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Softa [21]
3 years ago
13

Recall that the product (a + b)(a - b) is the

Mathematics
2 answers:
Aleks [24]3 years ago
8 0

Answer:

The third option (9+3\sqrt{7}-3\sqrt{7}-\sqrt{49})

Step-by-step explanation:

With FOIL, this can be expanded. (a+b)(a-b) is equal to a²+ab-ab-b² or a²-b².

In this case, all the answers have 4 terms, so we want the first option. This makes the equation 3²+(3×\sqrt{7})-(3×\sqrt{7})-(\sqrt{7})².

Solving these gives 9+3\sqrt{7}-3\sqrt{7}-7. This is the same as  9+3\sqrt{7}-3\sqrt{7}-\sqrt{49}.

**This content involves multiplying with surds and expanding perfect squares, which you may wish to revise. I'm always happy to help!

igor_vitrenko [27]3 years ago
8 0

Answer:

D

Step-by-step explanation:

Edge 2021

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A glass is
fenix001 [56]

Step-by-step explanation:

x=volume of the glass

(1/3)x+63=(5/8)x

63=(5/8)x-(1/3)x

63=(15/24)x-(8/24)x

63=(7/24)x

multiply both sides by 24/7

(24/7)(63)=(24/7)(7/24)x

216=x

216 cm3 is the volume (answer)

1/3 of 216 is 72

72+63=135

135/216=0.625=5/8

4 0
3 years ago
Of the people who fished at Clearwater Park today, 48 had a fishing license, 32and did not. Of the people who fished at Mountain
horrorfan [7]

Answer:

The probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

Step-by-step explanation:

Denote the events as follows:

<em>X</em> = a fisher at Clearwater Park had a fishing license

<em>Y</em> = a fisher at Mountain View Park had a fishing license

The two events are independent.

The information provided is:

n (X) = 48

n (X') = 32

n (Y) = 72

n (Y') = 18

Then,

N (X) = n (X) + n (X')

        = 48 + 32

        = 80

N (Y) = n (Y) + n (Y')

        = 72 + 18

        = 90

Compute the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license as follows:

P(X'\cap Y)=P(X')\times P(Y)

                 =\frac{n(X')}{N(X)}\times \frac{n(Y)}{N(Y)} \\\\=\frac{32}{80}\times\frac{72}{90}\\\\=0.32

Thus, the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

7 0
3 years ago
Define the double factorial of n, denoted n!!, as follows:n!!={1⋅3⋅5⋅⋅⋅⋅(n−2)⋅n} if n is odd{2⋅4⋅6⋅⋅⋅⋅(n−2)⋅n} if n is evenand (
tekilochka [14]

Answer:

Radius of convergence of power series is \lim_{n \to \infty}\frac{a_{n}}{a_{n+1}}=\frac{1}{108}

Step-by-step explanation:

Given that:

n!! = 1⋅3⋅5⋅⋅⋅⋅(n−2)⋅n        n is odd

n!! = 2⋅4⋅6⋅⋅⋅⋅(n−2)⋅n       n is even

(-1)!! = 0!! = 1

We have to find the radius of convergence of power series:

\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{2^{n}[(n+9)!]^{3}(4n+3)!!}](8x+6)^{n}\\\\\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{2^{n}[(n+9)!]^{3}(4n+3)!!}]2^{n}(4x+3)^{n}\\\\\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{[(n+9)!]^{3}(4n+3)!!}](x+\frac{3}{4})^{n}\\

Power series centered at x = a is:

\sum_{n=1}^{\infty}c_{n}(x-a)^{n}

\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{2^{n}[(n+9)!]^{3}(4n+3)!!}](8x+6)^{n}\\\\\sum_{n=1}^{\infty}[\frac{8^{n}n!(3n+3)!(2n)!!}{2^{n}[(n+9)!]^{3}(4n+3)!!}]2^{n}(4x+3)^{n}\\\\\sum_{n=1}^{\infty}[\frac{8^{n}4^{n}n!(3n+3)!(2n)!!}{[(n+9)!]^{3}(4n+3)!!}](x+\frac{3}{4})^{n}\\

a_{n}=[\frac{8^{n}4^{n}n!(3n+3)!(2n)!!}{[(n+9)!]^{3}(4n+3)!!}]\\\\a_{n+1}=[\frac{8^{n+1}4^{n+1}n!(3(n+1)+3)!(2(n+1))!!}{[(n+1+9)!]^{3}(4(n+1)+3)!!}]\\\\a_{n+1}=[\frac{8^{n+1}4^{n+1}(n+1)!(3n+6)!(2n+2)!!}{[(n+10)!]^{3}(4n+7)!!}]

Applying the ratio test:

\frac{a_{n}}{a_{n+1}}=\frac{[\frac{32^{n}n!(3n+3)!(2n)!!}{[(n+9)!]^{3}(4n+3)!!}]}{[\frac{32^{n+1}(n+1)!(3n+6)!(2n+2)!!}{[(n+10)!]^{3}(4n+7)!!}]}

\frac{a_{n}}{a_{n+1}}=\frac{(n+10)^{3}(4n+7)(4n+5)}{32(n+1)(3n+4)(3n+5)(3n+6)+(2n+2)}

Applying n → ∞

\lim_{n \to \infty}\frac{a_{n}}{a_{n+1}}= \lim_{n \to \infty}\frac{(n+10)^{3}(4n+7)(4n+5)}{32(n+1)(3n+4)(3n+5)(3n+6)+(2n+2)}

The numerator as well denominator of \frac{a_{n}}{a_{n+1}} are polynomials of fifth degree with leading coefficients:

(1^{3})(4)(4)=16\\(32)(1)(3)(3)(3)(2)=1728\\ \lim_{n \to \infty}\frac{a_{n}}{a_{n+1}}=\frac{16}{1728}=\frac{1}{108}

4 0
3 years ago
5.45 times what is 65 real urgent
Sonbull [250]
Opposite operation of multiplication = division. 
65/5.45 = 11.93
Simply divide 65 by 5.45
8 0
3 years ago
If someone could please help me then that would be great.
postnew [5]

Answer: Infinite Solutions

Step-by-step explanation: Make the top x and y values times -2 to cancel all the variables and numbers out to get 0 = 0 so it would be Infinite Solutions.

And if you multiply by 2 you get the exact same equation.

If I am wrong let me know!

Hope this helps!  

6 0
3 years ago
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