Answer:
a) 54.6
b) 140
Step-by-step explanation:
7644 ÷ 140 = 54.6
so;
7644 ÷ 54.6 = 140
Answer:
a) 54.6
b) 140
these are the answers :))))
When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 974,728 radioactive atoms, so 25,272 atoms decayed during 365 days a. Find the mean number of radioactive atoms that decayed in a day b. Find the probability that on a given day, 50 radioactive atoms decayed
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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If 0° < x < 90° and
2 1
2sin
2
x
, then the value of x
is:
The value of x within the given range is x = 45°.
We have the equation 2sin^2(x) = 1. To find the value of x within the given range, we can solve for sin(x) first and then find the corresponding angle.
Starting with 2sin^2(x) = 1, we divide both sides by 2 to get sin^2(x) = 1/2. Taking the square root of both sides, we have sin(x) = √(1/2). Since 0° < x < 90°, we know that sin(x) is positive in this range.
The value of √(1/2) is approximately 0.707. Therefore, sin(x) = 0.707.
To find the corresponding angle x, we can use the inverse sine function (sin^(-1)). Taking the inverse sine of both sides, we have x =[tex]sin^(^-^1^)^(^0^.^7^0^7^)[/tex].
Evaluating sin^(-1)(0.707) using a calculator, we find that x is approximately 45°.
Note that sine is a periodic function, and there are other angles that satisfy the equation 2sin^2(x) = 1. However, within the specified range of 0° < x < 90°, the value of x is 45°.
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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 $2 per week. The
total cost of a membership and a rental is given by g(x) = 9x.
What is the difference between a 12-week membership
if you get a locker and if you don't? Explain how you
got your answer.
A student said that 42% of 78 is 45. Is this answer reasonable? Explain.
Answer:
No because 42% of 78 is 32.76
Step-by-step explanation:
Answer:
Answer: Sample response: 42% can round to 40%, and 78 can round to 80. 40% of 80 is 32, so 42% of 78 should be about 32. 45 is much greater than 32, so the answer is not reasonable.Step-by-step explanation:
Hope this helps :) Develop a POQ solution and calculate total relevant costs for the data in the following table.
Period 1 2 3 4 5 6 7 8 9 10 11 12
Gross requirements 30 40 30 70 20 10 80 50
fill in the table and calculate total costs.
*Holding cost =$ 3.50 / unit/week; setup cost =$ 200 ; lead time =1 week; beginning inventory =40 . a lot-for-lot solution (enter your responses as whole numbers).
Using the information provided in the table, The total holding cost is $547.50, the total setup cost is $600 and the total cost is $1,147.50.
How to calculate the total costTo develop a POQ (Periodic Order Quantity) solution use a lot-for-lot solution, which means that we will order exactly what we need for each period.
The missing values can be found on the attached table.
From the table, the total holding cost which is the sum of the holding costs for all periods is $547.50 while the total setup cost which is the sum of the setup costs for all periods is $600.
Therefore, the total cost is the sum of the holding cost and the setup cost and it is calculated as $1,147.50.
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which twos ratios represent quantities that are proportional?
14/37 and 37/14
10/15 and 14/21
7/11 and 28/48
15/27 and 8/12
Answer: it’s 10/15 and 14/21 ;)
Step-by-step explanation:
What is the value of the expression - 25(12)?
Answer:
300
Step-by-step explanation:
multiply 25 by 12
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
Factorise the given question: 3p^-7p-6
Answer:
(p−3)⋅(3p+2)
Step-by-step explanation:
STEP 1 :
Equation at the end of step 1
(3p2 - 7p) - 6
STEP 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3p2-7p-6
The first term is, 3p2 its coefficient is 3 .
The middle term is, -7p its coefficient is -7 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 3 • -6 = -18
Step-2 : Find two factors of -18 whose sum equals the coefficient of the middle term, which is -7 .
-18 + 1 = -17
-9 +2 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 2
3p2 - 9p + 2p - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
3p • (p-3)
Add up the last 2 terms, pulling out common factors :
2 • (p-3)
Step-5 : Add up the four terms of step 4 :
(3p+2) • (p-3)
Which is the desired factorization
Final result :
(p - 3) • (3p + 2)
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
:)
What is the slope of the graph?
Answer:
-3
Step-by-step explanation:
It's a negative slope and you do 3/1= 3 as it is negative the slope is -3
Hope this helped :)
a cleaning service lets customers decide which way they would like to be charged.
• for choice A, the total cost is $25 dollars per hour of cleaning.
•for choice B, the total cost is $50+$15h, where h is the number of hours of cleaning.
which of the following statements is true?
• Choice A always costs more $10 more than choice B
• Choice B is always more expensive
• Choice A charges less for a cleaning job that takes 5 hours
• Choice B charges more for a cleaning job that takes 3 hours.
Answer:
the 4th statement
Step-by-step explanation:
subsititute the values for h, use numbers between 1-10 to help find the answer.
15+5n+-5n-5+6n
-5, 5, -1, -3
WHICH ONE
Answer:
it is th3 or forth your welcome
Step-by-step explanation:
farmer janet can plant nine feet of carrots in 15 minutes while her daughter Amy can plant 17 feet of carrots in half an hour.Justify your answer.
Answer:
a. Farmer janet
b.Farmer janet = 36 feet, daughter = 34 feet
Step-by-step explanation:
a. When moving both rates to the same common denominator we get 18/30 for janet and 17/30 for daughter
b. janet = 18/30 = 36/60, daughter = 17/30 = 34/60
heyy guys me and my friends are struggling on this question on our post test in anyone know how to do it could u lend a hand :(
Answer:
40
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
how many bottles of chocolate can you buy with $20 if one cost $4?
One step equation
Silva set up a dog-walking business. He earned $60 in June. He is projected to earn 110% more in July. How much is Silva projected to make in July?
$126
$170
$176
$660
9514 1404 393
Answer:
$126
Step-by-step explanation:
110% more than 100% is 210% of his June earnings:
july = 2.10×$60 = $126
Silva is projected to make $126 in July.
_____
As always, you can think of % and /100 as being interchangeable.
210% = 210/100 = 2.10
Answer:
126
Step-by-step explanation:
please help me! <3 :(
Answer:
ill help
Step-by-step explanation:
Answer:
Slope = 2 (i think)
Step-by-step explanation:
Models of inventory systems frequently consider the relationships among a beginning inventory,
a production quantity, a demand or sales, and an ending inventory. For a given
production period j, let
sj-1 = ending inventory from the previous period (beginning inventory for period j)
xj = production quantity in period j
dj = demand in period j
sj = ending inventory for period j
a. Write the mathematical relationship or model that shows ending inventory as a function
of beginning inventory, production, and demand.
b. What constraint should be added if production capacity for period j is given by Cj?
c. What constraint should be added if inventory requirements for period j mandate an
ending inventory of at least Ij?
a. This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).
b. This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).
c. This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).
a. The mathematical relationship or model that shows ending inventory as a function of beginning inventory, production, and demand can be represented as:
sj = sj-1 + xj - dj
This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).
b. If the production capacity for period j is given by Cj, the constraint that should be added is:
xj ≤ Cj
This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).
c. If inventory requirements for period j mandate an ending inventory of at least Ij, the constraint that should be added is:
sj ≥ Ij
This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).
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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.
What is the average speed of the diver in the water? How can you tell from the graph?
Write these fractions in their simplest form:
A. 49/84
B. 216/64
Answer:
A. 7/12
B. 27/8 or 3 & 3/8
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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#1 Find the Area*
7 in
11 in
Your answer
170
Answer:
The area is 77
Step-by-step explanation:
7*11=77
Answer:
area = 77
Step-by-step explanation:
if 7 is one side, and 11 is the other, and we know that length times width is the area of a rectangle or a square, we can set up a simple equation to solve for the area:
7 x 11 = ?
when looking at multiplying by 11s, the pattern is 2 of the number your multiplying it by until you exceed 9 (ex. 11 x 5 = 55, 11 x 4 = 44, 11 x 9 = 99, etc.) so:
7 x 11 = 77. which is your answer.
i hope this helped :))
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.
helpp!!! i will mark as brainliest
Answer:
i. no
ii. yes
iii.no
️️️️
can you tell me what function family this graph belongs to
Answer:
Quadratic
Step-by-step explanation:
The type of graph is quadratic
There are 10 fish in a tank. 30% of them are guppies. What is the probability that
fish chosen at random will be a guppy?
GUYS I NEED HELP!!
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Answer:
30%
Step-by-step explanation:
If 30% of the fish are guppies, a randomly chosen fish will be a guppy with probability 30%.
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
