MATHEMATICS COLLEGE

Find the distance between two points A (-2,-3) B (6,8)

Answers

Answer 1

Answer:

Answer:

√185 units.

Step-by-step explanation:

To find the distance between two points, A (-2, -3) and B (6, 8), you can use the distance formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

In this formula:

(x₁, y₁) represents the coordinates of point A (-2, -3).

(x₂, y₂) represents the coordinates of point B (6, 8).

Now, plug the values into the formula:

Distance = √[(6 - (-2))² + (8 - (-3))²]

Distance = √[(6 + 2)² + (8 + 3)²]

Distance = √[(8)² + (11)²]

Distance = √[64 + 121]

Distance = √185

So, the distance between points A (-2, -3) and B (6, 8) is √185 units.

Related Questions

Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions. (a) How many ways can the letters of the word DANCER be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with elements. So the answer is . (b) How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit? (c) How many ways can the letters of the word DANCER be arranged in a row if the letters NCE must remain together (in order) as a unit?
If f(x) = 2x – 5 and g(x) = x +4, then f(g(2)) =
Yolanda is preparing a liquid fertilizer that she will use on her lawn. she mixes 4 tablespoons of liquid fertilzer with 6 gallons of water. using this ratio, how many gallons of water should be mixed with each tablespoon of liquid fertilizer?A. 1.5 gallons B. 2.0 gallons C. 4.6 gallons D. 5.0 gallons E. 6.6 gallons
A basket of fruit contains 4 bananas, 3 apples, and 5 oranges. You intend to draw a piece of fruit from the basket, keep it, and then draw a 2nd piece of fruit from the basket. What is the probability of selecting two oranges in a row from the basket if you are blindfolded?
Perform the indicated operations. Write answer in descending order.Add -3x, 5x + y, and 7x - 8 - 3y

-14<7x<21 solve the inequality and graph the solution

Answers

To solve, divide by 7.
-2 < x < 3

The graph is a number line with open circles at -2 and 3 and a solid line between them.

Please answer question 10 and 11 please

Answers

Answer:

d7-dx=(20x|x-3|+40)x x-3 (|x-3+2)x| x-3|

Step-by-step explanation:

Hope this helps :D

6.3% of the 6,540,000 Indiana residents were listed as Hispanic or Latino in 2012, how many people would this be?

Answers

Answer:

412020

Step-by-step explanation:

It is given that,

6.3% of the 6,540,000 Indiana residents were listed as Hispanic or Latino in 2012. We need to find the no of people for this.

Using the concept of percentage as follows :

$(6.3)/(100)* 6540000 =412020$

Hence, there would be 412020 people.

Solve for x x/10+5=−1

x=

Answers

Answer:

x=-60

Step-by-step explanation:

You solve for x by simplifying both sides of the equation, then isolating the variable.

Suppose that, from measurements in a microscope, you determine that a certain layer of graphene covers an area of 1.60μm2. Convert this to square meters.

Answers

Answer:

1.60×10^-12 m^2

Step-by-step explanation:

The prefix μ stands for "micro-", which means 10^-6. So, 1 micro-meter is ...

1 μm = 10^-6 m

A square micrometer is then ...

(1 μm)^2 = (10^-6 m)^2 = 10^-12 m^2

1.6 of them is ...

1.6 μm^2 = 1.6×10^-12 m^2

The inside diameter of a randomly selected piston ring is a randomvariable with mean value 12 cm and standard devtiation of .04cm. a. If Xbar is the sample mean diameter form a random sample of=16 rings, where is the sampling distrbution of Xbar centered andwhat is the standard deviation of the Xbar distribution?

b. Answer the questions above for a sample of size n=64

c.find the probability that the average diameter of pistonrings from a sample size 16 is more than 11.95cm

d. For which of the above two random saples is Xbar morelikely to be within .01cm of 12cm? Explain.

Answers

Using the normal distribution and the central limit theorem, it is found that:

a) The sampling distribution is approximately normal,centered at 12 cm and with a standard deviation of 0.01 cm.

b) The sampling distribution is approximately normal,centered at 12 cm and with a standard deviation of 0.005 cm.

c) 100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm.

d) Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

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 $s = (\sigma)/(√(n))$ .

In this problem:

Mean of 12 cm, thus $\mu = 12$
Standard deviation of 0.04 cm, thus $\sigma = 0.04$ .

Item a:

Sample of 16, thus $n = 16$ and $s = (0.04)/(√(16)) = 0.01$

The sampling distribution is approximately normal,centered at 12 cm and with a standard deviation of 0.01 cm.

Item b:

Sample of 64, thus $n = 64$ and $s = (0.04)/(√(64)) = 0.005$

The sampling distribution is approximately normal,centered at 12 cm and with a standard deviation of 0.005 cm.

Item c:

This probability is 1 subtracted by the p-value of Z when X = 11.95, thus:

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem:

$Z = (X - \mu)/(s)$

$Z = (11.95 - 12)/(0.01)$

$Z = -5$

$Z = -5$ has a p-value of 0.

1 - 0 = 1.

100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm.

Item d:

Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.

A similar problem is given at brainly.com/question/24663213

Answer:

The answer is below

Step-by-step explanation:

Given that:

mean value (μ) = 12 cm and standard deviation (σ) = 0.04 cm

a) Since a random sample (n) of 16 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:

$\mu_x=\mu=12\ cm\n\sigma_x=(\sigma)/(√(n) )=(0.04)/(√(16) )=0.01$

The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.01 cm

b) Since a random sample (n) of 64 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:

$\mu_x=\mu=12\ cm\n\sigma_x=(\sigma)/(√(n) )=(0.04)/(√(64) )=0.005\ cm$

The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.005 cm

c) n = 16 and the raw score (x) = 11.95 cm

The z score equation is given by:

$z=(x-\mu_x)/(\sigma_x) =(x-\mu)/(\sigma/√(n) ) \nz=(11.95-12)/(0.04/√(16) )\n z=-5$

P(x > 11.95 cm) = P(z > -5) = 1 - P(z < -5) = 1 - 0.000001 ≅ 1 ≅ 100%

d) for n = 64, the standard deviation is 0.01 cm, therefore it is more likely to be within .01cm of 12cm

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