Answer:
[tex]Q(t) = 50e^{-0.0527t}[/tex]
Step-by-step explanation:
A certain radioactive material is known to decay at a rate proportional to the amount present.
This means that the situation can be described by the following differential equation:
[tex]\frac{dQ}{dt} = -rQ[/tex]
In which r is the decay rate.
Solving the differential equation by separation of variables, we have that:
[tex]\frac{dQ}{Q} = -r dt[/tex]
Integrating both sides:
[tex]\ln{Q} = -rt + K[/tex]
In which K is the integrative constant.
Applying the exponential to both sides, to remove the ln, we get:
[tex]Q(t) = Ke^{-rt}[/tex]
In which K is the initial amount present.
Initially there is 50 mg/L
This means that [tex]K = 50[/tex].
After 2 hours it is observed that the material has lost 10 percent of its original concentration
This means that [tex]Q(2) = 0.9K[/tex]. So
[tex]0.9K = Ke^{-2r}[/tex]
[tex]e^{-2r} = 0.9[/tex]
[tex]\ln{e^{-2r}} = \ln{0.9}[/tex]
[tex]-2r = \ln{0.9}[/tex]
[tex]r = -\frac{\ln{0.9}}{2}[/tex]
[tex]r = 0.0527[/tex]
So
[tex]Q(t) = Ke^{-rt}[/tex]
[tex]Q(t) = 50e^{-0.0527t}[/tex]
3 2/3 x 1/5= please help
Answer: 11/15
Step-by-step explanation:
Type your number answer in decimal form. Do not round. (help pls)
( ? )millimeters = 9.2 centimeters.
Answer:
hope im not late but its 92
Step-by-step explanation:
yea
If 6^ = 1/126 find the value of x
Please ask help with b
9514 1404 393
Answer:
a) x = -3
b) 1/250
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
__
a) It is helpful to know that 216 = 6^3.* Then you would realize that ...
[tex]6^x=\dfrac{1}{216}=\dfrac{1}{6^3}=6^{-3}\\\\x=-3[/tex]
If you don't know that, then you can solve the equation using logarithms. Taking the log of both sides, you have ...
x·log(6) = log(1/216)
x = log(1/216)/log(6) = -3
__
b)
[tex]5^{-3}\times 2^{-1}=\dfrac{1}{5^3}\times\dfrac{1}{2^1}=\dfrac{1}{125}\times\dfrac{1}{2}=\boxed{\dfrac{1}{250}}[/tex]
_____
* This would be on your list of cubes of small integers that you might want to memorize, along with squares of numbers less than 20.
Which shows one way to determine the factors of X-92 + 5x - 45 by grouping?
x2(x-9)-5(x-9)
x2(x+9)-5(x+9)
x(x2+5)-9(x2+5)
x(x2-5)-9(x2-5)
Which graph represents
y =7/2 X – 2?
Answer:
pie chart
Step-by-step explanation:
i had the same thing
Select the correct solution for 9x = 81.
O A. x = 72
O B. x =)
O c. x = 9
O D. x = 90
Answer:
c
Step-by-step explanation:
9x=81
9x/9=81/9
x=9
Option C is correct, the solution of 9x = 81 is x=9.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 9x=81
Nine times of x equal to eighty one.
We have to solve for x
Divide both sides by 9
x=81/9
Divide numerator and denominator by 9
x=9
Hence, Option C is correct, the solution of 9x = 81 is x=9.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ5
Simplify the following.
Answer:
Step-by-step explanation:
a). 3x²y⁴ × 2x⁶y
= 6(x² × x⁶)(y⁴× y)
= [tex]6x^{(2+6)}y^{(4+1)}[/tex]
= 6x⁸y⁵
b). xz³ × 4x⁴z⁵
= [tex]4x^{(1+4)}\times z^{(3+5)})[/tex]
= 4x⁵z⁸
c). 4a³b² × 3a⁶b⁵
= [tex]12a^{(3+6)}b^{(2+5)}[/tex]
= 12a⁹b⁷
d). 6s⁵t × s⁴t²
= [tex]6s^{(5+4)}t^{(1+2)}[/tex]
= 6s⁹t³
which statement about these triangles is true?
Answer:
I think it's D
Step-by-step explanation:
Answer:
i think it's a or d
but d is more have percent
Write the linear equations in slope-intercept form with a slope of 5 and point (2, -20)
Answer:
We conclude that the linear equation in slope-intercept form with a slope of 5 and point (2, -20) is:
y = 5x - 30Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven
The slope m = 5
The point (2, -20)
now substitute (x, y) = (2, -20) and m = 5 in the slope-intercept form of the line equation
y = mx+b
-20 = 5(2) + b
10 + b = -20
subtracting 10 from both sides
10 + b - 10 = -20 - 10
b = -30
Thus, the y-intercept b = -30
so substituting b = -30 and m = 5 in the slope-intercept form of the line equation
y = mx+b
y = 5x + (-30)
y = 5x - 30
Therefore, the linear equation in slope-intercept form with a slope of 5 and point (2, -20) is:
y = 5x - 30Your community is having a carnival. Admission into the carnival is $6 and
each game inside the carnival costs $0.75. Which of the following inequalities represents
the possible number of games g that can be played with $30?
a. 6g +0.75 s 30
b. 6g +0.75 2 30
C. 0.75g + 6 2 30
d 0.75g + 6 3 30
Hello!
Answer:[tex]\boxed{ \bf d.~0.75g~+~6~≤~30}[/tex]
Explanation:The variable “g“ represents games, so the coefficient in front of it CANNOT be 6 (since $6 is the cost of the admission and you only have to pay it once).
This automatically eliminates options A and B.
We are now left with C and D.
Since the questions asks for the possible number of games played with $30, we cannot go above it. Therefore, this eliminates option C because that sign is basically telling us that the cost of the admission fee ($6) + the number of games is either greater than or equal to $30. We need it to be LESS than or EQUAL to $30.
Which equations for the measures of the unknown
angles x and y are correct? Check all that apply.
A- x= cos-1[a/c]
B- x= sin-1[c/b]
C- x= tan-1[c/a]
D- x= sin-1[a/c]
E- x= cos-1[c/b]
Answer: B, C, and E
Step-by-step explanation:
I just did the assignment
(8.75-2.16)÷7.1+(4.5+1.3)÷4.3
Answer:
2.27700622339
Step-by-step explanation:
Calculated your welcome
Answer:
2.277
Step-by-step explanation:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
1. 6.59/7.1+(4.5+1.3)/4.3
2. 6.59/7.1+5.8/4.3
3. 0.928+5.8/4.3
4. 0.928+1.3488
5. = 2.277
8 / 16 if you answer this you get points yaaaaaaaaaaaaay
8 over 16
eight over sixteen
What is the value of this expression? 6 1/3+ 8 3/4- 7 1/6 Enter your answer as a mixed number in simplest fo
A nicotine patch on the skin absorbs nicotine directly into the bloodstream some stronger patches contain 20 mg nicotine how many patches would kill half of people weighing 60 kg.
(Please answer)
Using only numbers in the following list,
46
53
89
21
48
47
32
write down
a)
two numbers that add up to 80
1
b)
two numbers which differ by 43
c)
a multiple of 6
Answer:
A) 48,32
B) 89, 46
C) 48
Step-by-step explanation:
The price of the tennis racket was estimated to be 200 dollars. However, the actual
prin of the tennis racket was 400 dollars What is the percent error?
The frequency distribution representing the number of frequent flier miles accumulated by employees at Brumley Statistical Consulting Inc. is given below.:
Frequent Flier Miles(000) Frequency
0 up to 3 5
3 up to 6 12
6 up to 9 23
9 up to 12 8
12 up to 15 2
Total 50
Required:
a. How many employees accumulated less than 3,000 miles?
b. Convert the frequency distribution to a cumulative frequency distribution.
c. Portray the cumulative distribution in the form of a cumulative frequency polygon.
d. Based on the cumulative frequency polygon, about 75 percent of the employees accumulated how many miles or less?
Answer:
A.) 5 employees
D.) 9 miles or less
Step-by-step explanation:
Frequent Flier Miles(000) ____ Frequency
0 up to 3 __________________ 5
3 up to 6 __________________ 12
6 up to 9 __________________ 23
9 up to 12 __________________ 8
12 up to 15 _________________ 2
Total ______________ 50
Required:
a. How many employees accumulated less than 3,000 miles?
5 employees (from the frequency table)
b. Convert the frequency distribution to a cumulative frequency distribution.
Frequent Flier Miles(000) ____ F ____ cumm/F
0 up to 3 __________________ 5 ____ 5
3 up to 6 __________________ 12 ___ 17
6 up to 9 __________________ 23 __ 40
9 up to 12 __________________ 8 __ 48
12 up to 15 _________________ 2 __ 50
c. Portray the cumulative distribution in the form of a cumulative frequency polygon.
d. Based on the cumulative frequency polygon, about 75 percent of the employees accumulated how many miles or less?
75% of employees
(75 / 100) * total number of employees
0.75 * 50
= 37.5
From the Cummulative frequency polygon, 75% of the employees accumulated about 9 miles or less
Check attached picture for Cummulative frequency polygon.
It is known that x and y are roots of the equation
[tex]6x^2 +7x +k =0[/tex], where [tex]2x +3y =-4[/tex].
Find k
Step-by-step explanation:
We are going to express
y in terms of x.
=> 2x + 3y = -4, y = (-4 - 2x)/3.
By Vieta's Formula,
We have SOR = -b/a and POR = c/a.
=> x + y = -7/6, xy = k/6.
When x + y = -7/6,
x + (-4 - 2x)/3 = -7/6.
=> (x - 4)/3 = -7/6
=> (x - 4) = -7/2
=> x = 4 - 7/2
=> x = 0.5.
When xy = k/6,
x(-4 - 2x)/3 = k/6.
Hence k = 6[x(-4 - 2x)/3]
= 2x(-4 - 2x) = 2(0.5)(-4 - 2(0.5)) = -5.
The value of k is -5.
Answer:
[tex]k = -5[/tex]
Step-by-step explanation:
We have the quadratic equation:
[tex]6x^2+7x+k=0[/tex]
Where x and y are the roots of the equation and:
[tex]2x+3y=-4[/tex]
First, using the quadratic formula with a = 6, b = 7, and c = k, we can find the roots to be:
[tex]\displaystyle x=\frac{-(7)\pm\sqrt{(7)^2-4(6)(k)}}{2(6)}[/tex]
Simplify:
[tex]\displaystyle x=\frac{-7\pm\sqrt{49-24k}}{12}[/tex]
So, our two roots are:
[tex]\displaystyle x=\frac{-7+\sqrt{49-24k}}{12}\text{ and } y=\frac{-7-\sqrt{49-24k}}{12}[/tex]
For our first root, we can multiply both sides by 2.
And for our second root, we can multiply both sides by 3.
So, this produces:
[tex]\displaystyle 2x=\frac{-7+\sqrt{49-24k}}{6}\text{ and } 3y=\frac{-7-\sqrt{49-24k}}{4}[/tex]
Since we are given that:
[tex]2x+3y=-4[/tex]
By substitution:
[tex]\displaystyle \Big(\frac{-7+\sqrt{49-24k}}{6}\Big)+\Big(\frac{-7-\sqrt{49-24k}}{4}\Big)=-4[/tex]
Remove the fractions by multiplying both sides by 12:
[tex]\displaystyle (-14+2\sqrt{49-24k})+(-21-3\sqrt{49-24k})=-48[/tex]
Combine like terms:
[tex]-35-\sqrt{49-24k}=-48[/tex]
Adding 35 to both sides produces:
[tex]-\sqrt{49-24k}=-13[/tex]
So:
[tex]\sqrt{49-24k}=13[/tex]
Squaring produces:
[tex]49-24k=169[/tex]
Therefore:
[tex]-24k=120\Rightarrow k=-5[/tex]
✨ILL GIVE Brainalist I SWEAR. BTW THERE coMparing uniT PROPORTIONS PLS
5) Derek was surfing through the internet for a good deal on t-shirts. Help Derek find the
best buy among the following deals: Three t-shirts for $28.95, four t-shirts priced at
$39, and an offer of five t-shirts for $49.95.
