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3 years ago

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)

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.

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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X =65$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=9 represent the sample standard deviation

n=11 represent the sample size

2) Confidence interval

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=11-1=10$

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):

$65-1.81\frac{9}{\sqrt{11}}=60.09$

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

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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3 years ago

I need help guys please help me !

Arisa [49]

S=49p+7*9p=(49+63)p=112P
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3 years ago

Whats 1 and 2/3 + 1 and 5/6

Dima020 [189]

1 2/3 + 1 5/6

We’ll start by converting the 2/3 to 6ths so we have a common denominator.

Look at the denominator first. 3 x 2 is 6, so we need to multiply the numerator by 2 as well. 2/3 = 4/6.

So we have 1 4/6 + 1 5/6 = 2 9/6
But you know they’ll want you to reduce that so it’s 3 3/6...or 3 1/2.

Let me know where you have questions.

7 0

3 years ago

Read 2 more answers

(1, 4); slope = -2 write the linear equation in slope intercept form given

jeka57 [31]

Answer:

y=-2x+2

Step-by-step explanation:

The slope is -2x, meaning that the y-intercept can be found by working backwards from the given point. If the y value of the point is 4, subtracting 2 to get you to the point (0, 2) would provide the y-intercept.

Slope Intercept form is y=mx+b (m is the slope, x is the entered value, b is the y intercept)

3 0

3 years ago

12 Rose and Haydn share £250 in the ratio 2:3

dalvyx [7]

Answer:

Amount = £37

Step-by-step explanation:

Let Rose be represented by R.

Let Haydn be represented by H.

Given the following data;

Total amount = £250

Ratio of R:H = 2:3 = 2 + 3 = 5

To find how much Rose earned;

R = 2/5 * 250

R = 500/5

R = £100.

For Haydn;

H = 3/5 * 250

H = 750/5

H = £150

Next, we calculate the amount Haydn gave to charity;

Percent = 42% = 42/100 = 0.42

H = 0.42 * 150

H = £63

To find how much more Rose gave to charity than Haydn;

Amount = R - H

Amount = 100 - 63

Amount = £37

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3 years ago