Ask question

Ask question

All categories

3 years ago

15

what are the coordinates of the point on the directed line segment (-1,-2) to (9,-10) that partitions the segment into a ratio o

f 3 to 1

1 answer:

Ymorist [56]3 years ago

4 0

Answer:

[6.5,-7.25]

Step-by-step explanation:

Given the partitioning ratio as 3:1

#Find the length of the x-coordinate and multiply by the ratio:

x length=9--1=10

=> $\frac{1}{4}\times 10=2.5$

#We subtract 2.5 from the x-max to get the point=9-2.5=6.5

#Find the length of the y-coordinate and multiply by the ratio:

x length=-9--2=-7

=> $\frac{1}{4}\times -7=-1.75$

#We subtract -1.75 from the y-max to get the point=-9--1.75=-7.25

Hence, the coordinates that partitions the segment into a ratio of 3 to 1 is [6.5,-7.25]

You might be interested in

James has a goal of saving $600 by the end of the month. He already has $150 in his bank account. He makes $25 an hour at his jo

Katyanochek1 [597]

Answer:

150+25x = 600

Step-by-step explanation:

Hope this helped!

7 0

2 years ago

N a small storage bin, there is a collection of Legos. There are 15 red bricks, 10 yellow bricks, 8 blue bricks and 7 green bric

olga nikolaevna [1]

Answer:

20 blue, 10 red, 40 yellow. There are no clues to how many black.

Step-by-step explanation:

3 0

3 years ago

What is x, y and z? show your work

Bas_tet [7]

Answer: z = -3 , y = 2 , x = 2

8 0

3 years ago

Principal=₹5000

puteri [66]

Answer:

512.5 and 5512.5

Step-by-step explanation:

p=5000,R=5%,T=3 comppund interest=p (1+R÷100)-1=5000×0.1025=512.5 again,amount=5000×1.1025=5512.5

8 0

2 years ago

At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen

guajiro [1.7K]

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

$p_1 = \frac{20}{100} = 0.2$

$s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04$

p2 -> 1997

10 out of 100, so:

$p_2 = \frac{10}{100} = 0.1$

$s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03$

Distribution of p1 – p2:

$p = p_1 - p_2 = 0.2 - 0.1 = 0.1$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05$

Confidence interval:

$p \pm zs$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower bound of the interval is:

$p - zs = 0.1 - 1.645*0.05 = 0.01775
$

The upper bound of the interval is:

$p + zs = 0.1 + 1.645*0.05 = 0.18225
$

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

6 0

3 years ago