a) The mean number of radioactive atoms that decayed in a day is approximately 69.28 atoms. and b) the probability that on a given day, 50 radioactive atoms decayed is approximately 2.314685e-47.
a. To find the mean number of radioactive atoms that decayed in a day, we can divide the total number of atoms decayed over 365 days by the number of days:
Mean number of radioactive atoms decayed per day = Number of atoms decayed / Number of days
Mean number of radioactive atoms decayed per day = 25,272 atoms / 365 days
Mean number of radioactive atoms decayed per day ≈ 69.28 atoms
Therefore, the mean number of radioactive atoms that decayed in a day is approximately 69.28 atoms.
b. To find the probability that on a given day, 50 radioactive atoms decayed, we can use the Poisson distribution. The Poisson distribution is often used to model the number of events occurring in a fixed interval of time or space.
The formula for the Poisson distribution is:
P(X = k) = [tex](e^(-λ) * λ^k) / k![/tex]
Where:
P(X = k) is the probability that k events occur,
e is Euler's number, approximately 2.71828,
λ is the average number of events occurring in the given interval,
k is the number of events we are interested in.
In this case, the average number of radioactive atoms decayed in a day is approximately 69.28 atoms (calculated in part a). Therefore, λ = 69.28.
Substituting the values into the Poisson distribution formula:
P(X = 50) =[tex](e^(-69.28) * 69.28^50)[/tex] / 50!
Calculating [tex]e^(-69.28):[/tex]
[tex]e^(-69.28)[/tex] ≈ 2.67048178576e-31
Calculating [tex]69.28^50:[/tex]
[tex]69.28^50[/tex] ≈ 2.64267020807e+80
Calculating 50! (factorial of 50):
50! ≈ 3.04140932017e+64
Substituting these values back into the formula:
P(X = 50) ≈ (2.67048178576e-31 * 2.64267020807e+80) / 3.04140932017e+64
P(X = 50) ≈ 2.314685e-47
Therefore, the probability that on a given day, 50 radioactive atoms decayed is approximately 2.314685e-47.
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15+5n+-5n-5+6n
-5, 5, -1, -3
WHICH ONE
Answer:
it is th3 or forth your welcome
Step-by-step explanation:
6(6b+7n-2n) btw its distrubitive property im kinda confused
Answer:
36b + 30n
Step-by-step explanation:
1. solve your like terms inside the parentheses to get 6(6b + 5n)
2. distribute the 6 on the outside, to get 36b + 30n
:)
please help me! <3 :(
Answer:
ill help
Step-by-step explanation:
Answer:
Slope = 2 (i think)
Step-by-step explanation:
What is the answer to 4 (-1/2)?
Answer:
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
-1/2 = -0.5
-0.5 x 4 = -2
Ali currently has $25. He is going to start saving $5 every week.
Which equation represents this situation?
Answer:
y=5x+25
Step-by-step explanation:
5 is the slope and 25 is the y-intercept
Answer:
5x+25 and the second part is YES
Step-by-step explanation:
What is 2+2? I NEED EXPLANATION PLS I DONT HAVE A LOT OF TIME I NEED EXPLANATION AND WHY I REALLY DONT KNOW I NEED HELP
Answer:
4
Step-by-step explanation:
WKKSKSK
BEACUSE
2+2=4
bOom
Answer:
4
Step-by-step explanation:
Because if you have 2 dollars and someone else has 2 dollars and they gave the 2 dollars to you. You have 4 dollars.
A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour. What is the amount if you rent the SCUBA equipment for 1 hour and 15 minutes? • $40.63 $28.13 $50 $41
The amount for renting SCUBA equipment for 1 hour and 15 minutes is (1) $40.63, including an up-front fee of $25 and an hourly rate of $12.50.
To calculate the amount for renting SCUBA equipment for 1 hour and 15 minutes, we need to consider the up-front fee and the hourly rate.
The up-front fee is $25, which is a fixed cost.
The additional fee for each hour is $12.50. Since we have 1 hour and 15 minutes, we can consider it as 1.25 hours.
