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3 years ago

Salama makes fruit baskets with oranges and bananas.

Mathematics

1 answer:

vovangra [49]3 years ago

8 0

<em><u>The ratio for problem is:</u></em>

oranges : bananas = 9 : 6 or oranges : bananas = 6 : 4

<em><u>Solution:</u></em>

Given that, Salama makes fruit baskets with oranges and bananas

She uses between 8 and 16 oranges and bananas in a ratio of 3 oranges to 2 bananas

Given ratio is:

Ratio of orange to bananas = 3 : 2

They add up to 5 fruits, so some possible values are 5, 10, 15 , 20, 25, etc

But we need a value between 8 and 16 oranges and bananas

So we can choose 15 or 10

Now let us choose 15 and solve

Let the oranges be 3x

Let the bananas be 2x

Therefore,

3x + 2x = 15

5x = 15

x = 3

Thus oranges = 3x = 3(3) = 9

Bananas = 2x = 2(3) = 6

Thus the ratio for problem is:

oranges : bananas = 9 : 6

Similarly solve for 10

3x + 2x = 10

5x = 10

x = 2

Thus oranges = 3x = 3(2) = 6

Bananas = 2x = 2(2) = 4

Thus the ratio for problem is:

oranges : bananas = 6 : 4

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Probabilities are used to determine the chances of Laura winning an activity

The value of p is 1/12
The expected score of the game is -1/6
The probability that she has a total score of 5 after two rounds is 0

<h3>How to calculate the value of p</h3>

To calculate the value of p, we make use of the following probability formula

$\sum P(x) = 1$

So, we have:

$\frac 3{12} + \frac 1{12} + \frac 4{12} + \frac 2{12} + p + \frac 1{12} = 1$

Collect like terms

$\frac 3{12} + \frac 1{12} + \frac 4{12} + \frac 2{12} + \frac 1{12} + p= 1$

Evaluate the sums, on the left-hand side

$\frac{11}{12} + p = 1$

Subtract 11/12 from both sides

$p = \frac 1{12}$

Hence, the value of p is 1/12

<h3>(b) How to calculate the expected score</h3>

This is calculated using the following expected value formula

$E(x) = \sum x * P(x)$

So, we have:

$E(x) = -3 * \frac{3}{12} -1 * \frac 1{12} + 0 * \frac 4{12} + 1 * \frac 2{12} + 2 * \frac 1{12} + 4 * \frac 1{12}$

Evaluate the products

$E(x) = -\frac{9}{12} - \frac 1{12} + \frac 2{12} + \frac 2{12} + \frac 4{12}$

$E(x) = -\frac 2{12}$

Simplify

$E(x) = -\frac 1{6}$

Hence, the expected score of the game is -1/6

<h3>(c) The probability that she has a total score of 5 after two rounds</h3>

From the table, we have:

$P(5) = 0$

For after two rounds, we make use of the following equation

$P(5) * P(5) = 0 * 0$

$P(5) * P(5) = 0$

Hence, the probability that she has a total score of 5 after two rounds is 0