Answer:
The half-life of the radioactive substance is of 3.25 days.
Step-by-step explanation:
The amount of radioactive substance is proportional to the number of counts per minute:
This means that the amount is given by the following differential equation:
[tex]\frac{dQ}{dt} = -kQ[/tex]
In which k is the decay rate.
The solution is:
[tex]Q(t) = Q(0)e^{-kt}[/tex]
In which Q(0) is the initial amount:
8000 counts per minute on a Geiger counter at a certain time
This means that [tex]Q(0) = 8000[/tex]
500 counts per minute 13 days later.
This means that [tex]Q(13) = 500[/tex]. We use this to find k.
[tex]Q(t) = Q(0)e^{-kt}[/tex]
[tex]500 = 8000e^{-13k}[/tex]
[tex]e^{-13k} = \frac{500}{8000}[/tex]
[tex]\ln{e^{-13k}} = \ln{\frac{500}{8000}}[/tex]
[tex]-13k = \ln{\frac{500}{8000}}[/tex]
[tex]k = -\frac{\ln{\frac{500}{8000}}}{13}[/tex]
[tex]k = 0.2133[/tex]
So
[tex]Q(t) = Q(0)e^{-0.2133t}[/tex]
Determine the half-life of the radioactive substance.
This is t for which Q(t) = 0.5Q(0). So
[tex]Q(t) = Q(0)e^{-0.2133t}[/tex]
[tex]0.5Q(0) = Q(0)e^{-0.2133t}[/tex]
[tex]e^{-0.2133t} = 0.5[/tex]
[tex]\ln{e^{-0.2133t}} = \ln{0.5}[/tex]
[tex]-0.2133t = \ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.2133}[/tex]
[tex]t = 3.25[/tex]
The half-life of the radioactive substance is of 3.25 days.
[cached] 0.020980834960938 ms
Answer:
Just hoping this helps.
5th grade math. correct answer will be marked brainliest
The answer is b
saddsadsadas
Answer:
B
Step-by-step explanation:
Cause he added 24.76 more pounds to the 3.6 pounds. So you can take 24+3=27 and you might think C, but 0.76+0.6 that equals more than 1, so 27+1=28, and B has 28 as its answer, so its B
B
Please answer the question below
Answer:
Kilo —> 1×10³ grams
nano —> 0.000000001 meters
micro —> mean " one millionth"
centi —> 0.01 liters
Which two discontinuities does the graph show
Answer:
A
Step-by-step explanation:
please check screen shot
Answer: D
Step-by-step explanation:
Solve for x.
x + 2 over 4 = 8
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x +2}{4}=8}[/tex]
[tex]\large\textsf{MULTIPLY 4 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{x +2}{4}\times4=8\times4}[/tex]
[tex]\large\textsf{CANCEL out: 4}\times\large\textsf{4.}[/tex]
[tex]\large\textsf{KEEP: 8}\times\large\textsf{4 because it helps you solve for x}[/tex]
[tex]\mathsf{8\times4=\bf 32}[/tex]
[tex]\large\text{New equation: \textsf{x + 32 = \bf 32}}[/tex]
[tex]\large\textsf{x + 2 = 32}[/tex]
[tex]\large\textsf{SUBTRACT 2 to BOTH SIDES}[/tex]
[tex]\mathsf{x +2-2=32-2}[/tex]
[tex]\large\textsf{CANCEL out: 2}-\large\textsf{2 because that gives you 0}[/tex]
[tex]\large\textsf{KEEP: 32}-\large\textsf{2 because that helps you solve for x}[/tex]
[tex]\large\textsf{New EQUATION: \mathsf{x = 32 - 2}}[/tex]
[tex]\mathsf{x = 32 - 2}[/tex]
[tex]\large\textsf{Simplify above and you have your result to this equation}[/tex]
[tex]\mathsf{32-2=\bf 30}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf x =30}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
find 3 rational numbers between 1/3 and 1/2
The ancient Temple of Thos is believed to be buried near the north-south directed main canal through the modern city of Gyre. There is considerable uncertainty, though as to where. A probabilist believes that the distance D of the temple in miles north from the center of Gyre follows a moment generating function
mD(mu) = E(euD) = e18u2 + 10 u
a) Find the expected value of the distance north from city center archaeologists will have to travel to find the temple.
b) Find the standard deviation of that distance.
