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Sveta_85 [38]
3 years ago
13

What are the slope and the y-intercept of the linear function that is represented by the table?

Mathematics
2 answers:
navik [9.2K]3 years ago
8 0

Answer:

slope rise 3 run 2 1/2

Step-by-step explanation:

if you start from the bottom and if you start from the top it's -3 and -2 1/2

Angelina_Jolie [31]3 years ago
5 0

Answer: The slope is 3 and the y-intercept is 3/2

Step-by-step explanation:

The slope of a linear function can be calculated as:

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

Where y2 = f(x2) and y1 = f(x1) and f(x) is the linear function.

So here we can use any two pairs of the set of data, for example, the first two.

(-1 , -3/2) and (-1/2,0)

s = (0 -(-3/2))/(-1/2 - (-1)) = (3/2)/(1/2) =(3/2)*(2/1) = 3

So the slope is equal to 3.

the y-intercept is the value of y when x = 0, in the table we can see that when x = 0. the value of y = 3/2

So the function is: y = 3*x + 3/2

and the correct option is the fourth one.

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Answer:

3(2 + x)

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You have to multiply 3 by the sum of 2 and any number, or x. So if you put the expression of 2 + x in parenthesis, and 3 next to it. You'll get your answer.

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When we toss a coin, there are two possible outcomes: a head or a tail. Suppose that we toss a coin 100 times. Estimate the appr
marin [14]

Answer:

96.42% probability that the number of tails is between 40 and 60.

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

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The expected value of the binomial distribution is:

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The standard deviation of the binomial distribution is:

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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)}.

In this problem, we have that:

100 tosses, so n = 100

Two outcomes, both equally as likely. So p = \frac{1}{2} = 0.5

So

E(X) = np = 100*0.5 = 50

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5

Estimate the approximate probability that the number of tails is between 40 and 60.

Using continuity correction.

P(40 - 0.5 \leq X \leq 60 + 0.5) = P(39.5 \leq X \leq 60.5)

This is the pvalue of Z when X = 60.5 subtracted by the pvalue of Z when X = 39.5. So

X = 60.5

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

Z = \frac{60.5 - 50}{5}

Z = 2.1

Z = 2.1 has a pvalue of 0.9821

X = 39.5

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

Z = \frac{39.5 - 50}{5}

Z = -2.1

Z = -2.1 has a pvalue of 0.0179

0.9821 - 0.0179 = 0.9642

96.42% probability that the number of tails is between 40 and 60.

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