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Answer:

For Q.1, the answer is 9

Step-by-step explanation:

The volume formula for a cylinder is V=πhr^2. The volume formula for a cone is V=(πhr^2)/3. You might notice that the formulas are very similar; the only difference is the divided by three at the end. Because we are going from cylinder to cone, we have to multiply by three instead of dividing. Doing this, we get 3*3=9.

Try solving the rest of the problems using these two formulas by yourself. :)

Therefore after using the Pythagorean Theorem and the properties of chords in a circle we got 626 when m+n is divided by 1000.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.

Let M and N be the midpoints of chords AB and CD, respectively.

Let X and Y be the foot of the perpendicular from P to chord AB and CD respectively.

Since X,Y are on the circle and P is the midpoint of XY,

OP = PX = PY = radius = 25

Now, using the Distance Formula:

(XM)^2 + (YN)^2 = (12)^2

By the Pythagorean Theorem, on triangle PXN and PYM,

(25)^2 + (YN)^2 = (PN)^2 = (14/2)^2 and

(25)^2 + (XM)^2 = (PX)^2 = (30/2)^2

OP^2 = 625 = 25^2

thus m+n = 625 + 1 = 626

and remainder when m+n is divided by 1000 is 626 % 1000 = 626

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From the given data, the first and third graph are correct.

1. For the first graph,

the two equation are -

y = -2x - 4

-4x + y = 2

Let us check the common points for the given graph,

(-1,-2)                                            

y = -2x - 4                              - 4x + y = 2

-2 = -2(-1) - 4                           -4(-1) + (-2) = 2

-2 = -2                                       2 = 2

Hence it is correct.

2. For the second graph,

y = -3/2x - 2

y = -1/4x + 3

Common points are - (4,4)

y = -3/2x - 2                               y = -1/4x + 3

4 ≠ -8                                          4 ≠ 2

Hence it is not correct.

3. For the third graph,

y = -5

y = 3x + 1

Common points are - (-2,-5)

y = 3x + 1

-5 = -5

Hence it is correct.

The correct graph for 2, graph is below,

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x + 2y = 3x + 4

2y = 3x + 4 - x

y = (2x + 4)/2

y = x + 2

Answer: y=x+2

Step-by-step explanation:

you subtract x on the left on both sides then you'll have 2y=2x+4 we have to get y by itself so divide it by 2 on both side and when you do that on the right you divide both 2x and 4 by 2 thus giving y=x+2

On solving the provided question we can say that It is isosceles triangle the value of QR is 1.3

Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal. An isosceles triangle is one that has two equal-length sides in geometry. With the latter specification, the equilateral triangle is included as a special case even though it is commonly stipulated that it must have at least two sides of equal length.

It is isosceles triangle so, that

ratio of QT/QR = ET/RS

4.7/X = 4.7/1.3

X = 1.3

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The sum of the first 11 terms of the geometric sequence aₙ = 2aⁿ - 1 with an initial value of a₁ = 1/8 is -10.71.

Therefore the answer is -10.71.

The geometric sequence aₙ = 2aⁿ - 1 with an initial value of a₁ = 1/8 represents the amount of money saved after n years of investing.

So sum of n terms

Sn = 2a - 1 + 2a² - 1 + ... + 2aⁿ - 1

Sn = 2( a + a² + ... + aⁿ) - n

The sum of the first n terms of a geometric sequence aₙ = arⁿ⁻¹ with first term a₁ and common ratio r is given by the formula:

Sn = a₁(1 - rⁿ)/ (1 - r), that is

[tex]S_{n} = a_{1}\frac{ (1 - r^n)}{1 - r}[/tex]

So a + a² + ... + aⁿ = a(1 - aⁿ)/ (1 - a)

Thus Sn = 2( a + a² + ... + aⁿ) - n

Sn = 2a(1 - aⁿ)/ (1 - a) - n

In this case, a₁ = a = 1/8 and n = 11

So the sum of the first 11 terms of the geometric sequence is:

Sn = 2×1/8×( 1 - (1/8)¹¹)/ (1 - 1/8) - 11

Sn = -10.71

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In mathematics, the symbol " σ" is "σ" (sigma) which is commonly used to represent the sum of a set of values.

It is used to indicate that a series of values are to be added together. For example, the notation "Σx" is read as "the sum of x" and it means to add all values of x together. It is often used in mathematical analysis, statistics, and physics.

For instance, in statistics, the symbol "σ" is used to represent population standard deviation, which is a measure of the dispersion of a set of data points from the mean.

In probability theory, the symbol "σ" is also used to represent the standard deviation of a random variable.

