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Natasha_Volkova [10]
3 years ago
6

Prove that 3(x+1)(x+7)-2x+5)^2 is never positive

Mathematics
1 answer:
lisov135 [29]3 years ago
5 0

Answer:

Yes, 3(x+1)(x+7)-(2x+5)² is never positive

Step-by-step explanation:

So....

3(x+1)(x+7)-(2x+5)(2x+5)

=3(x²+8x+7)-(4x²+20x+25)

=3x²+24x+21-4x²-20x-25

=-x²+4x-4

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Of the cartons produced by a​ company, ​% have a​ puncture, ​% have a smashed​ corner, and ​% have both a puncture and a smashed
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Full Question

<em>Of the cartons produced by a​ company, 10​% have a​ puncture, 6​% have a smashed​ corner, and 0.4​% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing​ ____%. ​(Type an integer or a decimal. Do not​ round.)</em>

<em />

Answer:

P(Punctured\ or\ Smashed\ Corner) = 0.156

Step-by-step explanation:

Given

Puncture\ Corner = 10\%

Smashed\ Corner = 6\%

Punctured\ and\ Smashed\ Corner = 0.4\%

Required

P(Punctured\ or\ Smashed\ Corner)

For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;

P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)

Substitute:

10% for P(Puncture Corner),

6% for P(Smashed Corner) and

0.4% for P(Punctured and Smashed Corner)

P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%

P(Punctured\ or\ Smashed\ Corner) = 15.6\%

Convert % to fraction

P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}

Convert to decimal

P(Punctured\ or\ Smashed\ Corner) = 0.156

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