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love history [14]
3 years ago
10

I really need help understanding this question! thank you!

Mathematics
2 answers:
aleksandr82 [10.1K]3 years ago
8 0

Answer:

\boxed{\text{6 and 7}}

Step-by-step explanation:

1. Set up the equation

        Let x = the first integer. Then

         x + 1 = the next integer

     x(x + 1) = the product of the integers

     x(x + 1) = 42

       x² + x = 42     Distributed the x

x² + x - 42 = 0

2. Solve for x

(x + 7)(x - 6) = 0            Factored the quadratic

x + 7 = 0     x - 6 = 0     Applied zero product rule

     x = -7         x = 6     Solved the binomials

We reject x = -7, because x must be positive

    x = 6

x + 1 = 7

\text{The two consecutive positive integers are \boxed{\textbf{6 and 7}}}

Check:

6(6+ 1) = 42

   6(7) = 42

     42 = 42

OK.

klasskru [66]3 years ago
4 0

n(n+1)=42\\n^2+n-42=0\\n^2-6n+7n-42=0\\n(n-6)+7(n-6)=0\\(n+7)(n-6)=0\\n=-7 \vee n=6

-7 is not positive

n=6\\n+1=7

The numbers are 6 an 7.

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Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \mu = np, \sigma = \sqrt{np(1-p)}.

For the binomial distribution, the parameters are given as follows:

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Hence the mean and the standard deviation of the approximation are given as follows:

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Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is <u>one subtracted by the p-value of Z when X = 66.5</u>.

Z = \frac{X - \mu}{\sigma}

Z = \frac{66.5 - 50}{5}

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Z = 3.3 has a p-value of 0.9995.

1 - 0.9995 = 0.0005.

0.0005 = 0.05%

More can be learned about the normal distribution at brainly.com/question/4079902

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