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loris [4]
3 years ago
11

Find midpoint of PQ with endpoints P (0,2) and Q (6,-2)

Mathematics
1 answer:
agasfer [191]3 years ago
6 0

Answer:

(3, 0)

Step-by-step explanation:

The easiest way to do this problem is to average the x-coordinates and y-coordinates.

So,  (0 + 6) / 2 = 6/2 = 3 = x   and (2 - 2)/2 = 0/2 = 0 = y

Therefore, the midpoint is (3,0)

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. upper left chamber is enlarged, the risk of heart problems is increased. The paper "Left Atrial Size Increases with Body Mass
Sonbull [250]

Answer:

Part 1

(a) 0.28434

(b) 0.43441

(c) 29.9 mm

Part 2

(a) 0.97722

Step-by-step explanation:

There are two questions here. We'll break them into two.

Part 1.

This is a normal distribution problem healthy children having the size of their left atrial diameters normally distributed with

Mean = μ = 26.4 mm

Standard deviation = σ = 4.2 mm

a) proportion of healthy children have left atrial diameters less than 24 mm

P(x < 24)

We first normalize/standardize 24 mm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (24 - 26.4)/4.2 = -0.57

The required probability

P(x < 24) = P(z < -0.57)

We'll use data from the normal probability table for these probabilities

P(x < 24) = P(z < -0.57) = 0.28434

b) proportion of healthy children have left atrial diameters between 25 and 30 mm

P(25 < x < 30)

We first normalize/standardize 25 mm and 30 mm

For 25 mm

z = (x - μ)/σ = (25 - 26.4)/4.2 = -0.33

For 30 mm

z = (x - μ)/σ = (30 - 26.4)/4.2 = 0.86

The required probability

P(25 < x < 30) = P(-0.33 < z < 0.86)

We'll use data from the normal probability table for these probabilities

P(25 < x < 30) = P(-0.33 < z < 0.86)

= P(z < 0.86) - P(z < -0.33)

= 0.80511 - 0.37070 = 0.43441

c) For healthy children, what is the value for which only about 20% have a larger left atrial diameter.

Let the value be x' and its z-score be z'

P(x > x') = P(z > z') = 20% = 0.20

P(z > z') = 1 - P(z ≤ z') = 0.20

P(z ≤ z') = 0.80

Using normal distribution tables

z' = 0.842

z' = (x' - μ)/σ

0.842 = (x' - 26.4)/4.2

x' = 29.9364 = 29.9 mm

Part 2

Population mean = μ = 65 mm

Population Standard deviation = σ = 5 mm

The central limit theory explains that the sampling distribution extracted from this distribution will approximate a normal distribution with

Sample mean = Population mean

¯x = μₓ = μ = 65 mm

Standard deviation of the distribution of sample means = σₓ = (σ/√n)

where n = Sample size = 100

σₓ = (5/√100) = 0.5 mm

So, probability that the sample mean distance ¯x for these 100 will be between 64 and 67 mm = P(64 < x < 67)

We first normalize/standardize 64 mm and 67 mm

For 64 mm

z = (x - μ)/σ = (64 - 65)/0.5 = -2.00

For 67 mm

z = (x - μ)/σ = (67 - 65)/0.5 = 4.00

The required probability

P(64 < x < 67) = P(-2.00 < z < 4.00)

We'll use data from the normal probability table for these probabilities

P(64 < x < 67) = P(-2.00 < z < 4.00)

= P(z < 4.00) - P(z < -2.00)

= 0.99997 - 0.02275 = 0.97722

Hope this Helps!!!

7 0
3 years ago
I need help on this I will give brainlist help it will mean a lot this is my last math problem help me!​
deff fn [24]

Answer:answer is b

Step-by-step explanation: Just makes since

6 0
3 years ago
A Toblerone candy bar is in the shape of a triangular prism. The area of the base is 3 in 2and the height of the prism is 5 in.
Mrac [35]

Answer:

  • 15 in³

Step-by-step explanation:

<u>Volume of the prism:</u>

  • V = Bh, where B- area of base, h- height

<u>Given:</u>

  • B = 3 in²
  • h = 5 in

<u>Volume is:</u>

  • V = 3*5 = 15 in³
8 0
3 years ago
There are 180 days in school year and you get 3 assignments per day. How many total assignments do you get in 1 school year
m_a_m_a [10]

Answer:

260 assignments in a school year

Step by Step:

There are 180 days in a school year and you do 3 assignments per day you multiple 180 and 3

6 0
3 years ago
Mrs. Carter puts a variety of wrapped chocolate candies into a bag. There are 5 silver-wrapped candies, 1 purple-wrapped candy,
Fantom [35]

Answer:

a

Step-by-step explanation:

it won't be 5

nor 60

and it won't be 15

3 0
3 years ago
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