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gtnhenbr [62]
3 years ago
9

The endpoint of MP are M(2,1) and P(14,10). If point K partitions MP in aratio of MK:KP=3:2, what are the coordinates of K?

Mathematics
2 answers:
maks197457 [2]3 years ago
8 0

Answer:  The required co-ordinates of he point K are (9.2, 7).

Step-by-step explanation:  Given that the the endpoint of MP are M(2,1) and P(14,10) and the point K partitions MP in the ratio of MK : KP = 3 : 2.

We are to find the co-ordinates of point K.

We know that

the co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by

\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{2}\right).

For the given division, m : n = 3 : 2.

Therefore, the co-ordinates of the point K are

\left(\dfrac{3\times14+2\times2}{3+2},\dfrac{3\times10+2\times1}{3+2}\right)\\\\\\=\left(\dfrac{42+4}{5},\dfrac{30+2}{5}\right)\\\\=\left(\dfrac{46}{5},\dfrac{35}{5}\right)\\\\=(9.2,7).

Thus, the required co-ordinates of the point K are (9.2, 7).

Paha777 [63]3 years ago
4 0

2(2,1)(14,10)

(4,2) - (14,10)= (-10, -8)

The coordinates of K are (-10, -8).

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The speeds of vehicles traveling on a highway are normally distributed with an unkown population mean and standard deviation. A
Maksim231197 [3]

Answer:

The 90% confidence interval would be given by (60.09;69.91)    

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Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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The confidence interval for the mean is given by the following formula:

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Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,10)".And we see that t_{\alpha/2}=1.81

Now we have everything in order to replace into formula (1):

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65+1.81\frac{9}{\sqrt{11}}=69.91

So on this case the 90% confidence interval would be given by (60.09;69.91)    

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

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