In general, the specific meaning of the symbol "σ" depends on the context in which it is used.

It is also known as Summation notation.

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The third term of the arithmetic sequence will be negative 14.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The first term is 20 and the common difference is calculated as,

aₙ = aₙ₋₁ - 17

aₙ - aₙ₋₁ = - 17

d = - 17

Then the third term is calculated as,

a₃ = 20 + (3 - 1) (-17)

a₃ = 20 + 2 (-17)

a₃ = 20 - 34

a₃ = - 14

The third term of the arithmetic sequence will be negative 14.

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Answer:

Step-by-step explanation:

55 times 25, making Angel attempt 1375 free throws

Answer:

Step-by-step explanation:

To translate a triangle with vector (-5/2), you need to subtract 5/2 from the x-coordinate and add 2 to the y-coordinate of each vertex of the triangle. This will move the triangle 5 units to the right and 2 units up.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

To translate a triangle with a vector, you can use the vector to adjust the coordinates of the triangle's vertices.

For example, if the triangle has vertices at (x1, y1), (x2, y2), and (x3, y3), you can translate it by the vector (-5/2) by subtracting 5/2 to the x-coordinates of the vertices. The new coordinates of the translated triangle would be (x1-5/2, y1), (x2-5/2, y2), and (x3-5/2, y3).

This will move the triangle 5/2 units to the left along the x-axis.

It is important to note that the translation vector you provided only has one component, which is -5/2. Since the vector only has x component, the translation will only occur along the x-axis and the y-coordinate of the vertices will not change.

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The inequality is solved as x < 5 and it is plotted on the number line.

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The given inequality is −8 + x < −3.

It can be solved as follows,

⇒ −8 + x < −3

Add 8 both sides as,

⇒ 8 + −8 + x < −3 + 8

⇒ x < 5

It can be plotted on the number line as follows,

Hence, the solution is given as x < 5 and it is represented on the number line with clarity.

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The common factors and the greatest common integer for each pair of numbers are:

               Common prime factors        Greatest common factor

30, 45        3 and 5                                     5

40, 70         2 and 5                                    5

63, 42         3 and 7                                     7

81, 54          3                                               3

33, 99         3 and 11                                    11

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

30 and 45

3 x  5 x 2 = 30

3 x 3 x 5 = 45

Common prime factors = 3 and 5

Greatest common factor = 5

40 and 70

2 x 5 x 4 = 40

2 x 7 x 5 = 70

Common prime factors = 2 and 5

Greatest common factor = 5

63 and 42

3 x 3 x 7 = 63

2 x 3 x 7 = 42

Common prime factors = 3 and 7

Greatest common factor = 7

81 and 54

3 x 3 x 3 x 3 = 81

2 x 3 x 3 x 3 = 54

Common prime factors = 3

Greatest common factor = 3

33 and 99

3 x 11 = 33

3 x 3 x 11 = 99

Common prime factors = 3 and 11

Greatest common factor = 11

Thus,

Common prime factors are given above.

The greatest common factor is given above.

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The complex numbers are solved using De Moivre's Theorem and then are matched with their respective solutions.

What is De Moivre's Theorem?

De Moivre's formula, also known as the theorem and identity of de Moivre, says that for any real number x and integer n, holds -

(cos x + i sin x)^n=cos nx + i sin nx

where i is the imaginary unit (i^2 = 1).

Also, [r(cos x + i sin x)]^n = r^n(cos nx + i sin nx) or [r cis x]^n = [r^n cis nx].

The first complex number is (1+i)^5.

Solve using De Moivre's formula -

(1+i)^5 = [√2{(1/√2)+(i/√2)}^5]

=(√2)^5[cos(π/4)+i sin(π/4)]^5

=(√2)^5[cos(5π/4)+i sin(5π/4)]

=(√2)^5[(-1/√2)-(i/√2)]

=4(-1-i)

=-4-4i

The second complex number is (-1+i)^6.

Solve using De Moivre's formula -

(-1+i)^6=(1-i)^6

=[√2{(1/√2)-(i/√2)}^6]

=(√2)^6[cos(-π/4)+i sin(-π/4)]^6

=(√2)^6[cos(-6π/4)+i sin(-6π/4)]

=8(0+1i)

=8i

The third complex number is 2[cos(20)+i sin(20)]^3.

Solve using De Moivre's formula -

2[cos(20)+i sin(20)]^3=2^3[cos(60)+i sin(60)]

=8[(1/2)+{(√3)i/2}]

=4+4√3i

The last complex number is 2[cos(π/4)+i sin(π/4)]^4.

