Complete the table shown to the right for the half life of a certain radioactive substance.
Decay rate:1.5% per year=-0.015
The half life is ___ years
Answers
Given:
Decay rate: 1.5% per year = -0.015
To find:
The half life.
Solution:
The continuous exponential decay function is
[tex]A(t)=Ae^{-kt}[/tex]
where, a is initial value, -k is decay rate and t is time period.
For half life, [tex]A(t)=\dfrac{A}{2}[/tex],
[tex]\dfrac{A}{2}=Ae^{-0.015t}[/tex]
Dividing both sides by A.
[tex]\dfrac{1}{2}=e^{-0.015t}[/tex]
Taking natural log on both sides.
[tex]\ln \dfrac{1}{2}=\ln e^{-0.015t}[/tex]
[tex]-0.69314718=-0.015t[/tex]
Divide both sides by -0.015.
[tex]\dfrac{-0.69314718}{-0.015}=t[/tex]
[tex]46.209812 =t[/tex]
[tex]t\approx 46[/tex]
Therefore, the half life is 46 years.
Related Questions
16.437 rounded to the nearest hundredth is 16.43 True or False? (I was just checking if this was false I think its true)
Answers
help me plz I can't get the answer right
Answers
Answer:
(If they give you a decimal place to round to use that) :)
9: 0.1026272578 mL/g
10: 1.8666666667 mL/g
Step-by-step explanation:
Density is M / V like a kinda heart you know? So mass divided by volume, the sink or float part you give context for although that is the density
Please answer this correctly fast!!
Options:
- SSS
- SAS
- ASA
- AAS
- HL
- Not Possible
Answers
Answer:
ASA
Step-by-step explanation:
Angle Side Angle
As two lines are parallel, alternate interior angles are congruent and the side between these angles are common for both triangles
Which starements are true about points A, B, and C? check all that apply.
Answers
Answer:
2
Step-by-step explanation:
2 seems to be the only one that is correct
Correct Statements: (modified the statements that are incorrect)
1. The coordinates of point A are (-3, 3)
2. Already correct
3. The coordinates of point C are (-2, -2)
4. Point B is the closest to the y-axis (only one away)
5. Point A is 3 away and Point B is 1 away
(sorry if this is confusing but this is what I got)
Connor used 2/3 inch of wire to make a small hook. How many hooks can he make
with 16 inches of wire?
Answers
Answer:
24
Step-by-step explanation:
you divide 16 by the decimal form of 2/3 (0.66666666666666666666666...) and you get your answer, 24.
I hope this helped :))
Answer:
24
Step-by-step explanation:
you divide 16 by the decimal form of 2/3
you get 24.
Given: FG is an median. What can you conclude?
Answers
Answer:
The last option line DG is congruent to line GE
Step-by-step explanation:
Median: a segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side
So basically G is the midpoint of DE because FG is the median.
The last option, we can conclude that line DG is congruent to line GE
What is median?Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong same number of observations.
Median is a line segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side.
We are given that FG is an median.
Thus, basically G becomes the midpoint of DE because FG is the median.
So, DG = GE
Hence,
The last option, we can conclude that line DG is congruent to line GE
Learn more about median;
https://brainly.com/question/17060266
#SPJ2
Timothy went to a baseball game. After the game, he wanted to ride the bus home. The red line and the blue line buses both stop at the stadium.
● A red line and a blue line bus both left the stadium at 4:00 p.m.
● Red line buses were scheduled to leave the stadium every 6 minutes.
● Blue line buses were scheduled to leave the stadium every 8 minutes.
If the buses run on schedule, when is the next time a red line and a blue line bus will leave together? Show your work.
Answers
Answer:
At 4:24 p.m.Step-by-step explanation:
We need to find the lowest number that is divisible by both 6 and 8.
LCM(6, 8) = 24So, next time is after 24 minutes and every 24 minutes after that.
4: 00 p.m. + 24 min = 4:24 p.m.Answer:
Solution :-For finding next time a red line and a blue line bus will leave together we will find LCM of 6 and 8.
LCM = (6,8) = 24
Now,
Let's find add the time to LCM
[tex] \tt \: 4 : 00 + 0 : 24 = 4 : 24[/tex]
0.095-20/5=
Write it as a decimal
Answers
Answer:
-3.905
Step-by-step explanation:
0.095 - 20/5
0.095 - 4
-|4-0.095|
-|3.905|
-3.905
At a school 1/2 of the pupils walk to school.
2/5 of the pupils get the bus.
The remaining 68 pupils get a lift in a car.
Calculate the number of pupils who get the bus and who walk to school.
Answers
Answer:
i guess the answer is 680.
who can help me solve this problem?
Answers
Answer:
30, 28, 34, -6, 44
Step-by-step explanation:
Which postulate or theorem can be used to prove ABC = DCB
Answers
Answer:
SSS theorem
Step-by-step explanation:
SSS theorem
The graph of f^ prime is shown. Find and sketch the graph of f given that fis continuous and f(0) = 1 .
(#72 in the pic)
Answers
9514 1404 393
Answer:
see attached (blue line)
Step-by-step explanation:
The slope in the first interval (0 to 2) will be -1, down from the y-intercept of 1.
