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Ray Of Light [21]
3 years ago
14

The heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. men the same

age have heights that are also approximately normal, with mean height 69.3 inches and standard deviation 2.8 inches. what is the z-score for a man 72 inches tall? round your answer to 3 decimal places.
Mathematics
1 answer:
Serjik [45]3 years ago
3 0
The number of standard deviations from the mean for a man 72 inches tall is
  Z = (72 -69.3)/2.8 ≈ 0.964
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Amanda leaned a 15-foot ladder against the top of her house so she could get on the roof, which is 12 feet from the ground.
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Using the Pythagorean theorem:

15^2 = 12^2 + X^2

225 = 144 + x^2

X^2 = 225 - 144

x^2 = 81

x = √81

x = 9


The distance is 9 feet.

The answer is A.

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Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14
PilotLPTM [1.2K]

Answer:

<em>Carbon-14 will take 19,035 years to decay to 10 percent.</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

N(t)=N_{0}e^{-\lambda t}

Where:

No  = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

\lambda     = The decay constant.

One important parameter related to radioactive decay is the half-life:

\displaystyle t_{1/2}=\frac {\ln(2)}{\lambda }

If we know the value of the half-life, we can calculate the decay constant:

\displaystyle \lambda=\frac {\ln(2)}{ t_{1/2}}

Carbon-14 has a half-life of 5,730 years, thus:

\displaystyle \lambda=\frac {\ln(2)}{ 5,730}

\lambda=0.00012097

The equation of the remaining quantity of Carbon-14 is:

N(t)=N_{0}e^{-0.00012097\cdot t}

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

0.10N_o=N_{0}e^{-0.00012097\cdot t}

Simplifying:

0.10=e^{-0.00012097\cdot t}

Taking logarithms:

ln 0.10=-0.00012097\cdot t

Solving for t:

\displaystyle t=\frac{log 0.10}{-0.00012097}

t\approx 19,035\ years

Carbon-14 will take 19,035 years to decay to 10 percent.

6 0
3 years ago
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Ray Of Light [21]
Roughly about 3:17 . Hope I helped!
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3 years ago
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