Solve using De Moivre's formula -

2[cos(π/4)+i sin(π/4)]^4=2^4[cos(4π/4)+i sin(4π/4)]

=16[cos(π)+i sin(π)]

=16(-1+i(0)]

=-16

Therefore, the complex numbers are solved using the theorem.

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Answer:

x = 2/3

Step-by-step explanation:

x - 5(x - 1) = x - (2x - 3)

x - 5x + 5 = x - 2x + 3

-5x + 5 = -2x + 3

-3x = -2

x = 2/3

The relationship between the natural logarithm (ln) and the natural exponential (e) is given by the equation ln(x) = e^x. This equation is known as the exponential form of the natural logarithm.

To explain this relationship, let's start with a simple example. Suppose we have a number x, and we want to find its natural logarithm. To do this, we can use the following equation:

ln(x) = e^x

This equation states that the natural logarithm of x is equal to the natural exponential of x. In other words, we can calculate the natural logarithm of x by raising e to the power of x. To illustrate this with an example, suppose we want to calculate the natural logarithm of 10. We can do this using the equation above as follows:

ln(10) = e^10

Now, we can use a calculator to calculate e^10. If we do this, we get the result of 22,366.48. Therefore, the natural logarithm of 10 is equal to 22,366.48.

The relationship between the natural logarithm and the natural exponential is important because it allows us to easily calculate the natural logarithm of any number. All we have to do is raise e to the power of that number, and the result will be the natural logarithm of that number. This is a very useful tool in mathematics and can be used to solve many problems involving logarithms.

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Therefore , the solution to the given problem of scatter plot comes out to be the data correctly represented as 0 has 8 dots, 1 has 3 dots, 2 has 3 dots, 3 has 5 dots, 4 has 0 dots, and 5 has 1 dot

Several dots are arranged along a vertical and horizontal axis to form a scatter plot. Because they can demonstrate the strength of the relationship, if any, between the two observed quantities or occurrences, scatter plots are crucial in statistics (called variables).

Here,

Given :  the number of coupons redeemed by the last 20 shoppers

and

center dot plot is 1

thus,

No one redeemed  each 4 coupons

So, In order to find the which plot displays data correctly

We get,

0 has 8 dots, 1 has 3 dots, 2 has 3 dots, 3 has 5 dots, 4 has 0 dots, and 5 has 1 dot

which represents the data correctly

Therefore , the solution to the given problem of scatter plot comes out to be the data correctly represented as 0 has 8 dots, 1 has 3 dots, 2 has 3 dots, 3 has 5 dots, 4 has 0 dots, and 5 has 1 dot

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Answer:

To construct a 98% confidence interval with a maximum error of 0.09 pounds and assuming a variance of 1 pound, the minimum sample size can be calculated using the formula:

n = (2 * standard error of the mean / margin of error)^2

Plugging in the values, we get:

n = (2 * (1 / sqrt(n)) / 0.09)^2

Solving for n, we get n = 832.6. Rounding up to the next integer, the minimum number of males over age 27 they must include in their sample is 833.

Step-by-step explanation:

Therefore , the solution of the given problem of ratio comes out to be

lim C(p) as p->19 = 152900.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Here,

a) To find the cost of removing 90% of the impurities, we can substitute 90 for p in the equation:

C(p) = 8100p / (100-p)

C(90) = 8100(90) / (100-90)

C(90) = 729000

So the cost of removing 90% of the impurities is Rs. 729000.

b) To find the limit of C(p) as p approaches 19, we can substitute 19 for p in the equation:

lim C(p) as p->19 = 8100(19) / (100-19)

lim C(p) as p->19 = 152900

The value of the limit of C(p) as p approaches 19 means that as the percentage of impurities approaches 19, the cost of purification approaches Rs. 152900.

c) It is not possible to purify completely as the percentage of impurities approaches 100. It's because as the percentage of impurities becomes closer to 100, the denominator of the fraction becomes smaller, thus the value of the cost of purification becomes larger, and it is impossible to pay an infinite amount of money.

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There are 8+9+10=27 equal parts, so Ben has 1/3 of the total amount of money.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.

For n/(8+9+10), where n is an integer <27

 Ali : Ben : Cathy

   8 : 9 : 10

Thus, there are 8+9+10=27 equal parts, so Ben has 1/3 of the total amount of money.

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The Equation of line F is y= -9/2x  + 59/2.

The Equation of line G  is y = 1/10 x .

