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Nesterboy [21]
3 years ago
9

Solve x^3+3x^2-23x-20=0

Mathematics
1 answer:
adoni [48]3 years ago
5 0

Hello from MrBillDoesMath!

Answer:

x = 4

x  =  ( -7 + sqrt(29)) /2

x =   ( -7 - sqrt(29)) /2

Discussion:

x^3+3x^2-23x-20 factors as (x - 4) (x^2 + 7 x + 5) so x =4 is one root

The roots of the quadratic factor, x^2 + 7x + 5, can be found using the quadratic formula where a = 1, b = 7, and c = 5

x =  (  -b +\- sqrt(b^2-4ac)) / 2a

x = ( -7 +\- sqrt( 7^2 - 4*1*5) ) / (2*1) =>

x =  ( -7 +\- sqrt (49-20) ) /  2 =>


The "+" root:    ( -7 + sqrt(29)) /2

The "-" root:    ( -7 - sqrt(29)) /2




Regards,  

MrB


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marusya05 [52]

Hello from MrBillDoesMath!

Answer:   21

Discussion:

g(3) = 3^2 -2 = 9 -2 = 7   =>

f(g(3)) = f ( 7) = 2(7) + 7 = 14 + 7 = 21

Thank you,

MrB


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3 years ago
Which unit rate corresponds to the proportional relationship shown in the graph
Ray Of Light [21]

Answer:

5/4 8.10.............0.0 5=7=9

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2 years ago
. 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!!!

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