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Klio2033 [76]
3 years ago
8

By far the largest and most widespread use of americium-241 is as a component in household and industrial smoke detectors, where

a small amount is used in an ionization chamber inside the detector. The half life of americium-241 is 432.2 years. If a smoke detector is buried in a land fill, how many years are required for the original amount of americium-241 to decay to less than 1% of the original amount? Round your numerical answer to the nearest tenth of a year.
1,435.7 years


4,322 years


2,871.5 years


43,220 years
Mathematics
1 answer:
svlad2 [7]3 years ago
3 0
<h3>Answer:</h3>

2871.5 years

<h3>Step-by-step explanation:</h3>

The number of half-lives can be found by solving ...

... (1/2)^x = (1/100)

Taking logs, you have ...

... x·(-log(2)) = -log(100)

... x = log(100)/log(2) ≈ 6.64386

Then the number of years for the desired decay is ...

... (432.2)×6.64386 ≈ 2871.5 . . . . years

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F(x) = 3x+2 what is f(5)
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Answer: 17

Step-by-step explanation:

3(5)+2

15+2

F(5)=17

6 0
3 years ago
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Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the co
laila [671]
For the answer to the two questions above,
3x + 2y = 36.50 (I)
2x + 5y = 50 (II)
Eliminating x from the two equations by subtraction:
first we multiply equation I by 2 and equation II by 3
6x + 4y = 73
6x + 15y = 150
Subtracting the two,
-11y = -77
y = 7
He earns $7 at the coffee cart
Substituting y into equation I,
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6 0
3 years ago
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An object is propelled upward from the top of a 300 foot building. The path that the object takes as it falls to the ground can
serg [7]

Answer:

As per the statement:

The path that the object takes as it falls to the ground can be modeled by:

h =-16t^2 + 80t + 300

where

h is the height of the objects and

t is the time (in seconds)

At t = 0 , h = 300 ft

When the objects hit the ground, h = 0

then;

-16t^2+80t+300=0

For a quadratic equation: ax^2+bx+c=0         ......[1]

the solution for the equation is given by:

x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}

On comparing the given equation with [1] we have;  

a = -16 ,b = 80 and c = 300

then;

t= \frac{-80\pm \sqrt{(80)^2-4(-16)(300)}}{2(-16)}

t= \frac{-80\pm \sqrt{6400+19200}}{-32}

t= \frac{-80\pm \sqrt{25600}}{-32}  

Simplify:

t = -\frac{5}{2} = -2.5 sec and t = \frac{15}{2} = 7.5 sec

Time can't be in negative;

therefore, the time it took the object to hit the ground is 7.5 sec

8 0
3 years ago
A media company wants to track the results of its new marketing plan, so the video production manager recorded the number of vie
Alisiya [41]

Answer:

f(x)=5120(1.25)^{x}

Step-by-step explanation:

As per the given question

As we know that

f(x) and x are related by following equation

f(x)=a( {b})^{x}

where

b is the common ratio

Now first we have to compute the value for b which are as follows

\frac{6400}{5120}= 1.25

\frac{8000}{6400}= 1.25

Like if we take the ratio by this method than it comes 1.25

Therefore the common ratio, b = 1.25

So,

a = 5,120

Hence, the equation which model the relationship between the number of weeks and the number of viewers is

f(x)=5120(1.25)^{x}

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Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?
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Answer:

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Step-by-step explanation:

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c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

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e = 1/2

Thus;

a = 4 × 1/2

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2² = b² - 2²

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x²/4 + y²/8 = 1

6 0
3 years ago
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