Answer:
2.5 half-lives
Step-by-step explanation:
Find [tex]t_{h}[/tex] in [tex]N(t)=N_{0}e^{-kt}[/tex] given [tex]N(t) = 2, N_{0} =64,t=\frac{25}{2}[/tex]
[tex]N(t)[/tex] is the amount after the time [tex]t[/tex], [tex]N_0[/tex] `is the initial amount, [tex]t_{h}[/tex] is the half-life
We know that after half-life there will be twice less the initial quantity:
[tex]N(t_{h})=\frac{N_{0} }{2}=N_{0}e^{kt_{h} }[/tex].
Simplifying gives [tex]\frac{1}{2} =e^{-kt_h} or k = -\frac{In(\frac{1}{2}) }{t_{h} } .[/tex]
Plugging this into the initial equation, we obtain that [tex]N(t)=N_{0}e^\frac{In(\frac{1}{2}) }{t_{h} }[/tex]or [tex]N(t)= N_{0} (\frac{1}{2})^\frac{t}{t_h}.[/tex]
Finally, just plug in the given values and find the unknown one.
From [tex]2=64(\frac{1}{2})^\frac{\frac{25}{2} }{t_h}[/tex], we have that [tex]t_h[/tex] = [tex]\frac{25 In (2)}{2 In (32)\\}[/tex]
So you should get: [tex]t_{h} =\frac{25 In (2)}{2 In (32)\\}=2.5.[/tex]
MARK ME AS BRAINLIEST IF YOU WISHThe number of half-lives that transpired during this time period is equal to 2.5 hours.
Given the following data:
Time = 12.5 hours.
Initial mass = 64 grams.
Remaining mass = 2.0 grams.
How to determine the number of half-lives.Mathematically, the amount of a radiocative element that is remaining after time (t-hours) is given by this formula:
[tex]ln(\frac{A}{A_0} )=ln(\frac{1}{2} )\frac{t}{H}[/tex]
Where:
A is the amount remaining.Ao is the initial amount.H is the half-life.t is the time.Substituting the given parameters into the formula, we have;
ln(2/64) = ln(1/2) × 12.5/H
-3.466 = -0.693 × 12.5/H
H = 12.5 × -0.693/-3.466
H = 12.5 × 0.1999
H = 2.5 hours.
Read more on half-life here: https://brainly.com/question/25750315
Which equation represents the function f(x) = (1.6)x after it has been translated 5 units up and 9 units to the right?
Answer:
It's C. g(x) = (1.6)x − 9 + 5
Step-by-step explanation: hope it helps ^w^
what shape can be formed from the following net?
Answer:
A Triangular Prism
Hope that helps!
Step-by-step explanation:
Answer: Triage
Step-by-step explanation:
Write an expression for the sequence of operations described below.
10 plus the quotient of 8 and u
Do not simplify any part of the expression.
Answer:
[tex]10 + \frac{8}{u}[/tex]
Step-by-step explanation:
Given
10 [tex]plus[/tex] the [tex]quotient[/tex]of 8 and u
Required
Represent as a mathematical expression
Square out the operators
10 [[tex]plus[/tex]] the [[tex]quotient[/tex]] of 8 and u
[tex]plus => +[/tex]
[tex]quotient => /[/tex]
Replace the operators with their signs
[tex]10 + \frac{8}{u}[/tex]
Is this right? Please help
Answer: I believe that is correct! good jobbb
Step-by-step explanation:
PLEASE HELP MEE it’s urgent
Answer:
positive9/50
Step-by-step explanation:
9/50
Answer:
the answer is 9/50 (fraction).
Step-by-step explanation:
hope this helped!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(x2 – 3x + 2)/(4x - 16)
Answer:
Pretty sure it's x^2−3x+2/4x-16
Step-by-step explanation:
8 friends go to Subway and each get 1/2 of a sandwich. How many sandwiches did they get altogether?
please help i will give brainliest
Make a equation for the scatter plot line
Answer:
y = -7.2x + 540
Step-by-step explanation:
to find the slope I used the x-and-y intercepts: (0, 540) and (75, 0)
slope = 540/-75 or -7.2
HELP HELP
Tommy rides in a motorboat against a river current for 25 km. Then he returns to his starting point by floating down river on a raft. Tommy travels 10 hours less on the motorboat than on the raft. Find the speed of the river current if the speed of the motorboat in still water is 12 km/h.
The speed of current is [tex]\rm 2 \:km/h[/tex].
What is the relation between distance,speed and time?The relationship between distance, time and speed can be presented as:
[tex]\begin{aligned} \rm Distance &= Speed \times Time\\\\Speed &= \dfrac{\rm Distance}{Time} \\\\\rm Time &= \dfrac{\rm Distance}{\rm Speed} \end[/tex]
Calculations:
Given:
[tex]\begin{aligned} \rm Distance\: traveled\: on\: motorboat &= 25\:km\\\rm Speed\:of\:motorboat\:in\:still\:water &= 12\:km/h \end[/tex]
Let the speed of the current be [tex]\rm x[/tex]
The speed of the boat traveling against the current is [tex]{(12 -\rm x) km/h}[/tex]
Time spent on motorboat is 10 hours less than time spent on raft.
Therefore:
[tex]\rm \dfrac{25km}{x\:km/h} - \dfrac{25km}{(12 - x)km/h} = 10[/tex]
The equation obtained will be:
[tex]\dfrac{25}{\rm x} - \dfrac{25}{(12-\rm x)} - = 10[/tex]
Multiplying both sides of the equation by [tex]\rm x(12 - x )[/tex]
[tex]\begin{aligned} \rm 25(12 - x) - 25x &= 10\times \rm x(12 - x)\\\\300 - 25x - 25x &= 120x - 10x^2\\\\300 - 50x &= 120x - 10x^2\\\\10x^2 - 120x - 50x + 300 &= 0\\\\10x^2 - 170x +300 &= 0\end[/tex]
Dividing the equation by 10
[tex]\rm x^2 - 17x + 30 = 0[/tex]
On factoring the equation,
[tex]\rm =x^2 - 2x -15x + 30 = 0\\\\=x(x - 2) -15(x - 2)\\\\=(x - 2)(x - 15)[/tex]
The values of x is 2 and 15.
Since speed of current i.e [tex](12 -\rm x)km/h[/tex] cannot be negative, [tex]\rm x = 2[/tex] is the only acceptable value.
Therefore the speed of current is 2 km/h.
Learn more about the topic here:
https://brainly.com/question/2292310
the tax on a purchase of $20 is $2.80. How much tax will there be on a purchase of $45.50?
Answer:
$6.37
Step-by-step explanation:
You divide 2.80 by 20 to find the percentage of tax then you simply multiply your percentange by the cost. In this problem the tax was 14% or .14, so you multiply .14 by 45.50 to find the amount of tax on the purchase
But least to greatest
Answer:
8.933,8.96,9.05,9.065,9.08,9.1
Step-by-step explanation:
What percent of $80 is $20
Answer: $20$20 is $25\%$25% of $80$80.
Step-by-step explanation:
25
98.8% of 668.49km NEED ANSWERS QUICK
Answer:
the answer would be 660.46812 km
Step-by-step explanation:
The computation is shown below:
According to the question it is mentioned what is the 98.8% of 668.49 km
So, it would be
= 98.8% of $668.49 km
= 98.8% × 668.49 km
= 660.46812 km
Hence, the answer would be 660.46812 km
The matrix is used to solve a problem. Which of the following would be a solution to the problem?
Answer:
(1,5)
Step-by-step explanation:
Hope this is right.
Answer:
It's (1,0)
Step-by-step explanation:
I got it right on the quiz
Don operates a small craft store in which he sells other peoples crafts. He takes a 45% commission from the sales of all crafts. If he earns $958.00 Commission last week, how much did he sell?
Answer:
2,128
Step-by-step explanation:
958=45/100 x
958= 0.45* x
x=958/0.45
x=2,128 approximately
Hope that helps!
The second term in a geometric sequence is 12. The fourth term in the same sequence is 4/3 what is the common ratio in this sequence
Answer:
The common ratio in this sequence is 6:2 or 4:3
Step-by-step explanation:
hopes this heklps
The factors of a polynomial are (x + 3x - 2)(x+ 7) The polynomial has been graphed. How do the zeros relate to the factors?
A. The zero is the sum of the numbers inside the parenthesis
B. There is no relationship between the factors and the zeros.
C. The number inside each parenthesis are the zeros of the equation.
D. If you set each factor equal to 0 and solved you would get the zeros.
Answer:
its C I am pretty sure about it
Answer:
D: If you set each factor equal to 0 and solved you would get the zeros.
Step-by-step explanation:
Completed it on PL also because 0 should be base
(9x10^10) - (4x10^10)
Answer: 50000000000 is your answer.
Step-by-step explanation:
Given that A and I are the centers of the congruent circles shown below, compare the quantity in column A with the quantity in column B. Choose the best answer. The quantity in column A is greater. The quantity in column B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
Answer: The two quantities are equal
Step-by-step explanation:
Edge2021
C. The two quantities are equal
Step-by-step explanation:
Edge 2020 2021
1344 divided by 16
(Pls ans)
Answer:
84
Step-by-step explanation:
Answer:
84
Step-by-step explanation:
1344/16=84
Please help when Kevin bought a new office phone, he borrowed $1,200 at a rate of 18% for 9 years
Answer:
where is the rest of the questions
what is the square root of -20
Answer:
4.47213595
Simplify in the tenths place and get 4.47
Step-by-step explanation:
Using lengths a, b, and c in the right triangle shown, how are the trigonometric functions of defined?
Answer:
take a pic.of question
Step-by-step explanation:
gotta see the triangle
Umm yea help me please:)
pls answer this-.....
AnswerS:
Let A be the surface area, b the base, h the height;
h₁=8.4 cm
h₂=7.8 cm
b= 9 cm
A= 3(1/2bh₁)+1/2 bh₂
A=3(1/2(9)(8.4))+1/2 (9)(7.8)
A= 148.5 cm³
Answer:
Step-by-step explanation:
The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.
Surface area of the square pyramid is given as:
Where,
B.A = Base Area of the pyramid = 9*9 = 81 in²
P = perimeter of the base = 4(9) = 36 in
L = slant height of pyramid = 9.2 in
Plug in the values into the given formula to find the surface are
PLS HELPPP
What value of x would make the following relation a function?
{(-3,-2),(2,3),(3,2),(x,2)}
A. -3
B. -2
C. 2
D. 3
which table shows ordered pairs that satisfy the function y=4x-2
A x -2, 0, 2
y -4, -2, 0
B x -2, 0, 2
y 10, 6, 2
C x -2, 0, 2
y -8, 0, 8
D x -2, 0, 2
y -10, -2, 6
==========================================================
Explanation:
If you plug in x = -2, then,
y = 4x-2
y = 4(-2)-2
y = -8-2
y = -10
This shows that the answer must be choice D, as this is the only answer that has x = -2 lead to y = -10. Note the first column of table D.
We could stop here if you wanted.
----------------------
If we kept going and plugged in x = 0, then,
y = 4x-2
y = 4(0)-2
y = 0-2
y = -2
We have x = 0 lead to y = -2. This matches with the second column of table D.
-----------------------
Lastly, if we plugged in x = 2, then we get,
y = 4x-2
y = 4(2)-2
y = 8-2
y = 6
So the third column of table D is also confirmed.
Can someone please help!!!
Answer:
its the 3rd one
Step-by-step explanation:
Use each number in the box once to complete the division
5÷6,206
Answer:
i believe it is 1,241.2
Step-by-step explanation:
well you use long division.