Answer:
Hence, the expected value of the distance north from city centre archaeologists will have to travel to find the temple is [tex]10[/tex] miles and the standard deviation of that distance is [tex]6[/tex] miles.
Step-by-step explanation:
Given :
Moment generating function.
[tex]m_D(u)=E(e^{uD})=e^{18u^2+10u}...(1)[/tex]
Any two functions can not have the same moment generating function.
The general moment generating function is :
[tex]m_D(u)=E(e^{uD})=e^{\frac{1}{2}\sigma^2u^2+\mu u}...(2)[/tex]
(a)
Now, compare the equation [tex](1)[/tex] and [tex](2)[/tex] we get,
[tex]\mu=10[/tex]
Therefore, the expected value of the distance north from city centre archaeologists will have to travel to find the temple is [tex]10 miles.[/tex]
(b)
Now, compare the equation [tex](1)[/tex] and [tex](2)[/tex] we get,
[tex]\frac{1}{2}\sigma^2=18[/tex]
[tex]\Rightarrow \sigma^2=18\times 2=36[/tex]
[tex]\Rightarrow \sigma=\sqrt{36}=6[/tex]
Therefore, the standard deviation of that distance is [tex]6[/tex] miles.
write the percent of each figure
that is shaded.
Answer:
1. 21% 2. 70%
Step-by-step explanation:
1. 21 out of 100 are filled in
2. 7/10 are filled in
Bill is selling stickers to raise money for a charity. He sold 36 stickers on the first day and 23 on the second day. He had 26 stickers left at the end of the second day. How many stickers did Bill have to start with?
Answer:
85 stickers
Step-by-step explanation:
y - 36 - 23 = 26
y - 59 = 26
y - 59 + 59 = 26 + 59
y = 85
Bill have to start with 85 stickers.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that Bill sold 36 stickers on the first day and 23 on the second day. He had 26 stickers left at the end of the second day.
Then the equation would be;
y - 36 - 23 = 26
y - 59 = 26
Subtract 59 from both the sides;
y - 59 + 59 = 26 + 59
y = 85
Hence, Bill have to start with 85 stickers.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest?
What is Tarah's new total balance?
Answer:
$258.48
Step-by-step explanation:
Help me guys find the solution please and thank you
4x+17=23
which equation is not a linear function:
y=2x
y=x+2
y=x-2
y=x²
Answer:
Step-by-step explanation:
A linear equation can be written in the form
y = mx+b.
y = x² is not linear.
Find the area of the parallelogram.
5 ft
10 ft
Answer:
50
Step-by-step explanation:
base x height is the area of a parallelogram
Evaluate each series.
Help pls 50 points
Answer:
1. 2,555
2. 23.25
Step-by-step explanation:
1. 5+10+20+...
S9 = 5(2^9-1)/(2-1)
= 5(511) = 2,555
2. 12+6+3+1.5+0.75 = 23.25
Someone help with this one please
Answer: 127.2
Step-by-step explanation: 1⁄2(a × b) + 3⁄2(b × s) is the formula for triangular pyramids. When you follow this formula for triangular pyramids, you will always get these correct.
Answer:
i forgot my answer this was my last weak module why am i so forgetfull
umm
127.2
How many solutions does this system have?
Answer: One
Step-by-step explanation: Recall that intersecting lines have one solution and therefore the system is consistent. Because the lines are not the same, the equations are independent.
In the diagram below, xy and z are tangent to 0. What is the measure of XZ?
Answer:
A. 130°
Step-by-step explanation:
Answer:130
Step-by-step explanation:
I just finished the quiz :)
Find the distance of the two given points (1,5) and (4,10)
Answer:
5.831
Step-by-step explanation:
Distance between both given points=Lenght=5.831
A bag contains eight white marbles, six red marbles and four blue marbles.
How many blue marbles must be added to the bag so that the probability
of choosing a blue marble is 1/2?
a. 6
b. 5
c. 10
d. 0
Answer:
c) 10
Step-by-step explanation:
you need to add the white and red marbles which would be 14.
then you subtract 14 by the amount of blue marbles.
Use this information for Items 5–7. There is a 60% probability of rain each of the next 5 days. Find each probability. Round to the nearest whole percent. PLEASE HELP ME!!!
Answer:
0.6808 = 68.08% probability that it will rain on at least 3 of the next 5 days.
0.9898 = 98.98% probability it will rain on at least 1 of the next 5 days.
0.84 = 84% probability it will rain on at least 1 of the next 2 days.
Step-by-step explanation:
For each day, there are only two possible outcomes. Either it rains, or it does not. The probability of raining on a day is independent of any other day. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
There is a 60% probability of rain each of the next 5 days.
This means that [tex]p = 0.6, n = 5[/tex]
Probability it will rain on at least 3 of the next 5 days:
This is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102[/tex]
[tex]P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768[/tex]
[tex]P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304[/tex]
So
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0120 + 0.0768 + 0.2304 = 0.3192[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.3192 = 0.6808[/tex]
0.6808 = 68.08% probability that it will rain on at least 3 of the next 5 days.
Probability it will rain on at least 1 of the next 5 days:
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
From the above item, we have that [tex]P(X = 0) = 0.0102[/tex]. So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0102 = 0.9898[/tex]
0.9898 = 98.98% probability it will rain on at least 1 of the next 5 days.
Probability it will rain on at least 1 of the next 2 days:
Two days means that [tex]n = 2[/tex].
The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.6)^{0}.(0.4)^{2} = 0.16[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.16 = 0.84[/tex]
0.84 = 84% probability it will rain on at least 1 of the next 2 days.
Simplify the radical plz help due in 10 min!!!!
In your own words, write three or four sentences explaining what exponents are and how they are used in math.
Answer:
Exponents are important in math because they allow us to abbreviate something that would otherwise be really tedious to write. If we want to express in mathematics the product of x multiplied by itself 7 times, without exponents we'd only be able to write that as xxxxxxx, x multiplied by itself 7 times in a row.
Step-by-step explanation:
what is the measure of EHG?
Hurry up please
Answer:
120 brainliest?
Step-by-step explanation:
Answer:
150°
Step-by-step explanation:
An obtuse angle is always 120°. You have to add 30 to it in order to get your final answer.
Can someone help with this ASAP
Answer:
x=7cm.
Step-by-step explanation:
A=1/2(a+b)h.
63=1/2(6+12)x.
63=1/2(18)x.
63=9×x.
63/9=9×x/9.
7cm=x.
x=7cm.
Is 2 a solution to the equation 1/2x-4=5?
9514 1404 393
Answer:
no
Step-by-step explanation:
Put 2 where x is and see if you get a true statement.
1/2(2) -4 = 5
1 -4 = 5
-3 = 5 . . . . . . False
2 is not a solution to the equation.
__
The solution is x=18.
(NO FILES OR LINKS OR RANDOM WORDS)
Answer:
Randomly selecting a six of diamonds - 1 / 52
Randomly selecting a 7, 8, 9 or 10 - 4 / 13
Step-by-step explanation:
There is only 1 six of diamonds in a standard deck of cards. There are 52 cards in a deck, thus the probability of pulling a six of diamonds is 1 in 52.
There are 4 of each card in a deck. so they are 4 7's, 4 8's. 4 9's and 4 10's. And there are a total of 52 cards in a deck. So the probability of pulling a 7,8,9 or 10 are 4 + 4 + 4 + 4 in 52
4 + 4 + 4 + 4 = 16
16 / 52 simplified is 4 / 13 Therefore the is a 4 in 13 chance of pulling a 7 8 9 or 10
The other ones are correct
FIRST TO ANSWER GETS BRAINLYEST WHATEVER ITS CALLED, PLEASE I NEED THIS DONE TODAY. JUST LOOK AT THE PICTURE
Answer:
28.83
Step-by-step explanation:
Find indicated side of right triangle 45 percent 7
Answer:
a = 7
b = 7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
in a 45-45-90° triangle, the length of legs to hypotenuse is 1 : [tex]\sqrt{2}[/tex]
please help, no links
Answer:
150
Step-by-step explanation:
Remark
The exterior angle = the sum of the two given interior angles. The first job is to solve for x and then use that to find the exterior angle.
Equation
83 + 6x + 7 = 15x
Solution
Combine like terms
90 + 6x = 15x Subtract 6x from both sides.
6x 6x
90 = 9x Divide both sides by 9
90/9 = 9x/9
x = 10
Now the exterior angle = 15x
Exterior angle = 15*10
Exterior angle = 150