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nadezda [96]
3 years ago
6

The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between (height) and (arm span) is shown

in the scatterplot below. The equation of the line of best fit modeling this relationship is given:
y=4.5+0.977x

Mike is 172 cm tall and George is 165 cm tall. Using the model, how many centimeters longer would we expect Mike's arm span to be than George's? Round your answer to the thousandths place.
Mathematics
1 answer:
sergeinik [125]3 years ago
6 0

Answer: Mike's arm span is 7.165 cm longer than the George's one.

Step-by-step explanation:

We have that the association between height and arm span is modeled by the equation

y = 4.5 + 0.977*x

where y is height and x is arm span.

Mike is 172 cm tall, so his arm span is:

172cm = 4.5 + 0.977*x

x = (172 - 4.5)/0.977 = 171.443 cm

and George is 165 cm tall, so his arm span is:

x = (165 - 4.5)/0.977 = 164.278 cm

Then the difference between their arm span is:

171.443cm - 164.278cm = 7.165 cm

So Mike's arm span is 7.165 cm longer than the George's one.

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A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and
nasty-shy [4]

Answer:

correct option is C)  2.8

Step-by-step explanation:

given data

string vibrates form =  8 loops

in water loop formed =  10 loops

solution

we consider  mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = \rho

case (1)  

when 8 loop form with 2 adjacent node is \frac{\lambda }{2}

so here

l = \frac{8 \lambda _1}{2}      ..............1

l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}

and we know velocity is express as

velocity = frequency × wavelength   .....................2

\sqrt{\frac{Tension}{mass\ per\ unit \length }}   =   f × \lambda_1

here tension = mg

so

\sqrt{\frac{mg}{\mu}}   =   f × \lambda_1     ..........................3

and

case (2)  

when 8 loop form with 2 adjacent node is \frac{\lambda }{2}

l = \frac{10 \lambda _1}{2}      ..............4

l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}

when block is immersed

equilibrium  eq will be

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T + v × \rho × g = mg

and

T = v × \rho - v × \rho × g    

from equation 2

f × \lambda_2 = f  × \frac{1}{5}  

\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}     .......................5

now we divide eq 5 by the eq 3

\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}

solve irt we get

1 - \frac{\rho _{stone}}{\rho _{water}}  = \frac{16}{25}

so

relative density \frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}

relative density = 2.78 ≈ 2.8

so correct option is C)  2.8

3 0
3 years ago
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