b)
What is the Lowest Common Multiple of 42 and 90?

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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Answer: 1/8

Step-by-step explanation: To calculate the probability, we first need to add up the total amount of CDs. 10+6+4+12 = 32. After this, we divide 4 by 32, getting 4/32 which can be simplified to 1/8

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 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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The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.

The hypotenuse of a 45 45 90 triangle is calculated as the square root of the length of the leg.

We plug the known length of the leg into our 45-45-90 theorem formula:

          Hypotenuse = leg * (√2)

Properties of 45-45-90 triangles :

To point out the 45-45-90 special right triangle, check for these three identifying properties:

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A simulation game attempts to copy various activities from real life in the form of a game for various purposes such as training, analysis, prediction, or entertainment.

The most suspicious set of outcomes for a simulated game of chess that is supposed to be biased in favor of player B winning 4 out of 5 times would be if player B won all 30 games. This outcome would be highly unlikely if the game was truly random and the bias towards player B was accurate. Other suspicious outcomes could include player B winning 29 out of 30 games or player B winning 28 out of 30 games with a high margin of victory in each game.

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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. :)

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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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:

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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Answer:

120 km/h

Step-by-step explanation:

average speed=total distance÷time

=1080÷9

=120 km/h

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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A unit for each quantity in the worksheet for the mat width are 5.357 inches.

The size of a rectangle. A = l × b. Once the length and width are known for any rectangle, the area may be determined. The area of the rectangle is calculated as a square-unit dimension by multiplying length and width.

Add the height and the width together to get the area of a rectangle. Given that each side of a square is the same length, all you need to do to determine its area is multiply the length of one of its sides by itself.

Length = 7 inches  

Width = 6 inches

Area of photograph = length  width = 7  6 = 42

Total area of photograph and frame = 84

frame length ( 7 + 2x)

frame width ( 6 + 2x)

Total area = Total area of photograph and frame

( 7 + 2x)  ( 6 + 2x) = 84

2 + 13x - 21 = 0

x = 5. 357

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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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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

Answer: x = 14

Step-by-step explanation:

    For points A, B, and C to be collinear, angle ABD and EBC must be vertical angles. Vertical angles are congruent so we will set them equal to each other and solve for x.

    Given:

126 = 9x

    Divide both sides of the equation by 9:

14 = x

    Reflexive property:

x = 14

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.

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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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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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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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:

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 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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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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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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Answer:

- ANTIFRAGILE -

Anti-ti-ti-ti fragile, fragile

Anti-ti-ti-ti fragile

Anti-ti-ti-ti fragile, fragile

(Anti-fragile)

(Anti-fragile)

가시밭길 위로 riding, you made me boost up (ah-ah-ah-ah)

거짓으로 가득 찬 party 가렵지도 않아

내 뒤에 말들이 많아, 나도 첨 듣는 내 rival

모두 기도해 내 falling 그 손 위로 I'ma jump in

Yes, gimme that

걸어봐 위엄 like a lion

눈빛엔 거대한 desire (nan-na-na-eh)

더 부어 gasoline on fire

불길 속에 다시 날아 rising (nan-na-na-eh)

잊지 마, 내가 두고 온 toe shoes

무슨 말이 더 필요해?

무시 마, 내가 걸어온 커리어

I go to ride 'til I die, die

더 높이 가줄게

내가 바랐던 세계 젤 위에 (ah-ah)

떨어져도 돼

I'm anti-fragile, anti-fragile (ah-ah)

난 지금 on my way

갖다버려 줘 너의 fairy tale (ah-ah)

Now you know my name

I'm anti-fragile, anti-fragile

Anti-ti-ti-ti fragile, fragile

Anti-ti-ti-ti fragile

Anti-ti-ti-ti fragile, fragile

(Anti-fragile)

(Anti-fragile)

Lovey, lovey, lovey

Dovey, dovey, dovey

멋대로 정하네 나란 애에 대해

I don't know what to say, I can't feel it

뜨거운 관심은 환영, 귀여운 질투는 go ahead

줄 달린 인형은 no thanks 내 미랠 쓸 나의 노래

Yeah, gimme that

걸어봐 위엄 like a lion

눈빛엔 거대한 desire (nan-na-na-eh)

더 부어 gasoline on fire

불길 속에 다시 날아 rising (nan-na-na-eh)

잊지 마, 내가 두고 온 toe shoes

무슨 말이 더 필요해?

무시 마, 내가 걸어온 커리어

I go to ride 'til I die, die

더 높이 가줄게

내가 바랐던 세계 젤 위에 (ah-ah)

떨어져도 돼

I'm anti-fragile, anti-fragile (ah-ah)

난 지금 on my way

갖다버려 줘 너의 fairy tale (ah-ah)

Now you know my name

I'm anti-fragile, anti-fragile

Anti-ti-ti-ti fragile, fragile

Anti-ti-ti-ti fragile

Anti-ti-ti-ti fragile, fragile

(Anti-fragile)

(Anti-fragile)

We can break it baby

Rock it, twist it, lock it baby

All I know is you can't chain me

'Cause I'm gonna break out

Gonna, gonna break out, out

We can break it baby

Rock it, twist it, lock it baby

All I know is you can't chain me

'Cause I'm gonna break out

Gonna, gonna break out, out (whoa-uh-oh-oh!)

더 높이 가줄게

내가 바랐던 세계 젤 위에 (ah-ah)

떨어져도 돼

I'm anti-fragile, anti-fragile (ah-ah)

난 지금 on my way

갖다버려 줘 너의 fairy tale (ah-ah)

Now you know my name

I'm anti-fragile, anti-fragile

Anti-ti-ti-ti fragile, fragile

Anti-ti-ti-ti fragile

Anti-ti-ti-ti fragile, fragile

(Anti-fragile)

(Anti-fragile)

- song by Le Sserafim

- song title : anti fragile

- stan Le Ssefarim for a better life <3

xoxo

Step-by-step explanation:

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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