus, by applying Centroid theorem, we have:

RD = 2(DK)

RD = 2 * 3.4

RD = 6.8

Thus:

RK = 6.8 + 3.4

RK = 10.2

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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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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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Alexa landed approximately 11.2 kilometers from the skydiving center. To find out how far from the skydiving center Alexa landed, we need to use some trigonometry.

Let's label the distance that Alexa traveled in the helicopter as "d" and the distance she fell from the helicopter as "x". We can see that the angle between the ground and the line connecting the skydiving center to Alexa's landing spot is 70°

70, degree, since the helicopter ascended at an angle of 20°

20 and the two angles add up to 90°

90.Now we can use the tangent function to find x. Tangent is defined as the opposite side (x) divided by the adjacent side (d), so we have:

[tex]tan(70^\circ) = \frac{x}{d}[/tex]

Solving for x, we get:

x = d * tan(70°)

We know that d = 3.43.43, point, 4 kilometers, so we can plug that in and calculate:

x = 3.43.43, point, 4 * tan(70°)

x ≈ 11.211.2 kilometers (rounded to one decimal place)

Therefore, Alexa landed approximately 11.2 kilometers from the skydiving center.

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Alexa's friends got her a skydiving lesson for her birthday. Her helicopter took off from the skydiving center, ascending in an angle of 20°

20, degree, and traveled a distance of 3.43.43, point, 4 kilometers before she fell in a straight line perpendicular to the ground.

How far from the skydiving center did Alexa land?

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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√87x = √(x * 87) = √(x * 3 * 29)

If x is a perfect square, say x = a^2, then we can rewrite the expression as:

√(a^2 * 3 * 29) = a√(3 * 29)

In this form, the expression is simplified further, because a is a constant and √(3 * 29) is a simplified radical.

The expression √87x cannot be further simplified because the square root and the variable are multiplied together. However, it is possible that the expression was meant to be written as √(87x) with the entire expression under the square root symbol. In this case, the expression can be further simplified by evaluating the square root of 87 times x, but the value of x is not relevant to this simplification.

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 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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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.

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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Answer:

area = 288.62 mm²

Step-by-step explanation:

To find the area we divide the complex shape into simple shapes whose areas we can find.

There is a rectangle in the center.

There are 2 congruent triangles on the sides.

We have the lengths of 2 perpendicular sides of the triangles, so they are the base and height.

For the rectangle, we only have the width. We need to find the length.

The length of the rectangle is the hypotenuse of the triangles.

We use the Pythagorean theorem to find the length of the hypotenuse of the right triangle. That is the length of the rectangle.

a² + b² = c²

(10.4 mm)² + (15.3 mm)² = c²

c² = 342.25 mm²

c = 18.5 mm

area = area of triangles + area of rectangle

area = 2 × (1/2)bh + LW

area = 2 × (1/2) × 15.3 mm × 10.4 mm + 18.5 mm × 7 mm

area = 159.12 mm² + 129.5 mm²

area = 288.62 mm²

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

There are three students in Mrs. Johansen's class who like sightseeing. We cannot estimate the total number of students in the class based solely on this information.

It is not possible to accurately predict the total number of students in Mrs. Johansen's class based on the information provided. However, we can make an estimate based on the assumption that the three students who responded to the survey are representative of the entire class.

It is impossible to create an accurate projection of the total number of pupils in Mrs. Johansen's class without knowing more about the survey or the class.

However, assuming that the survey was distributed to all students in the class, we may create an approximation based on the proportion of students who stated that their favourite holiday was sightseeing. For example, if we believe that the three students who stated that their favourite holiday was touring reflect 25% of the whole class (i.e., one-fourth of the class), we may estimate that the class has about 12 students.

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The given question is incomplete. the complete question is given below:

If three students in Mrs. Johansen's class said their favourite vacation was sightseeing, what is a reasonable estimate for the total number of students in her class based on this survey?