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3 years ago

12

The common ratio of a geometric sequence cannot be: a) 3 b) 1 c) 2 d) 0

1 answer:

MA_775_DIABLO [31]3 years ago

4 0

The correct answer is d.

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A. Find the mean median and mode of the data.

IrinaK [193]

26 26 29 30 31 33 33 33 34 34 70

A.
Mean:30.9
Add all numbers up and divide by however many there are.
Median:32
Number in the middle spot
Mode:33
Number that occurs the most

B.
Mean:34.45
Median:33
Mode:33

4 0

3 years ago

Prove the divisibility of the following numbers:

Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

$75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}$

(B)

$72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}$

In this case, it is easier to also factor the divisor to primes:

$72^{63}=2^{189}\cdot 3^{126}$

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

$2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}$

6 0

3 years ago

Please please help me -

Hitman42 [59]

Answer:

ok

Step-by-step explanation:

7 0

3 years ago

On Tuesday Conrad had 3 times as many sales as on Monday. On Wednesday, he had 9 times as many sales as on Monday. Over the thre

Vlad1618 [11]

Answer:

Conrad had 56 sales on Monday , 168 sales on Tuesday and 504 sales on Wednesday.

Step-by-step explanation:

Let x be the no. of sales on Monday

We are given that On Tuesday Conrad had 3 times as many sales as on Monday.

So, Conrad had sales on Tuesday = 3x

We are also given that On Wednesday, he had 9 times as many sales as on Monday.

So, Conrad had sales on Wednesday = 9x

Over the three days, he had a total of 728 sales

So, x+3x+9x=728

13x=728

$x=\frac{728}{13}$

x=56

Conrad had sales on Tuesday = 3x =3(56)=168

Conrad had sales on Wednesday = 9x=9(56)=504

Hence Conrad had 56 sales on Monday , 168 sales on Tuesday and 504 sales on Wednesday.

7 0

3 years ago

Solve:<br> 3x - 9 = 5(x-3)

Viefleur [7K]

Hi,

$3x - 9 = 5(x-3)\\3x - 9 - 5(x-3)= 0\\3x -9 -5x +15 =0\\6-2x=0\\6=2x\\x=3$

Have a good day.

3 0

3 years ago