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3 years ago

Is the binomial theorem and pascal's formula the same?

1 answer:

3 0

They are closely related. The Binomial Theorem expands (a+b)ⁿ as the sum of a series of terms involving progressive powers of a and b with a coefficient based entirely on the exponent n. Coefficients of consecutive terms in the series are the same as the nth rows of Pascal’s Triangle. This means that the formula used for calculating the coefficients in the Binomial expansion is the same one used to calculate the numbers in the corresponding row of Pascal’s Triangle. The nomenclature ⁿcᵣ for the number of ways of combining r objects out of n objects invokes this formula.

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Determine the mean for: 57 59 60 58 58 56

Maurinko [17]

I think the answer is 69.6

3 0

3 years ago

3. Solve the equation using square roots. If the equation has no real solution, write

noname [10]

3) x² - 121 = 0

x² = 121

x' = +√121

x' = 11

_______________

x'' = - √121

x'' = -11

Solution ⇒ S{-11 ; 11 } or (x-11)(x+11)

4) 4x² + 144 = 0

4x² = -144

x² = -144 / 4

x² = -36

x = √-36

No solution ⇒ S = ∅

5) z²+10z+21 = 0

Δ = 10² - 4(1)(21)

Δ = 100 - 84

Δ = 16

x' = (-10+4) / 2 = -6/2 = -3

x'' = (-10-4) / 2 = -14/2 = -7

Solution ⇒ S{ -7 ; -3} or (x+3)(x+7)

4 0

3 years ago

Jack and Andrea want to create a right triangle together using values of x and y and the polynomial identity to generate Pythago

leva [86]

A right triangle can be considered as a special type because the relationship of its sides can be described using the hypotenuse formula:

c^2 = a^2 + b^2

c^2 = x^2 + y^2

where,

c is the hypotenuse of the triangle and is the side opposite to the 90° angle

while a and b are the sides adjacent to the 90° angle

In the problem statement, we are given that one of the side has a measure of 2 = x, while the hypotenuse is 5 = c, therefore calculating for y:

y^2 = c^2 – x^2

y^2 = 5^2 – 2^2

y^2 = 21

y = 4.58

The natural number is the number before the decimal. Therefore the answer is:

y = 4

6 0

2 years ago

Read 2 more answers

A dog runs 100 meters in 30 seconds. How fast is he running

matrenka [14]

Answer:

3.33 m/s

Step-by-step explanation:

Distance divided by time = speed

100/30 = 3.33 m/s

6 0

2 years ago

Rework problem 35 from the Chapter 2 review exercises in your text, involving auditioning for a play. For this problem, assume 9

sweet-ann [11.9K]

Answer: 1) 6300 ways

2) 2520 ways

3) 0.067

Step-by-step explanation:

For this problem, assume 9 males audition, one of them being Winston, 5 females audition, one of them being Julia, and 6 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

How many different ways can these roles be filled from these auditioners?

Available: 9M and 5F and 6C

Cast: 3M and 1F and 2C

As it is not ordered: C₉,₃ * C₅,₁ * C₆,₂

C₉,₃ = 9!/3!.6! = 84

C₅,₁ = 5!/1!.4! = 5

C₆,₂ = 6!/2!.4! = 15

C₉,₃ * C₅,₁ * C₆,₂ = 84.5.15 = 6300

How many different ways can these roles be filled if exactly one of Winston and Julia gets a part?

2 options Winston gets or Julia gets it:

1) Winston gets it but Julia no:

8 male for 2 spots

4 females for 1 spot

6 children for 2 spots

C₈,₂ * C₄,₁ * C₆,₂

C₈,₂ = = 8!/2!.6! = 28

C₄,₁ = 4!/1!.3! = 4

C₆,₂ = 6!/2!.4! = 15

C₈,₂ * C₄,₁ * C₆,₂ = 28.4.15 = 1680

2) Julia gets it but Winston does not

8 male for 3 spots

1 female for 1 spot

6 children for 2 spots

C₈,₃ * C₆,₂

C₈,₃ = 8!/3!.5! = 56

C₆,₂ = 6!/2!.4! = 15

C₉,₃ * C₆,₂ = 56.15 = 840

1) or 2) = 1) + 2) = 1680 + 840 = 2520

What is the probability (if the roles are filled at random) of both Winston and Julia getting a part?

8 male for 2 spots

1 female for 1 spot

6 children for 2 spots

C₈,₂ * C₆,₂

C₈,₂ = = 8!/2!.6! = 28

C₆,₂ = 6!/2!.4! = 15

C₈,₂ * C₆,₂ = 28.15 = 420

p = 420/6300 = 0.067

6 0

3 years ago