Answers
Answer:
a) [tex]k \approx 0.0602\,\frac{1}{min}[/tex] ([tex]k\approx 6.02\,\frac{\%}{min}[/tex]), b) [tex]k \approx 0.0648\,\frac{1}{min}[/tex] ([tex]k \approx 6.48\,\frac{\%}{min}[/tex]), c) [tex]t_{1/2} \approx 60.274\,days[/tex], d) [tex]t_{1/2}\approx 4.305\,min[/tex], e) [tex]k \approx 0.3\,\frac{1}{min}[/tex] ([tex]k\approx 30\,\frac{\%}{min}[/tex]), f) [tex]k \approx 0.0120\,\frac{1}{min}[/tex] ([tex]k \approx 1.20\,\frac{\%}{min}[/tex]), g) [tex]k \approx 2.876\times 10^{-5}\,\frac{1}{yr}[/tex] ([tex]k \approx 2.876\times 10^{-3}\,\frac{\%}{yr}[/tex])
Step-by-step explanation:
All radioactive isotopes decay exponentially, the mass of the isotope as a function of time ([tex]m(t)[/tex]), measured in grams, is defined by:
[tex]m(t) = m_{o}\cdot e^{-k\cdot t}[/tex] (1)
Where:
[tex]m_{o}[/tex] - Initial mass of the isotope, measured in grams.
[tex]k[/tex] - Decay rate, measured in [tex]\frac{1}{min}[/tex] or [tex]\frac{1}{day}[/tex] or [tex]\frac{1}{yr}[/tex].
[tex]t[/tex] - Time, measured in minutes, days or years.
We define the decay rate in terms of half-life by using the following expression:
[tex]k = \frac{\ln 2}{t_{1/2}}[/tex] (2)
Where [tex]t_{1/2}[/tex] is the half-life of the isotope, measured in minutes or years.
Now we proceed to determine the missing values:
a) Polonium-200 ([tex]t_{1/2} = 11.5\,min[/tex])
[tex]k = \frac{\ln 2}{11.5\,min}[/tex]
[tex]k \approx 0.0602\,\frac{1}{min}[/tex]
b) Lead-194 ([tex]t_{1/2} = 10.7\,min[/tex])
[tex]k = \frac{\ln 2}{10.7\,min}[/tex]
[tex]k \approx 0.0648\,\frac{1}{min}[/tex]
c) Iodine-125 ([tex]k = 0.0115\,\frac{1}{day}[/tex])
[tex]t_{1/2} = \frac{\ln 2}{k}[/tex]
[tex]t_{1/2} = \frac{\ln 2}{0.0115\,\frac{1}{day} }[/tex]
[tex]t_{1/2} \approx 60.274\,days[/tex]
d) Kryption-75 ([tex]k = 0.161\,\frac{1}{min}[/tex])
[tex]t_{1/2} = \frac{\ln 2}{k}[/tex]
[tex]t_{1/2} = \frac{\ln 2}{0.161\,\frac{1}{min} }[/tex]
[tex]t_{1/2}\approx 4.305\,min[/tex]
e) Strontium-79 ([tex]t_{1/2} = 2.3\,min[/tex])
[tex]k = \frac{\ln 2}{2.3\,min}[/tex]
[tex]k \approx 0.3\,\frac{1}{min}[/tex]
f) Uranium-229 ([tex]t_{1/2} = 58\,min[/tex])
[tex]k = \frac{\ln 2}{58\,min}[/tex]
[tex]k \approx 0.0120\,\frac{1}{min}[/tex]
g) Plutonium-239 ([tex]t_{1/2} = 24100\,yr[/tex])
[tex]k = \frac{\ln 2}{24100\,yr}[/tex]
[tex]k \approx 2.876\times 10^{-5}\,\frac{1}{yr}[/tex]
Related Questions
solve 2sin(2x) - 2sinx +2sqrt3 cosx - sqrt3 = 0
Answers
Answer:
2sin(2x)-2sinx+2sqrt3cosx-sqrt3 = 0
-----
4sin(x)cos(x) - 2sin(x) + 2sqrt(3)cos(x) - sqrt(3) = 0
-----
Factor:
2sin(x)[2cos(x)-1] + sqrt(3)[2cos(x)-1] = 0
-----
[2cos(x)-1][2sin(x)+sqrt(3)] = 0
Solve:
2cos(x)-1 = 0 or 2sin(x)+sqrt(3) = 0
cos(x) = 1/2 or sin(x) = -sqrt(3)/2
x = +/-pi/3 or x = -pi/3 or (4/3)pi
hope this helps!
