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2 years ago

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The relationship between men’s whole-number shoe sizes and foot lengths is an arithmetic sequence, where an is the foot length i

n inches that corresponds to a shoe size of n. A men’s size 9 fits a foot 10.31 inches long, and a men’s size 13 fits a foot 11.71 inches long. What is the explicit formula for the arithmetic sequence? Round to the nearest hundredth, if necessary.
Ok so what I dont understand is how to get the common difference. I tried getting the slope and it just gives me 11.71-10.31/13-4, Which is apparently wrong, how do I find the common difference?

2 answers:

Gennadij [26K]2 years ago

7 0

Answer:

Explicit formula for the sequence will be f(x) = 7.16 + 0.35n

Step-by-step explanation:

As we know explicit formula of an arithmetic mean is given by

f(x) = a + (n-1)d

where a = first term of the sequence

n = number of term

d = common difference

Now it has been given that a men's size 9 fits a foot 10.31 inches long, means in an arithmetic sequence 9th term is 10.31. So by explicit formula

f(9) = a + (9-1)d = 10.31

⇒ a + 8d = 10.31-----(1)

Now from second statement

f(13) = a + (13-1)d = 11.71

⇒a + 12d = 11.71---------(2)

Now we subtract equation 1 from 2.

(a + 12d) - (a + 8d) = 11.71 - 10.31 = 0.40

4d = 1.40

d = 1.40/4 = 0.35

By putting the value of d in equation 1

a = 10.31 - 2.8 = 7.51

Finally we get the explicit formula of arithmetic formula as

f(x) = 7.51 + (n-1)(.35) = 7.51 + 0.35n - 0.35 = 7.16 + 0.35n

f(x) = 7.16 + 0.35n

Helga [31]2 years ago

3 0

7.51+0.35(n-1) that's going to be the answer

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c) If we compare the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% the proportion of business owners providing holiday gifts had decreased from the 2008 level.

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Step-by-step explanation:

Data given and notation

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X represent the business owners plan to provide a holiday gift to their employees

$\hat p=0.35$ estimated proportion of business owners plan to provide a holiday gift to their employees

$p_o=0.46$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Part a

On this case w ejust need to multiply the value of th sample size by the proportion given like this:

Number = 60 *0.35=21

2) Part b

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Alternative hypothesis: $p < 0.46$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

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Since we have all the info requires we can replace in formula (1) like this:

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