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ehidna [41]
4 years ago
13

The average age for a person getting married for the first time is 26 years (U.S. News and World Report, June 6, 1994). Assume t

he ages for first marriages have a normal distribution with a standard deviation of four years.90% of people getting married for the first time get married before what age?
Mathematics
1 answer:
leva [86]4 years ago
5 0

Answer: 90% of people getting married for the first time get married before age of 31.13.

Step-by-step explanation:

Given : The average age (\mu) for a person getting married for the first time is 26 years (U.S. News and World Report, June 6, 1994).

We assume that  the ages for first marriages have a normal distribution with a standard deviation (\sigma) of 4 years.

Let x be the age before that 90% of people getting married for the first time get married.

From z-table , the value corresponds to p-value of 0.90 is 1.28155.

Formula : z=\dfrac{x-\mu}{\sigma}

1.28155=\dfrac{x-26}{4}\\\\ x-26=4\times1.28155\\\\ x-26=5.1262\\\\ x=5.1262+26=31.1262\approx31.13

Hence, 90% of people getting married for the first time get married before age of 31.13.

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The length width and height of a rectangular solid are 8,4,1 respectively what is the length of the longest line segment whose e
LUCKY_DIMON [66]

Answer:

9 units

Step-by-step explanation:

Given

Length = 8

Width = 4

Height = 1

Required

Determine the length of the longest segment

To do this, we use:

Longest = \sqrt{Length^2 + Width^2 + Height^2}

So, we have:

Longest = \sqrt{8^2 + 4^2 + 1^2}

Longest = \sqrt{64 + 16 + 1}

Longest = \sqrt{81}

Take positive square root

Longest = 9

<em>Hence, the length of the longest segment is 9 units</em>

3 0
3 years ago
A population of rabbits triples every month. The population starts with two rabbits. How many rabbits are there after three mont
yanalaym [24]
If it triples every month, we would multiply last month's by 3. Sooo...
Month 1: 3 rabbits.
Month 2: 9 rabbits.
Month 3: 27 rabbits.
Month 4: 81 rabbits.
We could keep going, but you're looking for after 3 months, which the answer would be 27 rabbits.

I hope this was helpful! :>
5 0
3 years ago
The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take f
Alexeev081 [22]

Answer:

It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Step-by-step explanation:

We can write a half-life function to model our function.

A half-life function has the form:

\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}

Where <em>A₀</em> is the initial amount, <em>t</em> is the time that has passes (in this case seconds), <em>d</em> is the half-life, and <em>A</em> is the amount after <em>t</em> seconds.

Since the half-life of the element is 30 seconds, <em>d</em> = 30. Our initial sample has nine grams, so <em>A₀</em> is 9. Substitute:

\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}

We want to find the time it will take for the element to decay to 0.72 grams. So, we can let <em>A</em> = 0.72 and solve for <em>t: </em>

<em />\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}<em />

Divide both sides by 9:

\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}

We can take the natural log of both sides:

\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)

By logarithm properties:

\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)

Solve for <em>t: </em>

<em />\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}<em />

<em />

So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

5 0
3 years ago
HELP!!!!!!!!!!!!!
natita [175]
A(x) = x^2 - 18x + 81
A(x) = (x - 9)(x - 9)
A(x) = (x - 9)^2

the length of the side is (x - 9)
7 0
3 years ago
HELP ASAP plz!! Find the value of each variable
Mamont248 [21]

Answer:y=12.1244

X=24.2487

Step-by-step explanation:

SOHCATOA or you could have used Pythagorean theorem after you found one of the sides, but I find that it’s quicker to use this.

3 0
3 years ago
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