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3 years ago

Radium-226 has a half-life of 1620 years. for a 150 gram sample, how many grams will remain after 200 years?

1 answer:

3 0

Ah, yes

if you start with P amount of something and the half life is h units (in years) and the time elapsed is t (in years) then the amount left is A

the equation is
$A=P(\frac{1}{2})^\frac{t}{h}$

so
given
h=1620
P=150
t=200
so
$A=150(\frac{1}{2})^\frac{200}{1620}$
$A=150(\frac{1}{2})^\frac{10}{81}$
use your calculator
A≈137.69781917515g
about 138grams left

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What is the slope of the line that passes through the points given in the table? ANSWER IN DECIMAL FORM

PolarNik [594]

Answer:

1.5

Step-by-step explanation:

the slope formula is y2-y1/x2-x1

so take two given points (I'll use (-1, -5) and (3,1))

1--5/3--1

6/4

1 2/4

1.5

3 0

3 years ago

In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.02, 0.07, and

Leviafan [203]

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

Name the probabilities:

p₁ = 0.02, p₂ = 0.07, p₃ = 0.91

q₁ = 1-p₁ = 0.98 , q₂ = 1-p₂ = 0.93 , q₃ = 0.09

Let X and Y be the number of bits with high and moderate distortion out of three.

The function will follow multinomial distribution:

$f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})$

Substitute the values and make a table.

TABLE IN ATTACHMENT

We calculate marginal distribution by:

$P (X=x)=$ <em>∑</em> $P(X=x,Y=y)$

$fx(x)$ can be found by adding all the probabilities in each row for different value of X

For X=0 , ∑P = 0.94157441

For X=1 , ∑P = 0.057624

For X=2 , ∑P = 0.001176

For X=3 , ∑P =0.000008

The mathematic expectation E is the sum of product of each possibility with its probabiity.

$E(X)=$ <em>∑ </em> $xP(X=x)$

Find E(X):

$E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)$

$E(X)=0.06$

Condition probability states:

$P(A|B)=\frac{P(A,B)}{P(B)}$

It can also be written as:

$f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}$

Where $f_x(1)\\$ = 0.057624

Calculate the quotient:

$Y|_{x=1}$ = 0 , $f_{Y|_X=1$ = 0.862245

$Y|_{x=1}$ = 1 , $f_{Y|_X=1$ = 0.132653

$Y|_{x=1}$ = 2 , $f_{Y|_X=1$ = 0.000510

$Y|_{x=1}$ = 3 , $f_{Y|_X=1$ = 0

Find the dependency:

$f_{XY}(y)=f_X(x)f_Y(y)$

We found that

$f_{Y|_X=1$ = 0.862245

Calculate $f_Y(1)$ from summing the column from the table

$f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141$

Which are not equal.

Conclusion:

X and Y are NOT Independent

7 0

4 years ago

50 points! Please help fast this is due soon and it confuses me. Will mark brainliest. Random answers will be reported. Please h

Ad libitum [116K]

Answer:(5,3)

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The graph shows the distance, y, that a car traveled in x hours:

vesna_86 [32]

Here, You need to calculate the slope of the graph by taking any two random points, as follows:
(x₁,y₁) = (0,0) & (x₂,y₂) = (1,55)

Now, we know,
y₂-y₁ = m(x₂-x₁)
55-0 = m(1-0)
m = 55/1
m = 55

Here m represents the slope of graph which is nothing but rate of change of distance.

In short, option A will be your answer.

Hope this helps!

7 0

4 years ago

Read 2 more answers

Convert 54 kg to g<br><br>0.54 g <br><br>54,000 g<br><br>0.054 g<br><br>5,400 g

Gekata [30.6K]

Answer:

54,000 g

Step-by-step explanation:

1 kg=1000 g

so,54 kg=54*1000 g=54,000 g

4 0

3 years ago