What is 43+5673+20(1)

₁₁C₈ * ₄C₃ as related to permutations is ₁₁P₈ / 8! * ₄P₃ / 3!

The term combination refers to a method of choosing where order does not matter. an instance forming 3 letter word from ABC. the combination is ₃C₃ = 1

In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6

All the items above are different permutations however for combination they are same.

The difference mathematically is dividing by the number of arrangements

₃C₃ = 3! / (3!(3-3)!) = 3! / (3!* 0!) = 3! / 3! = 1

₃P₃ = 3! / (3-3)! = 3! / (0!) = 3! / 1 = 3! = 6

Therefore ₃C₃ = ₃P₃ / 3!

similarly

₁₁C₈ * ₄C₃ = ₁₁P₈ / 8! * ₄P₃ / 3!

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The plan that fits to Landyn's budget is plan B

What is percentage and how to calculate it?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. Two methods exist for calculating a percentage. By adjusting the fraction's denominator to 100 and applying the unitary approach.

We are given that Landyn's current monthly net pay is $560

And he does not wish to spend more than 10% of his current net pay

That means not more that $56

Now we are given 3 choices

Out of which the third one is more than 60 hence this rules out the third option. Now the first option the value is 55+55(0.005) which again is more than $56

Consider the option B)

50 + 50(0.05)

= 52.5

Which is less than $56

Hence, The plan that fits to Landyn's budget is plan B

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The equation of the parabola exists y = 3/80(x - 20)² - 15

In the coordinate plane, a parabola exists algebraically represented using the standard equation. A parabola's general equation exists written as,

y = a(x - h)² + k

where (h, k) signifies the vertex.

y² = 4ax is the typical equation for a normal parabola.

substitute the values in the above equation, we get

y = a(x - 20)² - 15

simplifying the above equation, we get

0 = a(0 - 20)² - 15

0 = 400a - 15

a = 15/400

a = 3 / 80

Therefore, the equation of the parabola exists y = 3/80(x - 20)² - 15.

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Answer:

[tex]f^{-1}(x)=\dfrac{3-x}{5-x}, \quad \{x|x\neq 5\}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\dfrac{5x-3}{x-1}[/tex]

As the given function is a rational function, the domain and range are restricted.

f⁻¹(x) is the notation for the inverse of the function.  

The inverse of a function is a reflection in the line y = x.

To find the inverse of the given function, swap f(x) for y:

[tex]\implies y=\dfrac{5x-3}{x-1}[/tex]

Rearrange the equation to isolate x:

[tex]\implies y(x-1)=5x-3[/tex]

[tex]\implies xy-y=5x-3[/tex]

[tex]\implies 3-y=5x-xy[/tex]

[tex]\implies 3-y=x(5-y)[/tex]

[tex]\implies x=\dfrac{3-y}{5-y}[/tex]

Swap the x for f⁻¹(x) and the y for x:

[tex]\implies f^{-1}(x)=\dfrac{3-x}{5-x}[/tex]

The range of the function is the domain of the inverse function.

Therefore, the domain of the inverse function is restricted:

Answer:

need more information to answer

Answer:

3y+3y-12

Step-by-step explanation:

we can add the coefficients of y to make 6y-12

And that is equivalent

Hopes this helps please mark brainliest

Using the formula, the real of z is 2 and the linear form of z is [tex](x-2)(x^2+2x+4)[/tex].

In the given question,

The given expression is z=x^3−8

We can given expression as [tex]x^3-8=(x)^3-(2)^3[/tex]...............(1)

We have to find the real root of the z.

We also have to find the z as a product of linear terms.

To solve the given expression using the formula

[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

If we compare equation 1 to the [tex]a^3-b^3[/tex].

After compare we get a=x and b=2

Now the linear form of the given expression is

[tex]z=(x)^3-(2)^2[/tex]

[tex]z=(x-2)(x^2+2x+(2)^2)[/tex]

Simplifying

[tex]z=(x-2)(x^2+2x+4)[/tex]

Now the real root of of z;

x-2=0

x=2

Hence, the real of z is 2 and the linear form of z is [tex](x-2)(x^2+2x+4)[/tex].

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The probability of the event that the first song played by Alan is a rock song is 0.01.

The probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes. But the probability of an event say event "a" not occurring is 1 - a.

