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3 years ago

I have three times as much money as does my brother. Our combined total is $42. How much does each of us have?

1 answer:

4 0

For an instance, i stands for the money that you have, and b stands for the money that brother has.
An equation system based on the problem would be
i + b = 42 (equation 1)
i = 3b (equation 2)

Use substitution method to solve the problem
substitute 3b into i in the equation 1
i + b = 42
3b + b = 42
4b = 42
b = 42/4
b = 10.5

substitute the value of b into the equation 1
i = 3b
i = 3(10.5)
i = 31.5

You have $31.5 and your brother has $10.5

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A group of friends were working on a student film that had a budget of $1300. They used $546 of their budget on props. What perc

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To find percentage: divide the given value by the total and multiply by 100

546/1300 x 100 = 42%

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2 years ago

What is the derivative of -5

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3 years ago

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:

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

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3 years ago

W(x)=-5(x-8)(x+4) what is the maximum height that the stone will reach?

Ganezh [65]

Answer:

the maximum height is 180 or y=180

Step-by-step explanation:

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3 years ago

Cole brought chocolate and vanilla cupcakes to school for his birthday. 40 students decided to take a cupcake, and 90% of them p

nikdorinn [45]

Answer:

36 people picked a vanilla cupcake

Step-by-step explanation:

40 * 90%

= 40 * 0.9

= 36

6 0

3 years ago

Read 2 more answers