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Rina8888 [55]
3 years ago
7

I need help to solve this problem p/0,05p

Mathematics
1 answer:
AfilCa [17]3 years ago
7 0

p / 0.05p

= 1 / 0.05

= 20  answer

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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
4 tomatoes and 8 avocados cost $10. Six tomatoes and 14 avocados cost $17. How much does a single avocado and a single tomato co
Nataly_w [17]

Answer:

One avocado costs $1 and one tomato costs $0.50

Step-by-step explanation:

Set up a system of equations where t is the number of tomatoes and a is the number of avocados:

4t + 8a = 10

6t + 14a = 17

Solve by elimination by multiplying the top equation by 3 and the bottom equation by -2:

12t + 24a = 30

-12t - 28a = -34

Add them together and solve for a:

-4a = -4

a = 1

Plug in 1 as a into one of the equations and solve for t:

4t + 8a = 10

4t + 8(1) = 10

4t + 8 = 10

4t = 2

t = 0.5

So, one avocado costs $1 and one tomato costs $0.50

3 0
3 years ago
How many 3/4 foot pieces of string can be cut from a piece of string 4 1/2 feet long
Gnom [1K]
3/4 foot is 9 inches, and 4 1/2 feet is 54 inches, so, 54/9 makes exactly 6 pieces of string. 
8 0
3 years ago
A bag has yellow, red, green, blue, black, and white marbles. There are 5 of each color in the bag. What fraction of the marbles
Ahat [919]

Answer:

2/3

Step-by-step explanation:

Have a great day

8 0
3 years ago
4 ^-3 rewrite without an exponent
hichkok12 [17]

Answer:

(1/4)³

Step-by-step explanation:

Hope it helps you

5 0
3 years ago
Read 2 more answers
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