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1 year ago

6

A sand dune stands 5 feet above sea level. The hill is eroding at a rate of 1 foot per 20 years. Let y represent the height of t

he sand dune after x years. Which equation represents the situation?

2 answers:

Soloha48 [4]1 year ago

7 0

Answer:

$y=-\frac{1}{20}x+5$

Step-by-step explanation:

Here we are given that the present height of the sand dune is 5 ft and it is eroding 1 ft in every 20 years. If x represent the number of years and y represents the height of the sand dune. Hence we can consider the coordinates be (0,5) (20,4) (40,3) (60,2) (80,1) (100,0)

Let us evaluate the equation of the line plotted on these coordinates

Here we can see the y intercept is 5

Let us find the slope

$m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{5-4}{0-20}\\m=\frac{1}{-20}\\m=-\frac{1}{20}$

The equation in slope intercept form is given as

y=mx+c

where c is y intercept i.e. 5

$y=-\frac{1}{20}x+5$

Hence this is our required equation

avanturin [10]1 year ago

4 0

y = -1/2x + 5 should be your equation because it is 5 ft above sea level and its eroding, or going down, 1 ft per 20 years. So every year, the sand dune erodes 1/20 ft more.

Hope this helps!

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During April of 2013, Gallup randomly surveyed 500 adults in the US, and 47% said that they were happy, and without a lot of str

Brilliant_brown [7]

Answer:

number of successes

$k = 235$

number of failure

$y = 265$

The criteria are met

A

The sample proportion is $\r p = 0.47$

B

$E =4.4 \%$

C

What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from the true population proportion will not more than 4.4%

Ci

$r = 0.514 = 51.4 \%$

$v = 0.426 = 42.6 \%$

D

This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%

E

Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

F

Yes our result would support the claim because

$\frac{1}{3 } \ of N < \frac{1}{2} (50\%) \ of \ N , \ Where\ N \ is \ the \ population\ size$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 500$

The sample proportion is $\r p = 0.47$

Generally the number of successes is mathematical represented as

$k = n * \r p$

substituting values

$k = 500 * 0.47$

$k = 235$

Generally the number of failure is mathematical represented as

$y = n * (1 -\r p )$

substituting values

$y = 500 * (1 - 0.47 )$

$y = 265$

for approximate normality for a confidence interval criteria to be satisfied

$np > 5 \ and \ n(1- p ) \ >5$

Given that the above is true for this survey then we can say that the criteria are met

Given that the confidence level is 95% then the level of confidence is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha =0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p}{n} }$

substituting values

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=> $E =4.4 \%$

What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from the true population proportion of those that are happy by more than 4.4%

The 95% confidence interval is mathematically represented as

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substituting values

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The upper limit of the 95% confidence interval is $r = 0.514 = 51.4 \%$

The lower limit of the 95% confidence interval is $v = 0.426 = 42.6 \%$

This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%

Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

Yes our result would support the claim because

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