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Nostrana [21]
3 years ago
7

When Hailey commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 21 minutes and a

standard deviation of 3.5 minutes. Out of the 211 days that Hailey commutes to work per year, how many times would her commute be between 19 and 26 minutes, to the nearest whole number?
Mathematics
1 answer:
miskamm [114]3 years ago
8 0

Answer: 135 days

Step-by-step explanation:

Since the amount of time it takes her to arrive is normally distributed, then according to the central limit theorem,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 21 minutes

σ = 3.5 minutes

the probability that her commute would be between 19 and 26 minutes is expressed as

P(19 ≤ x ≤ 26)

For (19 ≤ x),

z = (19 - 21)/3.5 = - 0.57

Looking at the normal distribution table, the probability corresponding to the z score is 0.28

For (x ≤ 26),

z = (26 - 21)/3.5 = 1.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.92

Therefore,

P(19 ≤ x ≤ 26) = 0.92 - 28 = 0.64

The number of times that her commute would be between 19 and 26 minutes is

0.64 × 211 = 135 days

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Answer:

4.0541

Step-by-step explanation:

I don't know if this is correct but this is what I got.

You would take the error and divide it by the theoretical value and then multiply that by 100.

7.7 - 7.4 = 0.3

0.3 ÷ 7.4 = 0.04054054

0.04054054 x 100 = 4.05405405 (simplify) = 4.0541%

Hope I helped in any way

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2 years ago
It takes Emmanuel 20 minutes to walk to school. It takes Liah 80% as long to walk to school. How long does it take Liaqh to walk
77julia77 [94]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
I do 10 - 8 for this, right...?
natima [27]
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3 years ago
A 10-pound block of ice melts at a rate of 3% per hour. Find the weight of the block of ice after 1 day.
mylen [45]

Answer:

The weight of the block of ice after 1 day is of 4.81 pounds.

Step-by-step explanation:

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The equation that models an amount after t hours, subject to exponential decay, is given by:

A(t) = A(0)(1 - r)^t

In which A(0) is the initial amount and r is the decay rate, as a decimal.

A 10-pound block of ice melts at a rate of 3% per hour.

This means that A(0) = 10, r = 0.03

So

A(t) = A(0)(1 - r)^t

A(t) = 10(1 - 0.03)^t

A(t) = 10(0.97)^t

Find the weight of the block of ice after 1 day.

One day has 24 hours, so this is A(24).

A(24) = 10(0.97)^{24} = 4.81

The weight of the block of ice after 1 day is of 4.81 pounds.

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2 years ago
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Answer:

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Step-by-step explanation:

We are given he following information in the question:

y(t)=43t-23t^{2}

B) Instantaneous Velocity at t = 1

y(1) = 43(1)-23(1)^2 = 20

A) Formula:

Average velocity =

\displaystyle\frac{\text{Displacement}}{\text{Time}}

1) 0.01

y(1 + 0.01)=y(1.01) = 43(1.01)-23(1.01)^{2} = 19.9677\\\\\text{Average Velocity} = \dfrac{y(1.01)-y(1)}{1.01-1} =\dfrac{19.9677-20}{1.01-1}= \dfrac{-0.0323}{0.01} = -3.230000 \text{feet per second}

2) 0.005 s

y(1 + 0.005)=y(1.005) = 43(1.005)-23(1.005)^{2} = 19.984425\\\\\text{Average Velocity} = \dfrac{y(1.005)-y(1)}{1.005-1} =\dfrac{19.984425-20}{1.005-1} = -3.1150000 \text{feet per second}

3) 0.002 s

y(1 + 0.002)=y(1.002) = 43(1.002)-23(1.002)^{2} = 19.993908\\\\\text{Average Velocity} = \dfrac{y(1.002)-y(1)}{1.002-1} =\dfrac{19.993908-20}{1.002-1} = -3.0460000 \text{feet per second}

4) 0.001 s

y(1 + 0.001)=y(1.001) = 43(1.001)-23(1.001)^{2} = 19.996977\\\\\text{Average Velocity} = \dfrac{y(1.001)-y(1)}{1.001-1} =\frac{19.996977-20}{1.001-1} = -3.0230000 \text{feet per second}

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