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topjm [15]
3 years ago
11

A student is asked to calculate the value of 752 − 702 using the identity x2 − y2 = (x − y)(x + y). The student's steps are show

n below.
Step 1: 752 − 702 = (75 − 70)(75 + 70)

Step 2: = (5)(155)

Step 3: = (5)(150) + 5(5)

Step 4: = 750 + 25

Step 5: = 775

The correct answer should be 725. In which step did the student make his first error?
Step 1
Step 2
Step 3
Mathematics
1 answer:
Mrrafil [7]3 years ago
7 0
Step 2, 5*155= 775,which means the steps after that would make the answer even more variable
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Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children. Let BBG ind
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Answer:

(a)

S = \{GGG, GGB, GBG, GBB, BBG, BGB, BGG, BBB\}

(b)

i.

1\ girl = \{GBB, BBG, BGB\}

P(1\ girl) = 0.375

ii.

Atleast\ 2 \ girls = \{GGG, GGB, GBG, BGG\}

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iii.

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Step-by-step explanation:

Given

Children = 3

B = Boys

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Solving (a): List all possible elements using set-roster notation.

The possible elements are:

S = \{GGG, GGB, GBG, GBB, BBG, BGB, BGG, BBB\}

And the number of elements are:

n(S) = 8

Solving (bi) Exactly 1 girl

From the list of possible elements, we have:

1\ girl = \{GBB, BBG, BGB\}

And the number of the list is;

n(1\ girl) = 3

The probability is calculated as;

P(1\ girl) = \frac{n(1\ girl)}{n(S)}

P(1\ girl) = \frac{3}{8}

P(1\ girl) = 0.375

Solving (bi) At least 2 are girls

From the list of possible elements, we have:

Atleast\ 2 \ girls = \{GGG, GGB, GBG, BGG\}

And the number of the list is;

n(Atleast\ 2 \ girls) = 4

The probability is calculated as;

P(Atleast\ 2 \ girls) = \frac{n(Atleast\ 2 \ girls)}{n(S)}

P(Atleast\ 2 \ girls) = \frac{4}{8}

P(Atleast\ 2 \ girls) = 0.5

Solving (biii) No girl

From the list of possible elements, we have:

No\ girl = \{BBB\}

And the number of the list is;

n(No\ girl) = 1

The probability is calculated as;

P(No\ girl) = \frac{n(No\ girl)}{n(S)}

P(No\ girl) = \frac{1}{8}

P(No\ girl) = 0.125

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