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aliya0001 [1]
3 years ago
8

Three aluminum cans can be recycled to make a new can. How many new cans can eventually be made from 243 aluminum cans? (Remembe

r that the first new cans that are made can then be recycled into even newer cans!) Do not include the original 243 cans in your count.
Mathematics
1 answer:
DENIUS [597]3 years ago
7 0

Answer:

121 new cans can eventually be made from 243 aluminum cans

Step-by-step explanation:

Unit rate defined as the rates are expressed as a quantity 1 such as 2 miles per second or 5 kilometer per hour.

As per the statement:

Three aluminum cans can be recycled to make a new can.

Unit rate per aluminium can = \frac{1}{3} new can

We have to find the new cans can eventually be made from 243 aluminum cans.

By definition of unit rate;

\text{Number of new cans made from 243 cans} = \text{Unit rate per aluminium can} \times 243

Substitute the given values we have;

\text{Number of new cans made from 243 cans} = \frac{1}{3} \times 243 = 81

Again do the same process:

Number of new can made from 81 can  is \frac{1}{3} \cdot 81 = 27

Similarly,

Number of new cans made from 27 can = \frac{1}{3} \cdot 27 = 9

Number of new cans made from 9 can =\frac{1}{3} \cdot 9 = 3

Number of new cans made from 3 can =  \frac{1}{3} \cdot 3 = 1

Now, No further new can made.

Therefore, total new can made from 243 is 81+27+9+3+ 1 =121 cans

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Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It c
aksik [14]

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The <em>expected value</em> is given by the <u>sum of each outcome multiplied by it's respective probability.</u>

In this problem:

  • The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is \frac{1}{6} \times \frac{1}{12} = \frac{1}{72}.
  • The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is \frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}
  • In the other cases, Ayo wins £1.40, with 1 - \frac{18}{72} = \frac{54}{72} probability.

Hence, his expected profit for a single game is:

E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583

For 216 games, the expected value is:

E = 216(0.2583) = 55.8

Ayo can be expected to make a profit of £55.8.

To learn more about expected value, you can take a look at brainly.com/question/24855677

6 0
2 years ago
Let f(x) = -20x2 + 14x + 12 and g(x) = 5x - 6. Find f/g and state its domain.
UkoKoshka [18]

Solution

f(x) = -20x^{2} +14x + 12 and g(x) = 5x - 6.

(f/g)(x) = \frac{f(x)}{g(y)}

(f/g)(x) = \frac{-20x^{2}+14x +12 }{5x - 6}

<u>Step 1: </u>Now we have to factorize the numerator.

f(x) = -20x^2 + 14x + 12

Factor out -2, we get

= -2 (10x^2 - 7x - 6)

Now we can factorize 10x^2 - 7x - 6                  

f(x) = -2(2x + 1) (5x - 6)

<u>Step 2: </u>Plug in the factors

(f/g)(x) = \frac{-2 (2x +1)(5x - 6)}{(5x - 6)}

<u>Step 3:</u> Cancel out the common factor (5x - 6) from the numerator and the denominator, we get

(f/g)(x) = -2(2x +1) = -4x -2

Since -4x -2 is linear expression, the domain is all the real numbers.

Therefore, the answer is –4x – 2; all real numbers

Thank you :)

4 0
3 years ago
A recipe calls for 3 cups of pecans for every 5 cups of walnuts. How many cups of pecans should be added to 8 cups of walnuts?
aliya0001 [1]

Answer:A

Step-by-step explanation:

8 0
3 years ago
The pressure at sea level is
seraphim [82]

Answer:

653

Step-by-step explanation:

gshsjfsffshdjfhfbfbrvdhegdvdvr

3 0
3 years ago
What are the values of A,B and C?<br><br> Please show all the work on how you got your answer
il63 [147K]

Answer:

a=35, b=14, c=5

Step-by-step explanation:

b+6=20, b+6-6=20-6, b=14

4c-6=14, 4c-6+6=14+6, 4c=20, 4c/4=20/4, c=5

a triangle's angles always add up to 180, 180-55-90(the square means right angle)=35

3 0
3 years ago
Read 2 more answers
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