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Jet001 [13]
3 years ago
11

Andrea bought 1 2/5 pounds of avocados at $4.20 per pound and ​ 2 1/

Mathematics
1 answer:
guapka [62]3 years ago
8 0

Answer:

$14.43¢

Step-by-step explanation:

We are given; 1\frac{2}{5} pounds, 1 pound = $4.20 and 2\frac{1}{4} pounds,1 pound = $3.80 that Andrea bought.

Now we need to find her total cost. To do that, we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert 1\frac{2}{5} to a decimal. It is 1.4. Now we can set up a graph.

<u>Avocados</u>

\frac{4.2}{1}=\frac{x}{1.4}

Switch sides

\frac{x}{1.4}=\frac{4.2}{1}

Apply rule: \frac{a}{1}=a

\frac{x}{1.4}=4.2

Multiply both sides by 1.4

\frac{1.4x}{1.4}=4.2\cdot \:1.4

Simplify

x=5.88

So, her cost for avocados is $5.88¢

Now we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert 2\frac{1}{4} to a decimal. It is 2.25. Now we can set up a graph.

<u>Asparagus</u>

\frac{3.8}{1}=\frac{x}{2.25}

Switch sides

\frac{x}{2.25}=\frac{3.8}{1}

Apply rule : \frac{a}{1}=a

\frac{x}{2.25}=3.8

Multiply both sides by 2.25

\frac{2.25x}{2.25}=3.8\cdot \:2.25

Simplify

x=8.55

So, her cost for asparagus is $8.55¢

<u>Total cost</u>

Now that we have found out how much both of the fruits Andrea bought costs, we need to sum it up (meaning add it) to find the total cost:

$5.88¢ + 8.55¢ =

5.88 + 8.55 = 14.43

Therefore, Andrea's total cost of the fruits is $14.43¢

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Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x
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Answer:

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
3 years ago
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