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Nimfa-mama [501]
3 years ago
15

How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 95% confidence that

the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.
Mathematics
2 answers:
Oduvanchick [21]3 years ago
8 0

Answer:

61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.  

Step-by-step explanation:

zimovet [89]3 years ago
6 0

Answer:

61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.                

Step-by-step explanation:

Given : We want 95% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.

To find : How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters?

Solution :

At 95% confidence the z-value is z=1.96

The sample mean is within 3 minutes of the population mean i.e. margin of error is E=3 minutes

The population standard deviation is s=12 minutes

n is the number of sample

The formula of margin of error is given by,

E=\frac{s\times z}{\sqrt{n}}

Substitute the value in the formula,

3=\frac{12\times 1.96}{\sqrt{n}}

3=\frac{23.52}{\sqrt{n}}

\sqrt{n}=\frac{23.52}{3}

\sqrt{n}=7.84

Squaring both side,

n=61.4656

Therefore, 61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.

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Natali [406]

Answer:

254.5 cm²

Step-by-step explanation:

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area = 3.14159 × (9 cm)²

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4 0
2 years ago
A car is driving at 100 kilometers per hour. How far does it travel in 2 seconds?
Alisiya [41]

Answer:

\frac{1}{18}\ km  or  \frac{500}{9}\ m

Step-by-step explanation:

Remember that

1 hour=3,600 seconds

so

by using proportion

\frac{100}{3,600}\frac{km}{sec} =\frac{x}{2}\frac{km}{sec} \\ \\x=2*100/3,600\\ \\x=\frac{1}{18}\ km

Convert to meters

(1,000)*(\frac{1}{18})=\frac{500}{9}\ m

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3 years ago
For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelog
natita [175]

Answer:

The area of a parallelogram is 360 in.²

Step-by-step explanation:

Where DG = GH

GP = 12 in.

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∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)

Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH

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Hence, ∠BPA = 90° (Sum of interior angles of a triangle)

cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}

We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)

∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)

Hence AD = DG (Side length of isosceles triangle)

The bisector of ∠ADG is parallel to BH and will bisect AG at point Q

Hence ΔDAQ  ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP

Hence, AP = 3 × GP = 3 × 12 = 36

cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}

\angle GAB = cos^{-1} \left (\dfrac{36}{39}  \right )

∠GAB = 22.62°

cos(\angle GAB) =  \dfrac{36}{39} = \dfrac{12}{GH}

GH =  \dfrac{39}{36} \times {12}

GH = 13 in.

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GH = √(GP² + HP²)

∠DAB = 2 × 22.62° = 45.24°

The height of the parallelogram = AD × sin(∠DAB) =  13 × sin(45.24°)

The height of the parallelogram = 120/13 =  9.23 in.

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7 0
3 years ago
Read 2 more answers
What are the steps to solving this?
Archy [21]

Answer:

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Step-by-step explanation:

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x 8 = 192

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Hope this makes sense. If you would like, I can l1nk to a very useful website, or I can explain it further.

- profparis

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