We shall calculate for the probability of the event that Alan's first song to be played is a rock song as follows:

probability of playing a rock song = 11/229

probability of not playing a Latin American song = 208/229

probability of not playing a gospel song = 183/229

probability of not playing a country song = 199/229

probability of not playing a rap song = 190/229

probability of not playing a classical song = 204/229

probability of not playing a pop song = 172/229

So,

The probability that the first song played is a rock song = (11/229) × (208/229) × (183/229) × (199/229) × (190/229) × (204/229) × (172/229)

The probability that the first song played is a rock song = 0.05 × 0.91 × 0.80 × 0.67 × 0.83 × 0.89 × 0.75

The probability that the first song played is a rock song = 0.01

Therefore the probability of the event that Alan's first song played is calculated to be 0.01 approximated to 2 decimal places.

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The picoseconds that are there in 6 minutes is 3.6 × 10^14.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

In this case, picosecond is one trillionth of a second. If one trillionth = 1 × 10^12

The seconds in 6 minutes will be:

= 60 × 6

= 360 seconds

= 3.6 × 10^2

The picoseconds in 6 minutes will be:

= 1 × 10^12 × 3.6 × 10^2

= 3.6 × 10^14

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Answer:

0.1364 miles per minute

Step-by-step explanation:

time = pace × distance

time = pace time per unit distance × distance

distance = time / pace

distance = time / pace time per unit distance

pace = time / distance

pace time per unit distance = time / distance

speed = distance / time

speed distance per unit time = distance / time

Answer:

x = 15

Step-by-step explanation:

since the sides are bisected, the inner line is parallel to the largest side.

8x+9 + 5x-24 = 180

In total there will be 397 dots after 100 minutes.

What do you mean by airthmetic sequences?

Arithmetic sequences are sequences of the form:

a, a+d, a+2d, a+3d, a+4d, …

a is the first term and d is the common difference

series. The n terms of the arithmetic progression are given by

[tex]a_{n}[/tex]  = a + (n - 1)d

The number d is called the common difference

Arithmetic progressions differ by d and any terms [tex]a_{n}[/tex] and [tex]a_{n-1}[/tex]

d = [tex]a_{n}-a_{n-1}[/tex] -  

According to the given pattern, in the first figure, number of dots is 1 , in the second figure, number of dots become 5 , similarly in the next the count is 9 and 14

So, the sequence become

1,5,9,14......

here first term , a = 1

common difference , d = 5-1 = 4

We need to find the number of dots after 100 minutes

So, here n = 100

We need to find [tex]a_{100}[/tex]

[tex]a_{100}[/tex] = a + (100 - 1) d = 1 + 99(4) = 1 + 396 = 397

Therefore, in total there will be 397 dots after 100 minutes.

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The missing x and y values in the ordered pair of the equation are:

x = 1

y = -4

Given the ordered pair (x, y) of an equation, y = mx + b, we can find their values by plugging in the given value of either of the x or y coordinates to find the other coordinate value.

The ordered pairs of y = -2x + 4 are given as:

(4, y) and (x, 2)

To find the value of y, substitute x = 4 into the equation y = -2x + 4:

y = -2(4) + 4

y = -8 + 4

y = -4

The value of y is -4.

To find the value of x, substitute y = 2 into the equation y = -2x + 4:

2 = -2x + 4

2 - 4 = -2x

-2 = -2x

-2/-2 = x

1 = x

x = 1

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Answer:

-4

Step-by-step explanation:

When answering questions like these first, combine like terms you get 3x+5 =3x+8, Subtract 5 from both of the sides you get 3x=3x+3 remove 3x from both sides and you got 0=3 this is a contradicting statement meaning no solution ∅

B) Distribute first, 3x + 2 -x  = x + 3 + 3x +4

2, Combine the like terms 2x - 1 = 7 + 4x

3, Isolate variable and constants 2x = 8 + 4x

3(1) Cont- Isolation -2x = 8

Thus divide both side by -2 giving us -4

The percentages, using the Empirical Rule, are given as follows:

a) Between 106 and 124: 32%.

b) Between 88 and 160: 95%.

c) Between 70 and 124: 49.85%.

d) Above 160: 2.5%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The mean and the standard deviation in this problem are given as follows:

Considering the symmetry of the normal distribution, to facilitate the calculations, we have that:

160 is two standard deviations above the mean, hence the percentage above it is of:

2.5%.

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The value of y is - 0.326 when x = 7.

A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is typically expressed as x: y or x/y, although it may alternatively be read as x is to y.

Comparatively speaking, a proportional equation states that two ratios are comparable. A ratio is expressed as x: y: : z: w and is understood to mean that x is to y as z is to w. Here, w and y are not equal to 0, therefore x/y Equals z/w.