Therefore, the total cost can be calculated as:
Total cost = up-front fee + (hourly rate × number of hours)
Total cost = $25 + ($12.50 × 1.25)
Total cost = $25 + $15.63
Total cost = $40.63
Hence, the amount for renting the SCUBA equipment for 1 hour and 15 minutes is $40.63.
Therefore, the correct answer is: (1) $40.63
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helpp!!! i will mark as brainliest
Answer:
i. no
ii. yes
iii.no
️️️️
Let f(x)= ax^2+bx+c and g(x)= ax^2-bx+c. If f(1) = g(1)+2 and f(2)=2, find g(2).
Answer:
first lets calculate f(1)=g(1)+2
a+b+c=a-b+c+2 so b=1
next lets calculate f(2)=2 remembering that we found b=1
4a+2*1+c=2 so c=-4a
Now lets find g(2)
g(2)=4a-2b+c= -c-2+c=-2 this is the final response
Let’s see who’s smart i made this myself
Answer:
$20.2
Step-by-step explanation:
Answer:
21.06
Step-by-step explanation:
17 percent of 18=3.06
3.06+18=21.06
.There is an island in which certain inhabitants called "knights" always tell the truth, and others called "knaves" always lie. We assume that all of the inhabitants are either knights or knaves. Match the statements on the left with the types on the right. (Based on a series of puzzles by Raymond Smullyan)
Answer:
Step-by-step explanation:
READ A BOOK
how are Mass and distance related to gravity
Answer:
here.
Step-by-step explanation:
The force of gravity depends directly upon the masses of the two objects, and inversely on the square of the distance between them. This means that the force of gravity increases with mass, but decreases with increasing distance between objects.
I hope this helps! :D
Answer:
look at explanation
Step-by-step explanation
The force of gravity depends directly upon the masses of the two objects, and inversely on the square of the distance between them. This means that the force of gravity increases with mass, but decreases with increasing distance between objects.
Rational number arithmatic
Answer:
A and D are the ones that are right
Answer:
a and d
Step-by-step explanation:
find the value of x or y so that the line through the points has the given slope. (7, -3) and (9, y) and Slope is 9/2
Answer:
almost answer
Step-by-step explanation:
can you tell me what function family this graph belongs to
Answer:
Quadratic
Step-by-step explanation:
The type of graph is quadratic
A pool membership during the summer
costs $7 per week. The total cost of a membership is given by
f(x) = 7x. The pool also rents out lockers for $2 per week. The
total cost of a membership and a rental is given by g(x) = 9x.
What is the difference between a 12-week membership
if you get a locker and if you don't? Explain how you
got your answer.
pls help now plz On your own paper, please write a fraction with x^-5*y^4*z^18 in the numerator and x^-6*y^19*z^-2 in the denominator. Simplify this fraction.
Answer:
xz^20 / y^15
Step-by-step explanation:
x^-5*y^4*z^18
------------------------
x^-6*y^19*z^-2
We are dividing so we subtract the exponents
First simplify the x terms
x^ -5 / x^ -6 = x^( -5 - -6) = x^ (-5+6) = x
Then simplify the y terms
y^ 4 / y^ 19 = y^( 4 - 19) = y^ (-15)
Finally simplify the z terms
z^ 18 / z^ -2 = z^( 18 - -2) = z^ (18+2) = z^20
x y ^ -15 z^20
The positive exponent terms are in the numerator and the negative exponent terms are in the denominator ( they change to positive exponents)
xz^20 / y^15
Answer:
I like gave the other dude the answr so I am chillin
Step-by-step explanation:
thanks for da points doe g
HELP ME PLEASE, SEE THE PICTURE!
Answer:
5 students
Step-by-step explanation:
85 has the stem of 8.
The only leaf in stem 8 that has a number higher than the leaf 5 is 8.
The stem 9 is higher than the stem 8 so all of it's leaves are higher than 85.
There are 4 leaves under the stem 9 and there is one leaf in stem 8 that's higher than 5.
So there are 5 students that have a score higher than 85.
The table below gives the lengths of the three sides of four triangles. Which triangle is NOT a right triangle?
Triangle A
Triangle B
Triangle C
Triangle D
Answer:
D
Step-by-step explanation:
(a^2)+(b^2)=c^2
how many bottles of chocolate can you buy with $20 if one cost $4?
One step equation
What is the standard form of this complex number? (24 - 10i) - (43 + 18i)
Answer:
-19-28i
Step-by-step explanation:
Answer:
-19-28i
Step-by-step explanation:
A forest covers 72,000 acres. A survey finds that 0.3% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answer:
21,600 acres of old-growth trees
Step-by-step explanation:
Mtiply 72,000 by 0.3%
0.3 * 72,000 = 21.6k (21,600)
Simplify by combining like terms.
25pq + 13pq - 6 - 35pq + 4
Answer:
3pq-2
Step-by-step explanation:
25pq + 13pq = 38pq
Next
38pq - 35pq = 3pq
so thats ur first like terms combined then you have to do.
-6+4 = -2
So then you have your answer
3pq-2
Answer:
-17pq-2
Step-by-step explanation:
If the semi-circle and the parabola are the respective graphs of fx= square root of 9-x2,gx=b- 1/4 x2, find the value of b.
The value of b is 2.
To find the value of b, we need to equate the equations of the semi-circle and the parabola.
The equation of the semi-circle is given as fx = √(9 - x²).
The equation of the parabola is given as gx = b - (1/4)x².
Since both graphs represent the same function, we can equate them and solve for the value of x:
√(9 - x²) = b - (1/4)x²
To simplify the equation, let's square both sides:
9 - x² = (b - (1/4)x²)²
Expanding the right side of the equation:
9 - x² = b² - 2b(1/4)x² + (1/16)x⁴
Combining like terms:
9 - x² = b² - (1/2)bx² + (1/16)x⁴
Since the two sides of the equation are equal for all values of x, the coefficients of each power of x must be equal. Comparing the coefficients, we have:
-1 = -b/2 (coefficient of x² term)
0 = 1/16 (coefficient of x⁴ term)
From the coefficient of the x² term, we can solve for b:
-b/2 = -1
b/2 = 1
b = 2
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Translate the word phrase into a variable expression:
five times the sum of 2 and y
Answer:
5×(2+Y) is one way you can put the expression. Hope this helps. :)
A project has an initial cost of $40,400, expected net cash inflows of $14,000 per year for 9 years, and a cost of capital of 12%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round your intermediate calculations. Round your answer to the nearest cent.
Answer:
$59,750
Step-by-step explanation:
According to the given situation, the calculation of net present value is shown below:-
Net present value = Net cash inflows × PVIFA factor(9,12%) - Initial cost
= $14,000 × 7.1607 - $40,400
= $100,250 - $40,500
= $59,750
Therefore as per the situation for computing the net present value we simply applied the above formula.
work work out the value of 3 ^ 2 plus 2 ^ 3
Answer:
Step-by-step explanation:
First 3 to the power of 2 is 3 X 3 which is nine. Next 2 the power of three is 2 X 2 X 2 which is 8. 9+8=17.
A lawnmower was purchased at rupees 1100 and rupees 50 were paid as transportation charges. It was sold at 14% profit. Find its selling price
Answer:
Rs 1311
Step-by-step explanation:
1100 + 50 = 1150
1150 * 114%
NB : since the profit is 14% means it is 14% hence 114% = 100% + 14% meaning the 100% original amount + the 14% profit
= Rs 1311
Write these fractions in their simplest form:
A. 49/84
B. 216/64
Answer:
A. 7/12
B. 27/8 or 3 & 3/8
Devin wants to buy some t-shirts from a store in the mall. He has $20 in his pocket and the t-shirts cost $5 each. The situation can be modeled by the function F(t) = 5t, where F(t) represents the total cost of t t-shirts. State a reasonable domain and range for this situation.
Pls help
Answer:
25 bbgdswweghjyyhhhhhh