The slope in the second interval will be 2. After that, the slope is zero, so the graph is a horizontal line.
The blue line in the attached is the graph of f(x).
Jess saved $500 working during the summer. He plans to buy school clothes with his money. He found jea
exactly twice as many shirts as jeans, how many pairs of jeans can Jess buy without exceeding $500?
Answers
Answer:
167 pairs
Step-by-step explanation:
Represent jeans with J and shirts with S
[tex]S = 2J[/tex]
[tex]Amount = \$500[/tex] --- Maximum
Required
Determine the number of pair of jeans he can buy
To represent as an inequality, we have:
[tex]S + J \leq Amount[/tex]
[tex]S + J \leq 500[/tex]
Substitute 2J for S
[tex]2J + J \leq 500[/tex]
[tex]3J \leq 500[/tex]
Divide through by 3
[tex]J \leq 500/3[/tex]
[tex]J \leq 167[/tex]
Hence, without exceeding $500, Jess can buy 167 pairs of jeans
Answer:
7
Step-by-step explanation:
30( 7 ) + 14( 12 ) =448 [tex]\leq[/tex] 500
What postulate/theorem can be used to prove the following triangles congruent?
Answers
Answer:
ASA
Step-by-step explanation:
since 2 angles and 1 side is the same, the triangles are congruent by the ASA theorem
Answer right and get branliest
Answers
Answer:
8 outfits
Step-by-step explanation:
Each number represent a different shirt and each letter represents a different skirt:
1 2 3 4
A B
Outfits:
1A 2A 3A 4A
1B 2B 3B 4B
(hope this helps, i don't really know how to explain it)
Answer:
I got 8!
Step-by-step explanation:
Alina and Asim share 210 dollars In the ratio 2:5 how much money did each of them get ?
Answers
Answer:
Let Alina share be 2x and asking share be 5x
then, 2x+5x =210 dollars
7x =210 dollars
x=30 dollars
then share of Alina = 2x = 2 * 30 = 60 dollars
and share of asim= 5x = 5 * 30 = 150 dollars
Answer:
I hope the above pic will help you I have done it in word
I will always help you understanding your assingments
have a great day
#Captainpower:)
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1
Axis of symmetry: x = -0.5; Vertex: (-0.5, -0.75); f(x) = x2 - x + 1
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = -x2 + x
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + 2x + 1
Answers
Answer:
Option A: Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1
Step-by-step explanation:
1) The axis of symmetry of quadratic graph is the vertical line that divides the graph curve into two congruent halves. In this case, it is: x = -0.5
2) Vertex is the point at which the graph curve changes direction or simply coordinates of the crest or trough of the curve.
The graph given has a trough with the coordinates: x = -0.5, y = 0.75. This is (-0.5, 0.75)
3) The roots of a quadratic equation are the points where the curve crosses the x-axis. In this case, it doesn't cross and so we have imaginary roots.
Now, formula for line of symmetry is; x = -b/2a
Thus; -b/2a = -0.5 or -b/2a = -1/2
Thus, b = 1 and a = 1
Our first and second terms will now be;
x² + x
Looking at the options, the only one with x² + x as it's first 2 terms is option A.
Thus, the complete equation will be x² + x + 1
Solve the system of equations using the elimination method.
(8x +11y = 37
8x+y=7
Answers
Answer:
8x +11y = 37 ---------(1)
_8x±y=_7 ----------(2)
-------------------
o+10y=30
Y=3
PUT Y IN EQ 2
8X+3=7
8X=7-3=4
X=1/2
Ans
I hope this Ans is helpful for you
Step-by-step explanation:
You are stuck at the Vince Lombardi rest stop on the New Jersey Turnpike with a dead battery. To get on the road again, you need to find someone with jumper cables that connect the batteries of two cars together so you can start your car again. Suppose that 16% of drivers in New Jersey carry jumper cables in their trunk. You begin to ask random people getting out of their cars if they have jumper cables. Use Scenario 6-17. On average, how many people do you expect you will have to ask before you find someone with jumper cables
Answers
Answer:
The expected number of people you will have to ask before you find someone with jumper cables is 6.25.
Step-by-step explanation:
The geometric distribution is the distribution of the number of X Bernoulli trials required for one success. If the one success requires k independent trials, each with the probability of success as p, then the probability that the kth trial is the one success is:[tex]p_{X}(k)=(1-p)^{k-1}p;\ k={1, 2, 3...}[/tex]
The geometric distribution is the distribution of the number of Y = X – 1 failures required before the first success. If the first success requires k failures, each trial with the probability of success as p, then the probability that the 1st success occurs after k failures is:[tex]p_{X}(k)=(1-p)^{k}p;\ k={0, 1, 2, 3...}[/tex]
In this case the first scenario follows.
X = number of people you will have to ask before you find someone with jumper cables.
p = 0.16
Compute the expected number of people you will have to ask before you find someone with jumper cables as follows:
[tex]E(X)=\frac{1}{p}\\\\=\frac{1}{0.16}\\\\=6.25[/tex]
Thus, the expected number of people you will have to ask before you find someone with jumper cables is 6.25.
Need help with this ASAP it’s due in 10 minutes
Answers
Answer:
Step-by-step explanation:
Formula to be used,
A = [tex]P(1+\frac{r}{n})^{nt}[/tex]
Here, A = Final amount
P = Principal amount
r = rate of interest
n = Number of compounding (In a year)
t = Duration of investment (In years)
Question (5)
P = $4250
r = 0.015
n = 4
t = 3 years
A = [tex]4250(1+\frac{0.015}{4})^{4\times 3}[/tex]
A = [tex]4250(1.00375)^{12}[/tex]
A = $4445.24
Part (C)
1). P = $6000
r = 0.03
n = 2
t = 10 years
A = [tex]6000(1+\frac{0.03}{2})^{2\times 10}[/tex]
= [tex]6000(1.015)^{20}[/tex]
= $8081.13
2). P = $9000
r = 0.05
n = 2
t = 8 years
A = [tex]9000(1+\frac{0.05}{2})^{2\times 8}[/tex]
= [tex]9000(1.025)^{16}[/tex]
= $13360.55
An emergency medical technician earns $19.71 per hour. One month she earns a gross pay of $3326.06. How much did she make per week if it was a 4.5 - week month? Round off the answer to two decimal places also. How much did she make per week if it was a 4.5 - week month? Round off the answer to two decimal places.
Answers
Answer:
The emergency medical technician made $739.12 per week
Step-by-step explanation:
Given that:
Per hour pay = $19.71
One month earning of emergency medical technician = $3326.06
Weeks in the following month = 4.5
For per week income, we will divide the monthly salary by number of weeks in the month.
Per week income = [tex]\frac{3326.06}{4.5}[/tex]
Per week income = $739.12
Hence,
The emergency medical technician made $739.12 per week
Todd has been helping his grandmother vanilla ice cream. Yesterday morning they made 4.5 quarts of ice cream. They are going to store the ice
cream in pint sized containers to place in the freezer.
Calculate how many pint-sized containers Todd needs to store 4.5 quarts of ice cream.
Todd will need
pint-sized containers to store 4.5 quarts of ice cream
Answers
Answer:
Todd will need 9 pint-sized containers to store 4.5 quarts of ice cream.
45.15 ÷ 21 pleases solve it for me
Answers
Answer:
2.15
Step-by-step explanation:
Write an equation for the line perpendicular to 4x - 12y = 2 and passing through point (10, -1)
Answers
Answer:
3x+y=-31
Step-by-step explanation:
[tex]4x - 12y = 2\\12y = 4x-2\\y=\frac{x}{3}-\frac{1}{6}[/tex]
Slope of perpendicular line is -3.
[tex]y=-3x+b[/tex]
Sub in the point (10, -1)
[tex]-1=-3(10)+b\\-1=30+b\\b=-31\\y=-3x-31\\3x+y=-31[/tex]
PLEASE PLEASE HELP ME
Which of the following angles is coterminal with -610?
1. 110
2. 70
3. 250
4. 20
Answers
Answer:
1. 110°Step-by-step explanation:
Given angle - 610°
Coterminal angle is an angle in the interval 0°- 360° added or subtracted to multiples of 360°:
-610° + 2*360° = -610° + 720° = 110°Correct option is 1.
What’s 3/8 OF 5 as a mixed number
Answers
Answer:
Step-by-step explanation:
2 3;8
Answer:
1 7/8.
Step-by-step explanation:
5 * 3/8
= 15/8
= 1 7/8.
Solve the system:
3x+6y=51
y=40-5x
Write down your solution here
Answers
Answer:
x=7 y=5
Step-by-step explanation:
3x+6(40-5x)=51
3x+240-30x=51
-27x+240=51
-27x=-189
27x=189
x=7
y=40-5(7)
y=40-35
y=5
You need to used the second equation and isolate either x or y. It’s your choice. Then, use that and substitute it in for the first equation. Then you will get an integer and substitute it back to the second equation.
ASAP please
If y is directly proportional with x and
y = 3.6 when x = 30, what is the
value of y when x = 40?
Answers
Answer:
y=k*x
plug in the known values of x and y and use them to solve for k
then you can use the new value of k to solve for y when x=40
Step-by-step explanation:
cuz cuz you need it to be directly that's what you need to
Pls help ASAP Explain why this mapping is or is not a function.
A. This is a function because every input maps to only one output
B. This is a function because every output maps only the input
C. This is not a function because more than on input maps to an output
D. This is not a function because more than one output maps the input
Answers
Answer:
correct answer is a
Step-by-step explanation:
its a function as long as every input has one output, 1 output can have any number of inputs
i choose d mb i got it wrong
find the inverse with respect to addition of 9
Answers
Work Shown:
Let x be the additive inverse of 9
This means it adds to 9 to get 0
x+9 = 0 which solves to x = -9 after subtracting 9 from both sides.
So -9+9 = 0 and 9+(-9) = 0.
Answer:
-9.
Step-by-step explanation:
Because 9 + (-9) = 0.
