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3 years ago

The sum of two numbers is 8, and their product is 80.

1 answer:

6 0

From their sum, the numbers are ' x ' and ' 8 - x ' .

From their product, x(8 - x) = 80 .

When you massage and manipulate this equation into the standard
quadratic form, you have

 x² - 8x + 80 = 0 .

Applying the quadratic formula to tease out the solutions of this equation,
we find that they are

  x = 4 + 64 i
and
  x = 4 - 64 i

You might be interested in

What is the slope of a line that passes through each pair of points (2,2), (3,1)

Harrizon [31]

The slope of a line that passes through each pair of points (2,2), (3,1) is (4,2), (0,2)

6 0

3 years ago

(6,-2), (12, 1) Write equation in slope intercept form

bazaltina [42]

Answer:

y=1/2x-5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(1-(-2))/(12-6)

m=(1+2)/6

m=3/6

simplify

m=1/2

----------------------

y-y1=m(x-x1)

y-(-2)=1/2(x-6)

y+2=1/2(x-6)

y=1/2x-6/2-2

y=1/2x-3-2

y=1/2x-5

5 0

2 years ago

An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2500 individ

Ne4ueva [31]

Answer:

The approximate distribution of the number who carry this gene is approximately normal with mean $\mu = 5$ and standard deviation $\sigma = 2.23$

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they carry the defective gene that causes inherited colon cancer, or they do not. The probability of a person carrying this gene is independent from other people. So the binomial probability distribution is used to solve this question.

A sample of 2500 individuals is quite large, so we use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .