Answer:
(0, 3) (0.75, 0)
Step-by-step explanation:
A baker made 30 pastries in 2 1/2 hours. how many pastries did the baker make in one hour?
Answer:
12 pastries
Step-by-step explanation:
30/2.5 = 12
check:
12(1 hour) +12(1 hour) +6(Half hour) = 30
After Verifying that the functions 1 2 satisfy the corresponding homogeneous equation of the given equation, find a particular solution of the non-homogeneous equation and then the general solution of the equation .
x²y'' + xy' + (x² - 0.25 ) y = 3x √xsinx
x> 0
y1(x) = sin (x) / √x
y2(x) = cos (x) / √x
To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.
First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):
W(y1, y2) = | y1 y2 |
| y1' y2' |
We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:
y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))
y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))
Substituting these values into the Wronskian:
W(y1, y2) = | sin(x) / √x cos(x) / √x |
| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |
Expanding the determinant:
W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))
Simplifying:
W(y1, y2) = -1 / (2√x)
Now, we can find the particular solution using the variation of parameters formula:
y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx
Here, g(x) = 3x√xsin(x). Substituting the values:
y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx
Simplifying the integrals:
y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)
Integrating:
y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C
Simplifying:
y_p(x) = 3x(sin^2(x) - cos^2(x)) + C
The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:
y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C
where C1, C2, and C are arbitrary constants.
Rolling a sum of 12 on two siz-sided dice?
Answer:
2/6 chance bc you have two dice that both need to roll a 6
Step-by-step explanation:
Given 2 lines cut by a transversal, what would the m<7 have to be if m <4=85 for the lines to be parallel and what is the relationship between <7 and <4
Answer:
85º
Step-by-step explanation:
<7=<4 since we know the lines are parallel, and intersected at the same angle
Therefore, <7=85º.
Find the total surface area of this triangular prism.
10 cm
6 cm
4 cm
8 cm
Answer:
I need the labels (Height , Width, Length)
Step-by-step explanation:
13) The pet shop has 6,157 dog treats. They packed the treats into bags with 7 pieces in each bag. Any treats
that did not fit into a bag of 7 were given to the groomer to use to reward animals getting bathed. How many
bags of treats did they fill? How many treats were given to the groomer?
bags of treats and gave
left over treats to the groomer.
Answer: The pet shop filled___bags of treats and gave ____left over treats to the groomer.
The number of bags filled by the pet shop is 879 and the number of treats they gave to the groomer is 4.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the data given in the question,
Total number of dog treats in the shop = 6157
Number of treats per bag = 7
Extra treats will be given to the groomer.
Then, the number of bags will be,
6157/7 = 879.57
This means that a total of 879 bags are there, with 7 pieces of treats per bag.
So, the total number of treats in 879 bags will be,
879 × 7 = 6153
So, the amount of treats left for the groomer is,
6157 - 6153 = 4 treats.
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help me with the last one 20 pointsss!!!!
Answer:
what you need help with? ill help if i can
Step-by-step explanation:
83. For what value of K will the points (1, 4), (-3, 16) and (k, -2) lie on one straight line.
Answer:
I don't know
Step-by-step explanation:
I don't know
Answer:
k = 3
Step-by-step explanation:
If the points lie on the same line then the slope between the points will be equal.
Calculate the slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (- 3, 16)
m = \(\frac{16-4}{-3-1}\) = \(\frac{12}{-4}\) = - 3
Repeat the process and equate to - 3
with (x₁, y₁ ) = (1,4) and (x₂, y₂ ) = (k, - 2)
m = \(\frac{-2-4}{k-1}\) = \(\frac{-6}{k-1}\) , then
\(\frac{-6}{k-1}\) = - 3 ( multiply both sides by k - 1 )
- 6 = - 3(k - 1) ← divide both sides by - 3
2 = k - 1 ( add 1 to both sides )
3 = k
(03.02 MC)
a
R
Which set of transformations would prove AQRS-AUTS?
Reflect AUTS over y = 2, and dilate AUT'S' by a scale factor of 2 from point S.
Reflect AUTS over y = 2, and translate AU'T'S' by the rule (x - 2, y + 0).
Translate AUTS by the rule (x + 0, y + 6), and reflect AUT'S' over y = 6.
Translate AUTS by the rule (x-2, y + 0), and reflect AU'T'S' over y = 2.
I am stuck please help with this graph.
An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.
How to interpret and determine the equation of g(x)?By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;
f(x) = |x|
y = A|x + B| + C
g(x) = -1/4|x + 1| - 2
In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.
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A paperclip weights 0.83g on average.
An empty envelope itself weighs 2.43g.
One such envelope contains a mystery number of paperclips inside.
With paperclips inside, it weighs 49.5g
Calculate number of paperclips
Step-by-step explanation:
Subtract the envelope weight from the total weight....this will result in the weight of the paperclips alone:
49.5 g - 2.43 g = 47.07 g of paper clips
Then:
47.07 g / ( .83 g /clip) = 56.7 = ~ 57 clips
answer for equation in picture
Answer: 2 time 3 C
Step-by-step explanation:
How much interest would 2000 earn, with simple interest, in two years at the rate of 1.2%?
The simple interest, in two years at the rate of 1.2% is 880
In this case, we must calculate how much interest 2000 would earn compounded yearly over two years at a rate of 1.2.
I = 880 in interest earned
Annually, the system may be evaluated in terms of simple interest.
A = P(rt) for the first year, where r = 1.2 and t = 1.
Therefore;
A = 2000(1.2×1).
A = 2400.
As a result, the revised Principal amount for the second year is 2400.
As a result, A' = 2400 (1.21).
A' = 2880.
As a result, the sum owing after two years is 2880.
However, because the initial principal is $2,000,
The interest is defined as I = A' - P, or I = 2880 - 2000.
I = 880 as a result of interest.
Simple interest is computed as S.I. = P R T, where P = Principal, R = Annual Rate of Interest in %, and T = Time, commonly expressed as the number of years. The interest rate is expressed as a percentage r% and is written as r/100.
The principle is the money borrowed from the bank or invested at the outset. P represents the principal.
Rate: The rate of interest at which the principle amount is handed to someone for a specific period of time; the rate of interest can be 5%, 10%, or 13%, for example. R represents the interest rate.
Time is the length of time for which the primary amount is supplied to someone. T represents time.
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Jordan is working two summer jobs, making $6 per hour walking dogs and making $15 per hour clearing tables. In a given week, he can work a maximum of 11 total hours and must earn at least $120. If xx represents the number of hours walking dogs and yy represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
xx=5 and yy=6
Step-by-step explanation:
Hope it helps you
Please help me answer this correctly,
anywhere you see x, input the value in the brackets.
eg f(-2) = 2(-2)+8
= -4+8
=4
Answer:
if x= -2
then f(x) = 2×(-2)+8
= -4+8
= 4
if x=0
then f(x)=2×0+8
=0+8
=8
if x=5
then f(x)=2×5+8
=10+8
=18
please help!! need it fast, will give brainliest!! and pls show work !!
Find the measure of angle AEB
Answer:
An acute angle
Step-by-step explanation:
An acute angle is smaller than an obtuse ad right angle.
hope this helps and hope it was right 'cause I really don't know what you meant. :)
Padma bought 3 pounds of grapes. Each pound of grapes costs $2.75. How much money did Padma spend on grapes?
Hii!
We need to multiply so
3×2.75= 8.25
So she paid $8.25
Brainliest!=
Problem 3.4 (Video 2.5 - 2.6, Lecture Problem) You are interested in calculating the probability that your favorite 1
Game of Thrones character is eliminated in episode X. You have decided to model X as a Geometric (1/4) random variable. (a) Unfortunately, you have learned a spoiler: your favorite character does not appear in episode 4 or beyond. What is the conditional PMF P X∣B
(x) of X given the event B={X<4} ? (b) Given this spoiler, what is the probability that your favorite character is eliminated in one of the first two episodes? (c) Given this spoiler, what is the expected value of X conditioned on the event B ? (d) Let's consider yet another scenario: After watching the show for 2 episodes, you are happy to see that your favorite character has not been eliminated yet. What is the conditional PMF P X∣C
(x) of X given the event C={X>2} ? 1
Somehow, you have already managed to decide on a favorite character before watching any episodes. 2 (e) Let Y=X−2 be the number of additional episodes after the 2 nd that it takes for your favorite character to be eliminated. Using part (d), quickly determine the conditional PMF P Y∣C
(y) of Y given the event C={X>2}. Determine the family of random variables this conditional PMF belongs to, along with the associated parameter(s). (f) Using what you learned in part (e), determine the conditional mean E[X∣C].
