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Lilit [14]
3 years ago
9

Please help! Thank you

Mathematics
1 answer:
Vanyuwa [196]3 years ago
5 0

Answer:

x = 82°

y = 59°

z = 39°

Step-by-step explanation:

∠x = 1/2(134° + 30°) = 82°

∠z = 180° - 59° - 82° = 39°

arc DF = 2(39°) = 78°

arc DB + arc DF = 134° + 78° = 212°

draw a diameter down from point B to the opposite side of the circle, call that point P:

arc BDP = 180°

(arc BDF) 212° - 180° = 32° (arc PF)

∠PBG = 1/2(32°) = 16°

∠DEB = 1/2(134°) = 67°

∠DBE = 180° - 59° - 67° = 54°

(∠DBE) 54° - (∠z) 39° + (∠PBG) 16° = (∠PBE) 31°

y = 90°- 31° = 59°

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The number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.
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Answer:

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Step-by-step explanation:

We are given that the number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.

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<em>Let X = number of hours spent per week on household chores</em>

So, assuming data follows normal distribution; X ~ N(\mu=28,\sigma^{2}=7^{2})

The z score probability distribution for sample mean is given by;

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So, probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is given by =P(\bar X > 26.75 hours)

    P(\bar X > 26.75 hours) = P( \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{26.75-28}{\frac{7}{\sqrt{49} } } ) = P(Z > -1.25) = P(Z < 1.25)

                                                                     = 0.89435  {using z table}

Therefore, probability that the mean hours spent per week on household chores is more than 26.75 is 0.89435.

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