Answer:
About 0.6548 grams will be remaining.
Step-by-step explanation:
We can write an exponential function to model the situation. The standard exponential function is:
[tex]f(t)=a(r)^t[/tex]
The original sample contained 510 grams. So, a = 510.
Each half-life, the amount decreases by half. So, r = 1/2.
For t, since one half-life occurs every 38 days, we can substitute t/38 for t, where t is the time in days.
Therefore, our function is:
[tex]\displaystyle f(t)=510\Big(\frac{1}{2}\Big)^{t/38}[/tex]
One year has 365 days.
Therefore, the amount remaining after one year will be:
[tex]\displaystyle f(365)=510\Big(\frac{1}{2}\Big)^{365/38}\approx0.6548[/tex]
About 0.6548 grams will be remaining.
Alternatively, we can use the standard exponential growth/decay function modeled by:
[tex]f(t)=Ce^{kt}[/tex]
The starting sample is 510. So, C = 510.
After one half-life (38 days), the remaining amount will be 255. Therefore:
[tex]255=510e^{38k}[/tex]
Solving for k:
[tex]\displaystyle \frac{1}{2}=e^{38k}\Rightarrow k=\frac{1}{38}\ln\Big(\frac{1}{2}\Big)[/tex]
Thus, our function is:
[tex]f(t)=510e^{t\ln(.5)/38}[/tex]
Then after one year or 365 days, the amount remaining will be about:
[tex]f(365)=510e^{365\ln(.5)/38}\approx 0.6548[/tex]
MANUFACTURING. The number of cars built varies
directly as the number of hours the production line
operates. What is the ratio of cars built to hours of
production? At this rate, how many cars can they
build in 5 hours?
Answer:
60 cars per hour
Step-by-step explanation:
What is the product ([tex](7\sqrt{8} +3\sqrt{12} )(7\sqrt{8} -3\sqrt{12})[/tex]?
The price of a technology stock was 9.57 yesterday. Today, the price rose to 9.66 . Find the percentage increase. Round your answer to the nearest tenth of a percent
Another submarine's descent can be represented as `y=-240x`, where u is the elevation and x is time in hours. How long will it take this submarine to make the descent (2,100 feet below the surface)?
Answer:
The time it will take is 8hours 45mins.
Step-by-step explanation:
Since y = –240x represents a submarine descent. We are looking for how long, that is the time, it will take for the submarine to make a descent of 2100. We know that y is the elevation, if it is descending it will be in the negative direction, making it -ve.
A descent of 2100 means y = –2100. Hence,
–2100 = –240x
x = –2100/–240 = 8.75hours = 8hours 45minutes. (0.75hours = 3/4hours = 3/4 x 60mins = 45mins).
how would you factor 12b^4+3b^2
Answer:
3b²(4b²+1)
Step-by-step explanation:
You can factor out a 3b²
3b²(4b²+1)
Answer:
Hey friend, need some help if you factor 3b^2 out of 12b^4+3b^2, in other words, 3b^2 (4b^2 + 1)
Show your work:
3b^2 (3b^2 / 12b^4) + (3b^2 / 3b^2)
PLZ give 5 stars, heart, and brainlyest
Equation
Number of Solutions
6(2.1 + 1) - 2 = 12.1 + 4
How many solutions does it have?
what is 8.154 to 1 decimal place?
A student has heard that spinning pennies on a table, rather than flipping them in the air, results in tails side up 65% of the time. If this is true, what is the probability that a student who spins 4 pennies will have them all land tails side up? 0.0150 0.1785 0.8215 0.9850
so I believe it is C 0.8215
The probability is 0.1785
What is probability?The study of how likely certain events are to occur is known as probability. In its simplest form, it is concerned with the fall of a game's cards or the roll of a dice. However, probability is also essential to life and science as a whole. Probability is used, for example, in weather forecasting and figuring out how much your insurance premiums will cost.
Given probability of tail by spinning a coin is 65% = 0.65
p(t) = 0.65 and p(h) = 0.35
where h= head and t= tail
coin spins 4 time
p(t) for first time = 0.65
p(t) for second time = 0.65 x 0.65 =0.4225
p(t) for third time = 0.65 x0.65 x 0.65 = 0.274
p(t) for fourth time = 0.65 x 0.65 x0.65 x 0.65 = 0.178
Hence probability that a student who spins 4 pennies will have them all land tails is 0.178
Learn more about probability;
https://brainly.com/question/9793303
#SPJ2
What is the slope of the line whose equation is -2y = -3x + 5?
Answer:
[tex]m = \frac{3}{2}[/tex]
Step-by-step explanation:
Use the slope-intercept form y = mx + b to find the slope m.
In this way, we can conclude that we can write it in slope-intercept form, y = mx + b:
[tex]y = \frac{3}{2} x - \frac{5}{2}[/tex]
Your correct answer would be:
[tex]y = \frac{3}{2} x - \frac{5}{2}[/tex]
Have a marvelous day.
Answer fast!!!!!!!!!!!!!!
Help me please I will give you brainlist!
Answer:
2x
Step-by-step explanation:
2x has a value of 4 because x = 0 and y = 4 so the answer would be 2x
I need help:(
Find x and y
Please let me know if my answer is right! Thanks!
Rename 2/3 and 4/5 so they have common denominators.
Answer:
2/3 multiply by 5 to get 10/15
4/5 mulitply by 3 to get 12/15
Step-by-step explanation:
Answer:
i mean wouldn't it be more like 2,3,4 2 , 3 , 4 is 2⋅2⋅3=12 2 ⋅ 2 ⋅ 3 = 12 ..
Step-by-step explanation:
Help please ASAP rn
Answer, population: 359 million
Answer:
Step-by-step explanation:
It went up 98 ten-tousandth, from 1950 to 1990 divide 2030, by 1990 and then multiply that answer by 98 ten-tousandth
What is 52% of 25? plzz helppp
Answer: its 13
Step-by- 52 percent *25 =
(52:100)*25 =
(52*25):100 =
1300:100 = 13
step explanation:
Answer:13
Step-by-step explanation:
25x0.52
Keelin’s hourly rate went from $9.50 per hour to $10.26 per hour. What is the percent increase?
Answer:
8%
Step-by-step explanation:
The vertex of the graph of g(x) = 3|x| + 4 is
Please help! Im failing math Rn! Please help!
Answer:
rickrolled.
Step-by-step explanation:
¯\_(ツ)_/¯
you won't learn by asking others. do it yourself.
Answer:
K
Step-by-step explanation:
which quadrilateral makes this statement true? Quadrilateral ABCD
Answer:
A.
Step-by-step explanation:
114.3 is what percent of 288? Round to the nearest hundredth. Please don’t get this wrong.
Answer:
39.69%
Step-by-step explanation:
Hope this helps!!
Savings Accounts
Alyssa starts with $30 and saves $5 each week. Bill has $16 and saves $7 each
week. At what week will Alyssa and Bill have the same amount of money?
Answer:
7 weeks
Step-by-step explanation:
Given data
Alyssa starts with $30 and saves $5 each week
let the number of weeks be x
y= 30+5x----------1
Bill has $16 and saves $7 each
week.
y= 16+7x----------------2
equate 1 and 2
30+5x= 16+7x
30-16= 7x-5x
14= 2x
x= 14/2
x= 7 weeks
if you know what’s going on pls help thanksss
basically u are representing the graphs below in symbols and words if that makes any sence
Answer:
1. > less than
2. =< (I can't find the symbol for this but a line should be under the < and thats it) Greater than or equal to
3. < greater than
4. >= less than or equal to
7/12
Which expression is equivalent to this fraction?
Answer:
12/7
Step-by-step explanation:
yes ! cd
Find each missing angle
Please
Answer:
m<1=61
m<2=40
m<3=60
m<4=80
m<5=100
Step-by-step explanation:
180/3=60
180/9=20
20x2=40
20x4=80
20x3=60
59+60=119
180-119=61
180-80=100
Please answer the correctly in the picture below 8TH GRADE MATHENMATICS?!
Answer:
B 3.5
Step-by-step explanation:
Hope it Helps!
ILL GIVE BRAINLIESAT FOR FIRST ANSWER!
Divide
3÷1/12
Step-by-step explanation:
is 36 hello my name is santiago i am fron Colombia
The vertices of parallelogram DEFG are E(-1,4) F(5,6) and G (8,0). Find the coordinates of D
Answer:
The coordinates of D are (2,-2)
Step-by-step explanation:
The coordinates of point D are (2,-2)
The coordinates of the parallelogram are given as:
E(-1,4), F(5,6) and G (8,0)
For the coordinates to represent a parallelogram, the following must be true
[tex]x_D - x_E = x_G - x_F[/tex]
[tex]y_D - y_E = y_G - y_F[/tex]
So, the equations become
[tex]x_D -(-1) =8-5[/tex] and
[tex]y_D -4 =0-6[/tex]
Solve for x and y in the above equations
[tex]x_D -(-1) =8-5[/tex]
[tex]x_D +1 = 3[/tex]
[tex]x_D = 3-1[/tex]
[tex]x_D = 2[/tex]
[tex]y_D -4 =0-6[/tex]
[tex]y_D - 4 = -6[/tex]
[tex]y_D = 4-6[/tex]
[tex]y_D =-2[/tex]
Hence, the coordinates of point D are (2,-2)
Read more about parallelograms at:
https://brainly.com/question/11874218
525 metres in 30 minutes
Answer:
what you want to know...
Step-by-step explanation:
please write complete question.....
So,I can understand it
the table shows a summary of the number of spots counted on 20 ladybug calculate the mean number of spots per lady bug
Answer:
bcbdjdsjxbxifjfbdbdbbxbxhxhdhdhbdbdbxbxbxbxbbxnxnxnxx
Can somebody plz help answer these correclty (only if done this before) like show the answer /how I’m suppose to write it thx :3
WILL MARK BRAINLIEST WHOEVER ANSWERS THESE FIRST :DDD!!!
Answer:
1) 3x = 39 ; x = 39/3 = 13
2) x + 7 = 15 ; x = 15-7 = 8
3) 6x = 18 ; x = 18/6 = 3
4) x-4 = 11 ; x = 11 + 4 = 15
5) 1/7 x = 3 ; x = 3 *7 = 21
6) 13+x = 21 ; x = 21 - 13 = 8
I hope im right!!!