Answer:
x = +/-pi/3 or x = -pi/3 or (4/3)pi
Step-by-step explanation:
2sin(2x)-2sinx+2sqrt3cosx-sqrt3 = 0
4sinxcosx - 2sinx + 2sqrt(3)cosx - sqrt(3) = 0
2sin(x)[2cos(x)-1] + sqrt(3)[2cos(x)-1] = 0
[2cos(x)-1][2sin(x)+sqrt(3)] = 0
2cos(x)-1 = 0 or 2sin(x)+sqrt(3) = 0
cos(x) = 1/2 or sin(x) = -sqrt(3)/2
x = +/-pi/3 or x = -pi/3 or (4/3)pi
Find the slope and y-intercept of the line in each graph. (Explore Activity 1) Please help me
Answers
Answer:
1. Slope = -2 , y-intercept = 1
2. Slope = 5 , y-intercept = -15
3. Slope = 1.5 , y-intercept = -2
4. Slope = -3 , y-intercept = 9
Step-by-step explanation:
1. The slope is -2 because using the formula y₁-y₂÷x₁-x₂ you can use the points given to you to get -2. It doesn't matter which one you pick as y1 or y2, just make sure you keep it consistent with the x numberings. I did 1--3 (which becomes 1+3) and 0-2. Those equal 4/-2 which gives you -2. Use these same steps for all of them, but with ones that don't have the points given, just pick two that are whole numbers and not decimals. For finding the y-intercept, just find the point that is on the y axis line. It is given on number one as (0,1). So, the y-intercept is 1. Hope this helps!
In the diagram m<3 = x +30 and m<4= 2x - 80. What is the measure of angle 3?
A)50
B)80
C)110
D)140
Answers
Answer:
110,........................
Simplify
x^2 + 3x + 2 over x+1
Answers
Answer:
x+2
Step-by-step explanation:
factor and you should get (x+2)(x+1)/(x+1) and then you cancel out the (x+1)
What is the result of 60-15? Use the model to find the answer. A 4 B 5 C 12 D 20
Answers
Answer:
its a).4
Step-by-step explanation: 60 divided by 15= 4 you can use a calculator to check if im right if you dont trust me
The answer would be 4 if the number expression is 60 ÷ 15 after using the arithmetic operation, option (A) 4 is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
The number expression is:
60 ÷ 15
Using model:
= (15 + 15 + 15 + 15) ÷ 15
= 1 + 1 + 1 + 1
= 4
Thus, the answer would be 4 if the number expression is 60 ÷ 15 after using the arithmetic operation, option (A) 4 is correct.
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slope of -3,-2 and -1,-5
Answers
Answer:
14
Step-by-step explanation:
-3-2 is a slope and you add numbers
If 12 cookies cost $3 how much would it be for 9 cookies
Answers
12:3
9:x
x is how much it would cost. so try to find x.
x= 2.25
9 cookies cost 2 dollars and 25 cents
what is -5 - 1/2 equal?
Answers
Answer:-5.5
Step-by-step explanation:1/2 is basically .50 so -5 - .50 gives you -5.5
Answer:
-5.5
Step-by-step explanation:
When you do -5 - 1/2, you get -5.5!
Which set of ordered pairs does not represent a function? O {(-3,-9), (7,9), (9, 1), (7,3)} O {(-3,8),(-6,5), (-5, -6), (1,-6)} O {(3,1),(-2,-9), (6,-9),(4,6)} o {(4,3), (-4,4),(-2,-5), (6,4)}
Answers
Answer:
The first set of ordered pairs is not a function.
Step-by-step explanation:
The X value of 7 repeats, which means that it is not a function
This is because each x value has to has their distinct y value. So you notice all sets of ordered pairs except the first one, two different x-values have the common y-value, which cannot be happen.
57.351 rounded to the ones place
Answers
How do you round to the ones place?
Look to the next smallest place value, the digit to the right of the place value you're rounding to. For example, if you want to round to the nearest ten you'd look at the ones place. If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round to as-is.
Answer:
Step-by-step explanation:
do u mean round to the nearest 10th as in one decimal place or to the nearest one not decimal place?
Multiplication Property of One
1⋅w⋅16
Answers
Answer:
The correct answer is 16w.
Step-by-step explanation:
w = 1w
1⋅w⋅16 =
1⋅1w⋅16 =
16w
Therefore, the correct answer is 16w.
Hope this helps! :D
Mark can type 20 words per minute. Carol can type 22 words per minute. Mark starts typing at 1:00 pm and Carol starts typing 6 minutes later. At 1:15 pm, both Mark and Carol stop typing. Together, how many words did Mark and Carol type between 1:00 and 1:15 pm?
