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3 years ago

Can someone help me solve these.

Mathematics

1 answer:

vazorg [7]3 years ago

4 0

(x-1)/-3 = (x+5)/6

You want to get x by itself. Start by multiplying both sides by -3 and 6:

6(x-1) = -3(x+5)

Distribute:

6x - 6 = -3x + 5

Add 6 and 3x to both sides:

6x + 3x = 5 + 6

9x = 11

Divide both sides by 9 to get x by itself:

x = 11/9

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Answer:

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3 years ago

Look at the table. Make a conjecture about the sum of the first 15 positive even numbers.

Olenka [21]

Be observing the table, we can write the following conjecture:

When adding consecutive even numbers, starting from 2 to $m$ .

Then the sum is equal to:
$\frac{m}{2}( \frac{m}{2} +1)$

Then, the sum of the first 15 positive even numbers (which is the sum of 2 to 30) can be calculated with the previous conjecture by setting $m=30$ :
$\frac{m}{2}( \frac{m}{2} +1)=\frac{30}{2}( \frac{30}{2} +1)=(15)(16)=240$

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4 0

4 years ago

A man is distributing his coin collection with 35 coins to his five grandchildren. How many ways are there to distribute the coi

Musya8 [376]

Answer:

a) $82251$

b) $2.91038 \cdot 10^{24}$

c) $1$

d) $3.17746\cdot 10^{21}$

Step-by-step explanation:

a) If the coins are all the same, we have a combination of 35 identical coins in 5 persons.

The amount of combinations is

$\binom{n+r-1}{r-1}=\binom{35+5-1}{5-1}=\binom{39}{4}=\frac{39!}{4!35!} =82251$

being n the number of coins and r the number of grandchildren.

b) If the coins are different, the number of combinations can be calculated as:

$r^n=5^{35}=2.91038 \cdot 10^{24}$

c) If the coins are all the same, and each grandchild gets the same number of coins, there is only one combination for that (everyone gets 35/5=7 coins)

d) If the coins are all distinct, but each of the grandchildren get the same numer of coins, the expression to calculate this is:

$\frac{n!}{(n/r)!^r} =\frac{35!}{(35/5)!^5}=\frac{35!}{7!^5}=\frac{1.03331\cdot 10^{40}}{3.25202\cdot 10^{18}} =3.17746\cdot 10^{21}$