(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula
P(X=x|B) = P(X=x and B)/P(B).
Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:
P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.
Therefore, the conditional PMF P X∣B (x) is given by:
P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13
(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.
(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.
(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:
P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...
(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.
(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.
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Find the area of the regular pentagon with apothem 3.5 and side. Not drawn to scale.
100 POINTS
SHOW WORK PLEASE
Answer:
52.5 inch square
Step-by-step explanation:
Area of pentagon: A = 1/2 × p × a;
where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.
A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5
The area of the regular pentagon with apothem 3.5 and side 6 is 52.5
What is the area of the regular pentagon?In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.
How to find the area of the regular pentagonGiven the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.
In order to find the area, the formula to calculate the area of the regular pentagon is given by:
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)
Where “s” is the side length. And “a” is the apothem length.Now,
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)
\(\text{Area of pentagon} =52.5\)
Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5
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Can someone please help me with this geometry question
Answer:
Step-by-step explanation:
PLEASE HELP!!!
Triangle ABC has vertices at A(-5,2), B(1,3), and C(-3,0). Determine the coordinates of the vertices for the image of the pre image is translated 4 units right.
A. A’(-9,2),B’(-3,3), C’(-7,0)
B. A’(-4,6),B’(0,7),C’(1,0)
C. A’(-1,2),B’(5,3),C’(1,0)
D. A’ (-5,-2), B’(-1,-1), C’(-3,-4)
The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).
What is translation on a coordinate plane?Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.
During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.
Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.
So,
\(\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}\)
\(\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}\)
\(\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}\)
Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).
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The 5-lb collar slides on the smooth rod, so that when it is at A it has a speed of 10 ft/s. A) if the spring to which it is at- tached has an unstretched length of 3 ft and a stiffness of k-= 10 lb/ etermine the normal force on the collar at this instant. B)Determine the acceleration of the collar at this instant.
The acceleration of the collar at point A is 5 ft/s^2.
A) To determine the normal force on the collar at point A, we need to consider the forces acting on the collar. The only force acting on the collar in the vertical direction is the weight of the collar (5 lb), which is balanced by the normal force exerted by the rod. Therefore, we can write:
N - 5 = 0
where N is the normal force. Solving for N, we get:
N = 5 lb
B) To determine the acceleration of the collar at point A, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force on the collar is given by the force exerted by the spring, which is equal to the spring constant times the displacement of the collar from its unstretched length. At point A, the displacement of the collar is:
x = L - y = 3 - 0 = 3 ft
where L is the length of the rod and y is the position of the collar on the rod. Therefore, the force exerted by the spring is:
F = kx = 10 lb/ft × 3 ft = 30 lb
The weight of the collar is:
W = mg = 5 lb
where g is the acceleration due to gravity. The net force on the collar is therefore:
Fnet = F - W = 30 - 5 = 25 lb
Using Newton's second law, we can write:
Fnet = ma
where a is the acceleration of the collar. Solving for a, we get:
a = Fnet / m = 25 lb / 5 lb = 5 ft/s^2
Therefore, the acceleration of the collar at point A is 5 ft/s^2.
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Explain how decimal place value is like place value with whole numbers. Use pictures or words to explain your thinking.
The Explanation of decimal place value is like place value with whole numbers is shown below.
We know,
Each place value to the left of a whole number is multiplied by ten, but a place value to the right of a decimal number is divided by ten.
For example,
We take whole number 254 where place values are
2- Hundred, 5- Tens and 4- Ones
and, take the decimal 2.369 where the place values are
3- Tenth, 6- hundredth and 9- thousandth
So, both decimal and whole number have similar concept of place value but one is multiplied by 10 and other is divided by 10.
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(a) From Latoya's results, compute the experimental probability of rolling a 1 or 6.
(b)Assuming that the cube is fair, compute the theoretical probability of rolling a 1 or 6.
(c)Assuming that the cube is fair, choose the statement below that is true.
A. The experimental and theoretical probabilities must always be equal.
B. As the number of rolls increases, we expect the experimental and theoretical probabilities to
become closer, though they might not be equal.
C. As the number of rolls increases, we expect the experimental and theoretical probabilities to
become farther apart.
(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.
Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.
Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.
(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).
Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.
(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.
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Steven travel for 10 hours at a constant rate of 53 miles per hour Stephanie traveled the same distance at a constant rate of 48 miles per hour how long did it take Stephanie to travel the same distance as Steven write your plan to solve in the correct order.
Answer:
11.04hrs
Step-by-step explanation:
Since Steven traveled 530 miles (number of hrs times mph) we would just divide 530 and 48 which is 11.04 hrs
The walls of a square room need painting. Each of the four walls is 12ft wide by 8.5 feet tall. One gallon of paint covers 75ft2. How many gallons will you need
Answer:
5.44 gallons of paint
Step-by-step explanation:
First, we calculate the total area of the walls we need to paint. To do this, we use the formula for the area of a rectangle and we multiply our answer by 4, since there are 4 walls.
Area=(length*width)4
Area=(12*8.5)4
Area=(102ft^2)4
Area=408ft^2
Therefore, the total area of the walls is 408ft^2.
Now, we need to calculate the number of gallons we need to paint 408ft^2 worth of wall. Because we know that one gallon of paint covers 75ft^2, we can calculate this by dividing 408 by 75.
408/75
=5.44 gallons
Therefore, we would need 5.44 gallons of paint to paint the four walls.
I hope this helps!
Please help me find the slope of the line which one would it be ? :) and why
Answer:
y = \(\frac{5}{2} x\) + \(\frac{1}{2}\)
Step-by-step explanation:
To find the slope you need to find rise over run. Rise is how many squares it went up or down (when it goes down make it negative) from the lowest point to the highest point. Run is how many squares it went to the side from the point on the left to the point to the right. In this case the rise is 5 because it went up 5 squares and the run is 2 because it went 2 squares to the right. This means the slope is \(\frac{5}{2}\).
Hope this helped! Please give Brainliest.
answer this please!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
200
Step-by-step explanation:
\(a^{2}\) + \(b^{2}\) = \(c^{2}\)
\(120^{2}\) + \(160^{2}\) = \(c^{2}\)
14400 + 25600 = \(c^{2}\)
40000 = \(c^{2}\)
\(\sqrt{40000}\) = \(\sqrt{c^{2} }\)
200 = c
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Exam Instructions
Question 16 of 20 :
Select the best answer for the question
16. Solve this equation: 4y + 228 = 352.
A. y = – 31
B. y = 31
ОС. у = 3
D.y = 145
Mark for review (Will be highlighted on the review page)
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1
Answer:
Answer is B. Y=31
Step-by-step explanation:
4y + 228 = 352
(4)(y) = 352 -228
y = 124/4
y = 31
Answer:
B. y = 31
Step-by-step explanation:
Subtract 228 from both sides
4y + 228 - 228 = 352 - 228
4y = 124
Divide both sides by 4 to solve for y
4y / 4 = 124 / 4
y = 31
The half-life of carbon-14 is 5,730 years. Suppose a fossil is found with 15 percent, as much of its carbon-14 as compared to a living simple. How old is the fossil? Round to the nearest year
Hello there. To solve this question, we'll have to remember some properties about half-life of carbon-14.
We can use the following formula to determine how many years has passed by finding how many half-life sessions the carbon-14 endured:
\(t=\mleft\lbrack\frac{\ln\mleft(\frac{N}{N_0}\mright)}{-0.693}\mright\rbrack\cdot t_{\frac{1}{2}}\)In which:
\(t_{\frac{1}{2}}=5730\)In this case, N is the amount of sample we have after the period t of time and N0 is what we started with.
Knowing that the fossil was found with 15% of its initial sample, this means that the ratio N/N0 = 15/100 = 3/20=0.15
Therefore we have:
Using a calculator, we find that ln(0.15) is approximately equal to -1.89712, thus
Multiply the numbers and round the answer to the nearest year: