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andrezito [222]
3 years ago
5

A recursive arithmetic sequence is defined ad f(1)=6, f(n+1)=f(n)+5 for n>1. The first four terms of the sequence are shown i

n the table. Write an explicit formula that represents the sequence using function notation. Find the slope of the line that passes through the points given in the table. The slope is

Mathematics
2 answers:
Dennis_Churaev [7]3 years ago
7 0
Write the first few terms of the sequence.
f₁ = 6
f₂ = f₁ + 5 = 11
f₃ = f₂ + 5 = 16
f₄ = f₃ + 5 = 21
and so on

The sequence is
6, 11, 16, 21, ...,
This is an arithmetic sequence with a common difference of 5.

In function notation, the sequence is
f_{n+1} = 6 + 5n, \\ \, n=0,1,2, \, ...,

This represents the equation of a straight line with n as the independent variable and f as the dependent variable.
The slope is 5. 
A graph of the line is shown below.

Answer:
The sequence is f_{n+1} = 6 + 5n, \,\, n=0,1,2, \, ...,
The slope is 5.

MrMuchimi3 years ago
7 0

<u>Answer:</u>

Find the slope of the line that passes through the points given in the table. The slope is 5.

Use one of the given points to find the y-intercept. Substitute values for x, y, and m into the equation y = mx + b and solve for b. The y-intercept is 1.

Write the formula as a function of n in slope-intercept form. The function is f(n) = 5n + 1 for n in the set of natural numbers.

Your Welcome and don't forget to press that <u>Thanks</u> button :)

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Answer:

-42.66666...

Step-by-step explanation:

-64 * 2/3 is -42.66666...

well, according to the calculator.

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3 years ago
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Jimmy notices 7oranges weigh the same as 5 apples. If Jimmy has 28 oranges, how many apples would Jimmy need to equal the weight
pychu [463]

Answer:

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A report indicated that 37% of adults had received a bogus email intended to steal personal information. Suppose a random sample
fiasKO [112]

Answer:

5.05% probability that no more than 34% had received such an email.

Step-by-step explanation:

We use the binomial approximation to the normal to solve this problem.

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)}.

In this problem, we have that:

n = 700, p = 0.37

\mu = E(X) = np = 700*0.37 = 259

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{700*0.37*0.63} = 12.77

In a random sample of 700 adults, what is the probability that no more than 34% had received such an email?

34% is 0.34*700 = 238

So this probability is the pvalue of Z when X = 238.

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

Z = \frac{238 - 259}{12.77}

Z = -1.64

Z = -1.64 has a pvalue of 0.0505

5.05% probability that no more than 34% had received such an email.

7 0
3 years ago
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ElenaW [278]

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Answer:

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4 0
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