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goldenfox [79]
2 years ago
15

Four times the sum of a number and 15 is at least 120. Let x represent the number. Find all possible values for x.

Mathematics
1 answer:
Aleksandr [31]2 years ago
4 0
4(x + 15) > = 120
4x + 60 > = 120
4x > = 120 - 60
4x > = 60
x > = 60/4
x > = 15...........so ur answer is 15 or more
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a) Figure attached

b) y=1.31 x +98.57

c) The correlation coefficient would be r =0.47719

d) y=1.31 x +98.57=1.31*21 + 98.57 =126.08

Step-by-step explanation:

(a) Draw a scatter diagram for the data.

See the figure attached

(b) Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x =__ y =__ b =__ y =__ + __x

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6576-\frac{300^2}{14}=147.429

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=38186-\frac{300*1773}{14}=193.143

And the slope would be:

m=\frac{193.143}{147.429}=1.31

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{300}{14}=21.429

\bar y= \frac{\sum y_i}{n}=\frac{1773}{14}=126.643

And we can find the intercept using this:

b=\bar y -m \bar x=126.643-(1.31*21.429)=98.571

So the line would be given by:

y=1.31 x +98.57

(c) Find the sample correlation coefficient r and the coefficient of determination r?2. (Round your answers to three decimal places.)

n=14 \sum x = 300, \sum y = 1773, \sum xy=38186, \sum x^2 =6576, \sum y^2 =225649  

And in order to calculate the correlation coefficient we can use this formula:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}

r=\frac{14(38186)-(300)(1773)}{\sqrt{[14(6576) -(300)^2][14(225649) -(1773)^2]}}=0.9534

So then the correlation coefficient would be r =0.47719

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

The % of variation is given by the determination coefficient given by r^2 and on this case 0.47719^2 =0.2277, so then the % of variation explaines is 22.8%.

(d) If a female baby weighs 21 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) ___ lb

So we can replace in the linear model like this:

y=1.31 x +98.57=1.31*21 + 98.57 =126.08

7 0
2 years ago
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