Answers
Answer:
C. 498
Step-by-step explanation:
Total number of words typed by both Mark and Carol is 498.
Rate of typing by Mark = 20 word per minute
Rate of typing by Carol = 22 words per minute
Since, Mark starts typing at 1:00 pm and stop at 1:15 pm.
So, time taken by Mark is 15 minute.
number of words typed by Mark = [tex]20*15=300[/tex]
Since, Carol starts typing 6 min late , i.e. at 1:06 pm and stop at 1:15 pm.
So, time taken by Carol is 9 minute.
number of words typed by Carol =[tex]22*9=198[/tex]
Total number of words typed by both Mark and Carol = [tex]300+198=498[/tex] words.
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5.6 x 10 __= 5,600
hurry
Answers
Answer:
its 10^3 power or 1000
Step-by-step explanation:
Pic below
....................
Answers
Answer:
b=2
Step-by-step explanation:
my uh head
but like u add 9/3 to -1 and get 2 so ya
hope this helps a bit <33
What is the area of this kite?
L2FwcGhvc3RpbmdfcHJvZC9ibG9icy9BRW5CMlVwNHJBVjU5YmlNNWhaTGZXMmhRVnNJTVJTSWFCSUVGQW5aQTBLVEhDWjEzdGxuY2xyRF9zcHhmVGxqV0ZBbl9IZXl3dlBvcW5SM01XZlFVVnNhNldHUjBmNzVmQS5jZV9xLXlWdzVyXzFWQ1pB?w=400&h=400
a
29 square meters
b
49 square meters
c
39 square meters
d
19 square meters
Answers
Answer:
39 square meters.
Step-by-step explanation:
9 times 3 is 27. You have two triangles with length and width of 9 and 3 so you multiply it and get 27. You also have two smaller triangles of 3 and 4 and if you combine them it is really just a square. It is 3 times 4 which is 12. Now, the answer is 12 + 27 and you get 39 square meters. Hope it helps. Brainliest would be cool
Does the graph represent a function?
Yes or No
Answers
Answer:
Yes, the graph is a function because the lines do not overlap one another (vertical line test)
- I hope this helps have a great night
Which is the same as 3 feet?
Answers
Answer: 36 inches
Step-by-step explanation:
hope this helps :)
Answer:
i wanna say something mean, buuuuut... water bottle
Step-by-step explanation:
when nicky tried to solve an equation using properties of equality, she ended up with the equation -3=-3. what equation mioght she have tried to solve? what is the solution of the equation?
Answers
Answer: -3 + 4*x^2 = - 3 + (2*x)^2
Any value of x is a solution for this eqution.
Step-by-step explanation:
She ended with -3 = -3
This is trivial, if we had an equation with one variable, something like:
f(x) = equation.
Ending with something like -3 = -3 means that we do not have any restriction with respect to x, so x could take any value.
This will happen if the terms with x in the left side are exactly the same as the terms in the right side, for exampe:
-3 + 4*x^2 = -3 + 4*x^2
In that case, we can substrrat 4*x^2 in both sides, and we will end with:
-3 = -3
This means that the solution for this equation is any value of x.
We also could rewrite this as:
-3 + 4*x^2 = - 3 + (2*x)^2
So the terms look different, but the terms are exactly the same for any value of x.
how much does 18cm are in mm
Answers
18 cm = 180 mm
Explanation:
18 cm • 10 cm (in one mm) = 180 mm
A student club has 20 members how many ways are there for the club to choose a president and a Vice President
Answers
Answer:
Everyone should get president every month simple
A local grocery store decides to offer a free piece of fresh fruit (banana or apple) to all shoppers in the produce department. The store is conducting an observational study to determine which type of fruit is selected more often. At the end of the first day, the store found that twice as many shoppers select an apple.
The grocery store then repeats the observational study for 14 days. All studies yield similar results. What generalization can be made from the results of this study?
A.
Given the choice of a banana or an apple, twice as many shoppers will select an apple.
B.
The results are inconclusive; therefore, a generalization cannot be made regarding which type of fruit is preferred by most shoppers.
C.
There is not enough information to generalize the study’s results.
D.
Given the choice of any type of fruit, twice as many shoppers will select an apple.
Answers
Answer:
A.
Step-by-step explanation:
If the results are similar (A) should be your answer!
Option A is correct.
What is generalization?Generalization is a process which leads to something more general and whose product consequently refers refers to an actual or potential manifold in a certain way.
According to the given question
"At the end of the first day, the store found that twice as many shoppers select an apple"
So, the generalization can be made from the above result is " from the given choice of a banana or an apple, twice as many shoppers will select an apple".
Hence, option A is correct.
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Find the possible range of c
Answers
Answer:
53
Step-by-step explanation:
trust me
The slope of the line y - 4x = -2 is 4.
False
O True
Answers
Answer:
True
Step-by-step explanation:
Set up the problem in slope intercept i.e y = mx + b. Add 4x to both sides to create y = 4x -2. Any number or fraction in the m part is the slope. So the slope is 4.
True, the slope of the line y - 4x = -2 is 4.
The equation of a line in slope-intercept form with slope m is,
y = mx + c
Where 'c' is the y-intercept of the line.
Given that,
The equation of a line is,
y - 4x = - 2
Now it can be written in a slope-intercept form as,
y - 4x = - 2
Add 4x on both sides,
y - 4x + 4x = - 2 + 4x
y = 4x - 2
By comparing with slope - intercept of the equation,
Slope (m) = 4
Therefore, the statement is true.
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In how many zeros does 75! end?
Answers
Answer: 0
Step-by-step explanation: 0 because 75 doesn't have a 0
How is the space between consecutive whole numbers divided on the number line?
O into halves
O into fifths
O into sixths
O into sevenths
Answers
C. INTO SIXTHS
I LITRALLY JUST TOOK THE TEST ON EDGE. SO YOU CAN TAKE MY WORD FOR IT
I HOPE I WASNT TOO LATE. IF I WAS, SORRY
The number of grids or intervals on the given number line between any two consecutive whole numbers is six thus option (C) is correct.
What is a number line?In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.
A horizontal number line is the most common representation and can be extended infinitely in any direction.
As per the given number line,
Since 1 is a whole number and 2 is also a whole number.
The number of intervals between 1 and 2 is 6.
Thus, between consecutive whole numbers divided on the number line is 6.
Hence "The number of grids or intervals on the given number line between any two consecutive whole numbers is six".
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5) The sales tax in the town where Amanda lives is 5%. Amanda paid $35
in sales tax on a new stereo. What was the price of the stereo?*
O a. $14.29
O b. $1.75
O c. $700
O d. $3,500
Answers
Answer:
$700
Step-by-step explanation:
Given that,
The sales tax in the town where Amanda lives is 5%.
Amanda paid $35 in sales tax on a new stereo.
We need to find the price of the stereo. Let it is x. Using the formula for percentage as follows :
[tex]\%=\dfrac{\text{sales tax}}{\text{total}}\times 100\\\\5\%=\dfrac{35}{x}\times 100\%\\\\x=\dfrac{35\times 100\%}{5\%}\\\\=\$700[/tex]
So, the price of the stereo is $700. Hence, the correct option is(c).
please answer it fast
Answers
Answer:
c
Step-by-step explanation:
ray bd bisects angle abc. solve for x
Answers
Answer:
x = 10
Step-by-step explanation:
Since, ray BD bisects ∠ABC,
Therefore, m∠ABD = m∠CBD
By substituting the values of the angles,
x° = (4x - 30)°
x - 4x = -30
-3x = -30
x = 10
Therefore, x = 10 will be the answer.
I will give brainliest
Find x and y, there is no given info, and the line that is 8 units long is not a midsegment, but it is parallel to the line that is ten units long
Answers
Answer:
x = 1.25
y = 1.75
Step-by-step explanation:
Since, the line that is 8 units long is parallel to the line that is ten units long.
Therefore, both the triangles are similar by AA postulate.
Corresponding sides of of the similar triangles are in proportion.
Therefore,
[tex] \frac{5}{x + 5} = \frac{7}{y + 7} = \frac{8}{10} \\ \\ \implies \frac{5}{x + 5} = \frac{8}{10} \\ \\ 5 \times 10 = 8(x + 5) \\ \\ 50 = 8x + 40 \\ \\ 50 - 40 = 8x \\ \\ 10 = 8x \\ \\ \frac{10}{8} = x \\ \\ x = 1.25 \\ \\ \\ \frac{7}{y + 7} = \frac{8}{10} \\ \\ 7 \times 10 = 8(y + 7) \\ \\ 70 = 8y + 56 \\ \\ 70 - 56 = 8y \\ \\ 14 = 8y \\ \\ \frac{14}{8} = y \\ \\ y = 1.75[/tex]
The area of rectangle is 35 square feet.the length of rectangle is 5feet what is the width of the rectangle
Answers
Answer:
the answer should be 7
Step-by-step explanation: