Answer:
The initial mass of the sample was 16 mg.
The mass after 5 weeks will be about 0.0372 mg.
Step-by-step explanation:
We can write an exponential function to model the situation.
Let the initial amount be A. The standard exponential function is given by:
[tex]P(t)=A(r)^t[/tex]
Where r is the rate of growth/decay.
Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:
[tex]\displaystyle P(t)=A\Big(\frac{1}{2}\Big)^{t/4}[/tex]
After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.
Therefore, when x = 12, P(x) = 2. By substitution:
[tex]\displaystyle 2=A\Big(\frac{1}{2}\Big)^{12/4}[/tex]
Solve for A. Simplify:
[tex]\displaystyle 2=A\Big(\frac{1}{2}\Big)^3[/tex]
Simplify:
[tex]\displaystyle 2=A\Big(\frac{1}{8}\Big)[/tex]
Thus, the initial mass of the sample was:
[tex]A=16\text{ mg}[/tex]
5 weeks is equivalent to 35 days. Therefore, we can find P(35):
[tex]\displaystyle P(35)=16\Big(\frac{1}{2}\Big)^{35/4}\approx0.0372\text{ mg}[/tex]
About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.
The perimeter of a square is 48 inches. What is the area, in square inches, of the square?
Answer:
the area is 144
Step-by-step explanation:
48 ÷ 4 (which is how many sides a square has) is 12
SO 12 × 12 bc l×w and all sides of a square are equal
the answer is 144
Please help.
Algebra.
Pls help me I will give the first answer brainlyist and thanks NO LINKS OR NO BRAINLYIST there are two questions please help
Answer:
h(3)= 2
g(8)-g(-5)= 39
Step-by-step explanation:
math is math
2x²-24x+64=0 How do you solve my factoring this
Sam is paid time and a half for overtime, if his basic hourly rate is $12.50 and he works 8 hours overtime, how much did he earn from working overtime?
I am confused Help me.
about what there is no question here....?
Point Q is located at (–3, 0) and point R is located at (1, 0) on the coordinate plane. What is the distance between points Q and R?
A.
0 units
B.
2 units
C.
3 units
D.
4 units
Answer:
C. 3 units
Step-by-step explanation:
I need help pleaseee
Answer:
Step-by-step explanation:
20 (8+5+4+3)
9 ( 3x + 5y - 11x + 8 )
Answer: -72x+45y+72
Step-by-step explanation:
At Thrasher Gaming Computers, Eli is the manager of the assembly department and has a team of employees that all build laptop computers. He made a graph representing the number of laptops built, y, based on the number of employee hours logged, x. The graph is a straight line that passes through the origin and the point (4, 15). Which of the following graphs and statements fit the situation? After 15 hours logged by employees, the department can build 4 laptops. After 4 hours logged by employees, the department can build 15 laptops.
I need this answered fast
What are the coordinates of point D find the slope
Answer:
D(8, 10 ) , slope = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = C(4, 5) and (x₂, y₂ ) = D(8, 10)
m = [tex]\frac{10-5}{8-4}[/tex] = [tex]\frac{5}{4}[/tex]
how many students can sit around 6 tables in a row arrangement?
-4(y-2)=12 help please
Answer:
-2
Step-by-step explanation:
(y-2)=-(12/4)
y-2= -4
y= -4+2
y = -2
Answer:
y = -1
Step-by-step explanation:
1. -4(y - 2) = 12
2. -4y + 8 = 12
3. -4y + 8 = 12 - 8
4. -4y = 4
5. -4y/-4 = 4/-4
6. y = -1
Check your answer:
-4(y - 2) = 12
-4(-1 - 2) = 12
4 + 8 = 12 True
Find the solution to the following system using substitution or elimination:
y = 3x + 2
y=-2x - 8
A. (-2,-4)
O B. (-ş; – 34)
O C. (-9,-)
D. (1, -6)
Answer:
A. (-2,-4)
x = -2,
y = -4
thats the only way ik how to explain but its the correct answer
What is 3 to the 4th power.
Answer:
81
Step-by-step explanation:
3*3=9
9*3=27
27*3=81
brainliest?
Anyone help ASAP pls!!!
Answer:
my answer is B
a baker can make 25 cds ales in 4 days at this rate how many cakes can he make in 7 days
Answer:
44
Step-by-step explanation:
25dided by 4 is 6.25
multiply 6.25 and 7 and you'll get 43.75
round that to the nearest whole and you get 44
notes i
Which graph represents the solution of -7(x + 3) S 28?
From N
whats
B.
From
10
9
8
7
-6
-5
4
10
9
8
7
6
5
4
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From N
D
kindad
4
5
6
7
8
9
10
4
5
6
7
8
9
10
From
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--7(x + 3) s.
28
Write the inequality
Distributive Property
From)
-73-21
28
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From
Good a
Answer:
fufyfyfugwner546df6f6f6ff5f
Select the correct answer.
The surface area of a cube is 600 square inches. What is the area of one of its faces?
O A 6 square inches
ОВ. 36 square inches
Ос.
75 square inches
OD. 100 square inches
Given the arithmetic sequence -9,-4, 1, 4,... Which term has a value of 166?
Answer:
36th term
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 9 and d = - 4 - (- 9) = - 4 + 9 = 5 , then
[tex]a_{n}[/tex] = - 9 + 5(n - 1) = - 9 + 5n - 5 = 5n - 14
Equate the nth term to 166 and solve for n
5n - 14 = 166 ( add 14 to both sides )
5n = 180 ( divide both sides by 5 )
n = 36
jimrgrant1 made this so give him the credit, i put it here because his was reported
Answer:
36th term
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 9 and d = - 4 - (- 9) = - 4 + 9 = 5 , then
= - 9 + 5(n - 1) = - 9 + 5n - 5 = 5n - 14
Equate the nth term to 166 and solve for n
5n - 14 = 166 ( add 14 to both sides )
5n = 180 ( divide both sides by 5 )
n = 36
Please help meeeeeeeeeeeeeeee
Answer:
h+9<20
h<20-9
h<11
Option C is your answer
Answer:
its c :)
Step-by-step explanation:
The school record for the 400-meter track relay was 65.5 seconds. This year s Speedsters would like to tie or break the record. It took them 53.96 seconds to run 300 meters, In how much time must they run the last 100 meters to tie the record?
PLS ANSWER FAST
65.5 - 53.96 = 11.54
So less than 11.54
SOMEBODY HELP PLEASEEE it’s due at 11:59 and it’s 11:24 right now
Answer:
I think its A but I could be wrong, I say this because is the most logical. I think its a 70% chance im right.
Step-by-step explanation:
Hope you get an A!
Answer:
Mr. Smith's age INCREASES the MEAN of the data
Step-by-step explanation:
The median is still 12 with and without Mr. Smith's age.
The mode is still 12 with and without Mr. Smith's age.
A mean can't decrease when there's an additional number
The only response that makes sense would be that his age increases the mean of the data
Say NANI and will give a lot of points
solve the equation sin38=x/10
Answer:
6.1566
Step-by-step explanation
Easy:
Sin 38 = x/10
Multiply 10 on both sides to cancel out the 10 under the x
This will equal to:
10(sin 38) = x
Simply enter 10(sin 38) in the calculator like desmos scientific.
Your answer is about 6.1566
Answer:
sin38=x/10
0.29=x/10.
doing crisscrossed multiplication
0.29×10=x
x=2.9=3 while doing round off
Use the property of parallelograms to solve for the missing variable
Answer:
x = 30, y = 6
Step-by-step explanation:
Here, we want to use the property of parallelograms
mathematically, the lengths of the parallel sides are equal
This mean:
2y + 3 = y + 9
2y - y = 9-3
y = 6
To get x;
Angles that face each other are supplementary; meaning they add up to 180
Thus, we have that
4x + 2x = 180
6x = 180
x = 180/6
x = 30
What is the coefficient of the third term in this expression?
5b³ - 10 + 4c³?
Answer:
4
Step-by-step explanation:
A coefficient is a number before the variable. The third term is 4c^3, and the coefficient is 4.
Hope this helps!
Help me with this please
Answer: (5,4)
4 + 6 / 2 = 5
10 + (-2) / 2 = 4
43 1/3 rounded to the nearest whole number
Answer:
43
Step-by-step explanation:
43 is the answer. here you go
can anyone pls help with this ASAP!!! :((
Answer: I believe your answer is C.
Answer:
the correct answer is C.
Step-by-step explanation: