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3 years ago

12

Given: Two distinct circles that are tangent to each other at a common point. How many tangent lines can be drawn that touch bot

h circles?
3
1
2

1 answer:

nika2105 [10]3 years ago

7 0

there are only 3 tangent lines can be drawn that touch both circles

ok done. Thank to me :>

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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

Anna11 [10]

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

Solve for the indicated variable.<br><br> 2a + 2b = c for b<br><br> B = ?/?

kodGreya [7K]

Answer:

b = c − 2a

------------

2

Step-by-step explanation:

2a + 2b = c

2b = c − 2a

b = c − 2a

------------

2

7 0

4 years ago

What is the slope (5,7) and (2,-2)

Romashka [77]

Answer:

slope = 3

Step-by-step explanation:

to find the slope you do (y2-y1)/(x2-x1)=m

so we can plug the points into this formula

(5,7) (2,-2)

x1 y1 x2 y2

-2-7/2-5=m

-9/-3=m

Simplifies to

3=m

4 0

3 years ago

26 ptss!! select the expressions that are equivalent to the expression below.

valkas [14]

Answer:

1st, 2nd, and last.

Step-by-step explanation:

For the first two common rules can be applied such as $n\sqrt{a/b}$ = $\frac{\sqrt[n]{a} }{\sqrt[n]{b} }$ and that $\sqrt[n]{\frac{a}{b} } = (\frac{a}{b})^{n}$

and for the last one this is just simplifying the radical and if you factor it you realize that, $\frac{750}{512} = \frac{5^3}{8^3}*6$ meaning that you can take the radical off of 5/8 and end up with that final answer

7 0

3 years ago

A farmer examines a sample of 25 cartons of eggs and finds that 3 contains cracked eggs. What is the best prediction of the numb

sertanlavr [38]

I believe it's C) 60 because ideally it would be 3 for every 25, 20 x 25 = 200, so then you would do 3 x 20 = 60

3 0

3 years ago

Read 2 more answers