Answer:
do the dead easy calculation read explanation I have no calculator atm
Step-by-step explanation:
so what you want to do is take the amount of cost and divide by number of shirts to find price per shirt and see which one is cheapest
Answer:
Three t-shirts for $28.95Step-by-step explanation:
Three t-shirts for $28.95
Cost of one: $28.95/3 = $9.65Four t-shirts priced at $39
Cost of one: $39/4 = $9.75Five t-shirts for $49.95
Cost of one: $49.95/5 = $9.99The cheapest option is the first one
If a girl on a bike travelled 2 miles in 15 minutes, how
far will she travel in 1 hour? Show your work!
Answer:
8 miles in an hour
Step-by-step explanation:
well if she went 2 evey 15 minutes, there are 60 minutes in an hour, so 15 times 4 is sixty. 2 times four is 8. she ran 8 miles in an hour.
Answer:
8 miles
Step-by-step explanation:
15 x 4 = 60 = 1 hr
2x4 = 8
You basically times how far the girl tracked in 15 minutes by 4
Suppose the ratio of baseball players who bat left-handed to the total players in the league is 6 to 15. What percent of players bat left-handed in the league?
6,2,2/3,..
Find the 8th term
Answer:
2/729
Step-by-step explanation:
This is a geometric progression.
[60 points. Help me.]
Monica jogged to her gym and is on her way home. She has walked 2/13 of a mile and has jogged 2/13 of a mile. If the total distance from the gym to Monica's home is 8/13 of a mile, how far from home is Monica now?
A.
5/13 of a mile
B.
4/13 of a mile
C.
9/13 of a mile
D.
7/13 of a mile
Step-by-step explanation:
Total distance = 8/13 mile
Distance left = 8/13 - 2/13 - 2/13 = 4/13 mile
Hence Monica is 4/13 of a mile from home now. (B)
Suppose KLMN - PORS. Find the value of %,
30
K 12
20
N
M
S
R
8,
4
8
b
C, 10
d. 2
Please select the best answer from the choices provided
Answer:
b. 8
Step-by-step explanation:
Since polygon KLMN and polygon PQRS are similar, it follows that their corresponding side lengths would be proportional to each other. Therefore:
LM/QR = KL/PQ
Plug in the values
x/20 = 12/30
Multiply both sides by 20
x = (12*20)/30
x = 8
A man chooses a card at random from a
pack of playing cards. What is the
probability that the card is a diamond?
Answer:
13/52
Step-by-step explanation:
as there are 13 diamond cards out of the total 52 cards
Probability that the card is drawn from a deck of cards diamond is equal to [tex]\boldsymbol{\frac{1}{4}}[/tex]
Define probability.Probability refers to a chance of occurrence of any event.
Value of probability is greater than or equal to zero and less than or equal to one.
Total number of cards in a pack of playing cards [tex]=52[/tex]
Number of diamonds [tex]=13[/tex]
Therefore,
Probability that the card is a diamond [tex]=\frac{13}{52}[/tex]
[tex]=\frac{1}{4}[/tex]
Find out more information about probability here:
https://brainly.com/question/11234923?referrer=searchResults
D 372
3. A jar of jelly contains 510 grams of
jelly. There are about 26 servings in
one jar. How much is one serving?
A About 159
® About 20 g
About 10,000 g
D About 12,500 g
b
Answer:
About 10,000
Step-by-step explanation:
I've been struggling to find the answer to 1+1?
Answer:
42
Step-by-step explanation:
trust the process shsuuchsisjfjsisine
Answer:
Hi! The answer is 2.
Step-by-step explanation:
1+1=2
Imagine having 1 cookie, then your friend gives you 1 more cookie. You would have two cookies.
y is the hourly wage I must pay, and x is the # lifeguards I want to hire
y = 10 - ½ x
Answer:
x = 20
Step-by-step explanation:
substitute y= 0 first and multuply both sides move the variable to the left.
DC= 10 what is the value of AD
Answer:
where is required question. comment me.
