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HACTEHA [7]
3 years ago
7

​On the directed line segment from R to S on the coordinate plane ​above, what are the coordinates of the point that partitions

the ​segment in the ratio 2 to 3?
The coordinates for R is (-6,4) and S is (8,-4)
Mathematics
1 answer:
Serjik [45]3 years ago
7 0

Answer:

\left(\displaystyle -\frac{2}{5},\frac{4}{5}\right)

Step-by-step explanation:

<u>Proportions</u>

The coordinates of the point R are (-6,4) and the coordinates of the point S are (8,-4). We must find the coordinates of a point P(x,y) such that the ratio of segment RP to segment PS is 2/3. Let's find the coordinates separately. In the x-axis:

\displaystyle \frac{-6-x}{x-8}=\frac{2}{3}

Operating and rearranging

-18-3x=2x-16

Solving

\displaystyle x=-\frac{2}{5}

Now for the y-axis

\displaystyle \frac{4-y}{y+4}=\frac{2}{3}

Operating and rearranging

12-3y=2y+8

Solving

\displaystyle y=\frac{4}{5}

Thus, the point that partitions the segment in the ratio 2 to 3 is

\left(\displaystyle -\frac{2}{5},\frac{4}{5}\right)

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Use the Binomial expansion theorem to find and simplify each term.

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8 0
3 years ago
The diameter of a circle is 28 millimeters. What is the circle's area<br><br> Use 3.14 for ​.
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615.44 mm²

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Before finding the area of the circle, first, let us find the radius of the circle.

Given that,

diameter ⇒ 28 mm

Therefore,

<h3>d = 2r</h3>

28 = 2r

Divide both sides by 2.

14mm = radius

<u>                                             </u>

And now, let us find the area.

The formula to find the area of the circle is :

<h3>Area = π r²</h3>

Let us solve now.

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8 0
2 years ago
Jenna has at most $100 to spend on clothes. She wants to buy a pair of jeans for $29 and spend the rest on shirts. Each shirt co
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Answer:

5 shirts (read explanation)

Step-by-step explanation:

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8 0
3 years ago
While researching the cost of school lunches per week across the state, you use a sample size of 45 weekly lunch prices. The sta
Drupady [299]

We assume the lunch prices we observe are drawn from a normal distribution with true mean \mu and standard deviation 0.68 in dollars.


We average n=45 samples to get \bar{x}.


The standard deviation of the average (an experiment where we collect 45 samples and average them) is the square root of n times smaller than than the standard deviation of the individual samples. We'll write


\sigma = 0.68 / \sqrt{45} = 0.101


Our goal is to come up with a confidence interval (a,b) that we can be 90% sure contains \mu.


Our interval takes the form of ( \bar{x} - z \sigma, \bar{x} + z \sigma ) as \bar{x} is our best guess at the middle of the interval. We have to find the z that gives us 90% of the area of the bell in the "middle".


Since we're given the standard deviation of the true distribution we don't need a t distribution or anything like that. n=45 is big enough (more than 30 or so) that we can substitute the normal distribution for the t distribution anyway.


Usually the questioner is nice enough to ask for a 95% confidence interval, which by the 68-95-99.7 rule is plus or minus two sigma. Here it's a bit less; we have to look it up.


With the right table or computer we find z that corresponds to a probability p=.90 the integral of the unit normal from -z to z. Unfortunately these tables come in various flavors and we have to convert the probability to suit. Sometimes that's a one sided probability from zero to z. That would be an area aka probability of 0.45 from 0 to z (the "body") or a probability of 0.05 from z to infinity (the "tail"). Often the table is the integral of the bell from -infinity to positive z, so we'd have to find p=0.95 in that table. We know that the answer would be z=2 if our original p had been 95% so we expect a number a bit less than 2, a smaller number of standard deviations to include a bit less of the probability.


We find z=1.65 in the typical table has p=.95 from -infinity to z. So our 90% confidence interval is


( \bar{x} - 1.65 (.101),  \bar{x} + 1.65 (.101) )


in other words a margin of error of


\pm 1.65(.101) = \pm 0.167 dollars


That's around plus or minus 17 cents.




3 0
3 years ago
Read 2 more answers
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