A connection between two quantities is said to be in inverse proportion if one quantity rises while the other falls, and vice versa. As a result, an inverse ratio is expressed as y ∝ 1/x.

The general equation of proportion is given by

y = k/x²

-4 = k/(-2)²

k = -4(4)=-16

y = -16/x²

When x=7, then

y= -16/49

y= - 0.326

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Answer:

b

Step-by-step explanation:

because you solve it and you get B

As per the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .

As given in the question,

Number of stacks of program to be divided = 1

Number of friends = 3

Number of people among whom stack of program is to be divided = 4

Let us consider stack of program divided equally

Fraction of stack of program each friend will get = 1 /4

As

( 1 / 4 ) +  ( 1 / 4 ) + ( 1 / 4 ) + ( 1 / 4 )

= ( 1+ 1+ 1+ 1) / 4

= 4/4

= 1

Therefore, for the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .

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Annual rate of return earned when the share was sold at $50 per share is 20%

Annual rate of return earned when the share was sold at $60 per share is 40%

Annual rate of return is given by the formula

let end of the year price = eyp

let beginning of the year price = byp

= {(eyp - byp) / byp} * 100

Annual rate of return at share price of $50 per share

when there is paying of dividends the value is added to the the eyp

eyp =  50 * 100 + 2 * 100 * 5 = 6000

byp = 50 * 100 = 5000

= {(6000 - 5000) / 5000} * 100

= 20%

Annual rate of return at share price of $60 per share

eyp =  60 * 100 + 2 * 100 * 5 = 7000

byp = 50 * 100 = 5000

= {(7000 - 5000) / 5000} * 100

= 40%

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84 i think?

im not sure if i did my math properly

Answer:

80

Step-by-step explanation:

40 ÷ 6 = 6.66666667 x 12 = 80

The distance between the two point of the line segment is 26.07

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates

d = √((x₂ – x₁)² + (y₂ – y₁)²

Substituting the values into the equation;

d = 2√170 = 26.07.

Kindly find the attached graph of the two points.

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Answer:

64

Step-by-step explanation:

8(x+2) when x=6

replace x with 6

8(6+2)

distribute 8

48+16= 64

For given equation y = ln(3 - 4 cos(x))​,

dy/dx =  4sin(x) / (3 - 4 cos(x))

In this question, we have been given an equation y = ln(3 - 4 cos(x))​

We need to differentiate y = ln(3-4cosx)​

dy/dx

= d/dx(ln(3 - 4 cos(x))​)

= 1/(3 - 4 cos(x))​ * d/dx(3 - 4cos(x))               .......(by Chain rule)

= 1/(3 - 4 cos(x))​ * [4 sin(x)]

= 4sin(x) / (3 - 4cos(x))

Therefore, for given equation y = ln(3 - 4 cos(x))​,

dy/dx =  4sin(x) / (3 - 4 cos(x))

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Answer:

Step-by-step explanation:

1 and 2 are supplementary angles and hence sum to 180°.

For the given roots and point, the polynomial is:

p(x) = (62/72)*(x + 3)²*(x - 2)²*(x + 2)

We know that a polynomial with leading coefficient a and the roots:

x₁, x₂, ..., xₙ

Can be written as:

p(x) = a*(x - x₁)*...*(x - xₙ)

Here we have the roots:

-3, -3, 2, 2, -2

Then we can write:

p(x) = a*(x + 3)*(x + 3)*(x - 2)*(x - 2)*(x + 2)

p(x) = a*(x + 3)²*(x - 2)²*(x + 2)

Now we also know that our polynomial passes through (0, 62), then:

p(0) = 62 = a*(0 + 3)²*( 0 -2)²*(0 + 2)

62 = a*9*4*2

62/(9*4*2) = a

62/72

then the polynomial is:

p(x) = (62/72)*(x + 3)²*(x - 2)²*(x + 2)

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Answer:

a = -10

So your answer is a = -10, I hope this helps!

Step-by-step explanation:

a + (-7) is the same as a - 7, so you could rewrite it as

a - 7 = -17

+ 7

If the value of R² in the regression equation is 0.810, the value of R is 0.9

From the question, we have the following parameters that can be used in our computation:

Regression equation: y = -2.6x + 10

Value of R2 = 0.810

Rewrite the above parameters properly

So, we have the following representation

y = -2.6x + 10

R² = 0.810

The variable r² represents the coefficient of determination

Recall that

R² = 0.810

This gives

r² = 0.810

Take the square roots of both sides

r = 0.9

Hence, the value of r is 0.9

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