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

For Line F:

slope = -9 /2

and, Equation of line F as

y - (-2) = -9/2 (x -(7))

y + 2= -9/2( x- 7)

y = -9/2x + 63/2 -2

y= -9/2x  + 59/2

For Line G:

Slope = (0 -(1))/ ( 0-(10))

slope = 1/10

and, Equation of line G as

y - (1) = 1/10 (x -10)

y-1 = 1/10 x - 1

y = 1/10 x

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On solving the provided question, we can say that vectors are -  4 miles E: <4, 0>; 4 miles SE: <2√2, -2√2>; 7 miles S: <0, -7>; 6 miles SW: <-3√2, -3√2>; 2 miles E: <2, 0>

In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow. Size and direction are two independent characteristics of a quantity or phenomena known as a vector. The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.

4 + 4 + 7 + 6 + 2 = 23 miles.

vectors are -

4 miles E: <4, 0>

4 miles SE: <2√2, -2√2>

7 miles S: <0, -7>

6 miles SW: <-3√2, -3√2>

2 miles E: <2, 0>

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Answer:

120 km/h

Step-by-step explanation:

average speed=total distance÷time

=1080÷9

=120 km/h

The explicit formula for an arithmetic sequence whose common difference is 8 and the first term is -2 is

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

The sequence is given by the formula

nth term = a + (n - 1) * d

where a = first term

n = the term

d = common difference

In the problem, d = -2 and a = 8, because of this we have

= a + (n - 1) * d

= 8 + (n - 1) * -2

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40% of Damien’s marbles are 6/5 or 1.2.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Damien has three marbles.

40% of Damien’s marbles are blue.

That means,

40% of 3 blue marbles.

So, using the percentage formula,

40% of 3,

= 40 x 3/100

= 120/100

= 12/10

= 6/5

= 1.2

Therefore, 1.2 marbles are blue.

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The way to find the horizontal asymptote of the limit is evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.

The term asymptote in math is defined as  a line that the graph of a function approaches as either x or y go to positive or negative infinity.

Here we have to find the horizontal asymptote of a limit.

The process of finding the horizontal asymptote is the line y = 0 is called the asymptote of the graph, and it also represents the value that f(x) will never quite reach.

Here we can also say that f ( x ) = 1 x is asymptotic to the line y = 0.

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Answer:

<1=75°[corresponding angles are equal]

<2=180-<1=(180-75)°=105°[sum of st.angles is supplementary]

<3=<2=105°[Vertically opposite angles are equal]

<4=75°[Alternate angles are equal]

<6=<2=105°[Corresponding angles are equal]

<7=<6=105°[Vertically opposite angles are equal]

<8=75°[Vertically opposite angles are equal]

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The probability of h that can be found using the discrete model but not the normal model is 0.03.

A discrete probability distribution or DPD (also known as a discrete probability model) records all possible values of a discrete random variable and gives their probabilities.

The normal probability model involves when the distribution of the continuous outcome conforms reasonably well to a normal or Gaussian distribution, which resembles a bell-shaped curve.

H represents the height of women

Determine P ( H < 60 ) using either a discrete or normal model

using discrete model

P ( H < 60 ) = ∑ relative frequencies of the women with height < 60 inches

P ( H < 60 ) = 0.01 + 0.02 = 0.03

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Different types of algorithms are:

As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search—also referred to as generate and test—involves iteratively listing all potential candidates for the solution and determining whether each one satisfies the problem's statement.

A brute-force algorithm would count all integers from 1 to n and determine whether each one divides n without a remainder in order to find the divisors of a natural number n.

For the eight queens puzzle, a brute force method would look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece could engage in mutually exclusive attacks for each configuration.

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Answer:

[tex] \sf \: (-3) × {( - 3)}^{2} = - 27[/tex]

Step-by-step explanation:

Given expression,

→ (-3) × (-3)²

Let's simplify the expression,

→ (-3) × (-3)²

→ (-3) × ((-3) × (-3))

→ (-3) × 9

→ (-3 × 9) = -27

Hence, the answer is -27.

The system of equations -3x + y = 4 and -9x + 5y = -1 has the solution (-3.5 , -6.5).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations. This is what is called as the solution.

Given two equations in x and y,

-3x + y = 4     (equation 1)

-9x + 5y = -1     (equation 2)

Rewrite equation 1 as an equation of y and substitute to equation 2.

(equation 1) -3x + y = 4     ⇒     y = 3x + 4

-9x + 5y = -1     (equation 2)

-9x + 5(3x + 4) = -1

-9x + 15x + 20 = -1

6x = -21

x = -3.5

Substitute the value of x in equation of y and solve for y.

y = 3x + 4

y = 3(-3.5) + 4

y = -6.5

Hence, the solution to the following system of equations is (-3.5 , -6.5).

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Answer:

(-3.5 , -6.5)

Step-by-step explanation: