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DerKrebs [107]
3 years ago
15

According to a survey conducted by Deloitte in 2017, 0.4702 of U.S. smartphone owners have made an effort to limit their phone u

se in the past. In a sample of 54 randomly selected U.S. smartphone owners, what is the probability that between 22 and 29 (inclusively) will have attempted to limit their cell phone use in the past?
1) 0.0241.
2) 0.1703.
3) 0.8779.
4) 0.0483.
5) 0.1221.
Mathematics
1 answer:
musickatia [10]3 years ago
5 0

Answer: 0.628

Step-by-step explanation:

Probability of U.S. smartphone owners have made an effort to limit their phone use in the past : p = 0.4702

Sample size : n= 54

Mean : \mu =(54)(0.4702)=25.39

Standard deviation:

\sigma=\sqrt{(54)(0.4702)}=\sqrt{25.39}\\\\\approx5.039

The probability that between 22 and 29 (inclusively) will have attempted to limit their cell phone use in the past will be :

P(22\leq x\leq29)=P(21

Hence, the required probability = 0.628

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Answer:

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2 years ago
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bazaltina [42]
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You can draw a right triangle with these values. (see attached)
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Let's convert (4, 16°) to Cartesian coordinates.

Note that since our angle is acute, (in Quadrant I) our sine and cosine will both be positive, as you should be able to derive from the unit circle, where cosine is represented as an x value and sine is represented as a y value.

cosine = adjacent / hypotenuse
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cos(16°) = x/4
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sine = oppsite / hypotenuse
sinθ = y/r
sin(16°) = y/4
4sin(16°) = y ≈ 1.10254942327<span>

So (4, 16°) </span>⇒ (3.84504678375, 1.10254942327).

Let's convert (-2, 177°)  to Cartesian coordinates.
Whenever you have a negative radius, that means to put the point opposite where it would have been if it had a positive radius. (see attached)

In that case, we can essentially add 180° to our current 177° to the same effect. That means that (-2, 177°) = (2, 357°).

Note that since our angle is in Quadrant IV, our cosine will be positive, but our sine will be negative. (as derived from the unit circle) We don't have to worry about this since our calculator figures this for us, but you should pay attention to it if you are converting from Cartesian to polar.

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sine = opposite / hypotenuse
sinθ = y/r
sin(357°) = y/2
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So (-2, 177°) ⇒ (1.99725906951, -0.10467191248).

Now we must use the distance formula with our two points.
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
d\approx\sqrt{(1.99725906951-3.84504678375)^2+(-0.10467191248-1.10254942327)^2}
d\approx\sqrt{-1.84778771^2+-1.20722134^2}
d\approx\sqrt{3.41431942+1.45738336}
d\approx\sqrt{4.87170278}
\boxed{d\approx2.20719342}

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Solve through substitution<br><br> –3x–8y=20<br><br> y=5x+19<br><br> Point of intersection, please
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Answer:

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