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yawa3891 [41]
2 years ago
7

Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.2cm and a standard deviation o

f 0.38cm. Using the empirical rule, what percentage of the apples have diameters that are no more than 7.96cm
Physics
1 answer:
Svet_ta [14]2 years ago
5 0

Answer:

97.5%

Explanation:

By the empirical rule (68-95-99.7),

  1. 68% of data are within <em>μ </em>- <em>σ</em> and <em>μ </em>+ <em>σ</em>
  2. 95% of data are within <em>μ </em>- 2<em>σ</em> and <em>μ </em>+ 2<em>σ</em>
  3. 99.7% of data are within <em>μ </em>- 3<em>σ</em> and <em>μ </em>+ 2<em>σ</em>

<em>σ </em> and <em>μ</em> are the standard deviation and the mean respectively.

From the question,

<em>μ</em> = 7.2 cm

<em>σ</em> = 0.38 cm

7.96 = 7.2 + (<em>n</em> × 0.38)

<em>n</em> = 2

Hence, 7.96 represents <em>μ </em>+ 2<em>σ</em>.

P(X < <em>μ </em>+ 2<em>σ</em>) = P(X < <em>μ</em>) + P(<em>μ</em> < X < <em>μ </em>+ 2<em>σ</em>)

P(X < <em>μ</em>) is the percentage less than the mean = 50%.

P(<em>μ</em> < X < <em>μ </em>+ 2<em>σ</em>) is half of P(<em>μ </em>- 2<em>σ</em> < X < <em>μ </em>+ 2<em>σ</em>) = 95% ÷ 2 = 47.5%.

Considering this, for apples that are no more than 7.96 cm,

P(X < 7.96) = P(X < 7.2) + P(7.2 < X < 7.96) = 50% + 47.5% = 97.5%

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Explanation:

what is gravity made of?

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2 years ago
Falling raindrops frequently develop electric charges. Does this create noticeable forces between the droplets? Suppose two 1.8
umka2103 [35]

Answer:

a) F=2.048\times 10^{-7}\ N

b) a=0.1138\ m.s^{-2}

Explanation:

Given:

  • mass of raindrops, m=1.8\times 10^{-6}\ kg
  • charge on the raindrops, q=+21\times 10^{-12}\ C
  • horizontal distance between the raindrops, r=0.0044\ m

A)

<u>From the Coulomb's Law the force between the charges is given as:</u>

F=\frac{1}{4\pi.\epsilon_0} .\frac{q_1.q_2}{r^2}

we have:

\epsilon_0=8.854\times 10^{-12}\ C^2.N^{-1}.m^{-2}

<em>Now force:</em>

F=\frac{1}{4\pi\times 8.854\times 10^{-12}} .\frac{21\times 10^{-12}\times 21\times 10^{-12}}{0.0044^2}

F=2.048\times 10^{-7}\ N

B)

<u>Now the acceleration on the raindrops due to the electrostatic force:</u>

a=\frac{F}{m}

a=\frac{2.048\times 10^{-7}}{1.8\times 10^{-6}}

a=0.1138\ m.s^{-2}

7 0
3 years ago
Read 2 more answers
Can somebody please help?
DedPeter [7]

Answer:

Im not sure

Explanation:

I don't take physics cuz im in 9th grade. so. idk but I will find out and come back with an answer.

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3 years ago
I need help with questions 6-8. Thank you!! Image is attached
Digiron [165]

6) b) 2.7 m/s

7) b) DCA

8) b) B

Explanation:

6)

In a displacement-time plot, the slope of the line is given by

m=\frac{\Delta y}{\Delta x}

where

\Delta y is the change in the y-variable, so it is the displacement

\Delta x is the change in the x-variable, so it is the time elapsed

So, the slope of the line in a displacement-time plot corresponds to the velocity:

v=m=\frac{d}{t}

Therefore, to find the velocity of the object, we have to estimate the slope of its curve.

To estimate the velocity of object B, we have to estimate the slope of the line tangent to curve B at 10 seconds.

By doing an estimate by eye, we see that the displacement of object B changes from -10 m to 0 m when time increases from about 8 s to 12 s, so the velocity is about:

v=\frac{0-(-10)}{12-8}\sim 2.5 m/s

So the closest option is b) 2.7 m/s.

7)

As we said in part A, the velocity of each object is given by the slope of each curve.

Therefore:

- The steeper the curve, the higher the velocity

- The less steep the curve, the lower the velocity

From the graph, we observe that, among A, C and D:

- Curve D has the largest slope (in absolute value), so object D has the largest magnitude of the velocity

- Curve C is less steep than curve C, so object C has the second largest magnitude of velocity

- Curve A is flat, so the slope is zero, so its velocity is zero

So, from greatest magnitude to lowest magnitude of velocity, we have:

b) DCA

8)

In the graph, the overall displacement of each object is given by the change in the y-variable, \Delta y.

This means that the object with largest displacement is the object whose curve has the largest variation in y.

From the graph, we see that:

- Object b has the largest variation in y,  from -15 m to 30 m, so

\Delta y=30-(-15)=45 m

- Then, object D has the second largest displacement (in magnitude), from -15 m to 25 m,

|\Delta y| = 25 -(-15)=40 m

Finally, object C has displacement

\Delta y = 20-(-5)=25 m

While object A has displacement zero. Therefore, the correct option is

b) B

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3 years ago
The rotating loop in an AC generator is a square 10.0 cm on each side. It is rotated at 60.0 Hz in a uniform field of 0.800 TO.
Genrish500 [490]

Answer:

Explanation:

Given a square side loop of length 10cm

L=10cm=0.1m

Then, Area=L²

Area=0.1²

Area=0.01m²

Given that, frequency=60Hz

And magnetic field B=0.8T

a. Flux Φ

Flux is given as

Φ=BA Sin(wt)

w=2πf

Φ=BA Sin(2πft)

Φ=0.8×0.01 Sin(2×π×60t)

Φ=0.008Sin(120πt) Weber

b. EMF in loop

Emf is given as

EMF= -N dΦ/dt

Where N is number of turns

Φ=0.008Sin(120πt)

dΦ/dt= 0.008×120Cos(120πt)

dΦ/dt= 0.96Cos(120πt)

Emf=-NdΦ/dt

Emf=-0.96NCos(120πt). Volts

c. Current induced for a resistance of 1ohms

From ohms law, V=iR

Therefore, Emf=iR

i=EMF/R

i=-0.96NCos(120πt) / 1

i=-0.96NCos(120πt) Ampere

d. Power delivered to the loop

Power is given as

P=IV

P=-0.96NCos(120πt)•-0.96NCos(120πt)

P=0.92N²Cos²(120πt) Watt

e. Torque

Torque is given as

τ=iL²B

τ=-0.96NCos(120πt)•0.1²×0.8

τ=-0.00768NCos(120πt) Nm

8 0
2 years ago
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