Christy should make at least 30 bracelets and at most 40 necklaces to maximize profit
<h3>How to determine how many bead of each type of bracelets and necklaces should Christy make to maximize his profit?</h3>
The given parameters can be represented in the following tabular form:
Bracelet (x) Necklace (y) Total
Labor (hour) 0.5 0.75 40
Profit 10 18
From the above table, we have the following:
Objective function:
Max P = 10x + 18y
Subject to:
0.5x + 0.75y <= 40
Because she wants to make at least 30 bracelets, we have:
x >= 30
So, we have:
Max P = 10x + 18y
Subject to:
0.5x + 0.75y <= 40
x >= 30
Express x >= 30 as equation
x = 30
Substitute x = 30 in 0.5x + 0.75y <= 40
0.5 * 30 + 0.75y <= 40
This gives
15 + 0.75y <= 40
Subtract 15 from both sides
0.75y <= 30
Divide by 0.75
y <= 40
Hence, Christy should make at least 30 bracelets and at most 40 necklaces to maximize profit
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Probabilities are used to determine the chances of an event
- The probability of choosing a black counter is 0.6
- The probability that both counters are white is 0.16
<h3>(a) Probability of selecting two blacks</h3>
The probability is given as:

Apply probability formula

Express as squares

Take the square root of both sides

Hence, the probability of choosing a black counter is 0.6
<h3>(b) Probability of selecting two white counters</h3>
In (a), we have:

Using the complement rule, we have:

So, we have:

Evaluate

The probability that both counters are white is then calculated as:

So, we have:


Hence, the probability that both counters are white is 0.16
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The answer is 35 hope this helps
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