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]
GUYS I NEED HELP PLSSSSSS! Ive been working on this ALL day!
First, let's write what we know.
We can represent the number of students in the play from each class as L, G, and C. We know that L = 7, and if Gardener has 4 more students than Cho, then G = C + 4.
Then, taking the third line, we can write an inequality:
C < L < G
C < 7 < C + 4
C - 4 < 3 < C
3 < C < 7
If C is greater than 3 and less than 7 and is an integer, than means C is 4, 5, or 6.
Then, we need to find how many students are in the play.
C + L + G
C + 7 + C + 4
2C + 11
So we have our expression for the number of students in the play. Then, we need to find the total number of students. We know that 2C + 11 will be 30% of the total, so if T is the total, we can find T.
0.3T = 2C + 11
(Divide by 3/10 or multiply by 10/3 on both sides)
T = 20/3 C + 110/3
We know from before that C is 4, 5 or 6. We can plug these into our equation here to find which one produces a whole number.
T = 20/3 * 4 + 110/3
T = 190/3
T = 20/3 * 5 + 110/3
T = 210/3
T = 70
T = 20/3 * 6 + 110/3
T = 230/3
We can see here that only when C is 5 will the total be a whole number. That means Mrs. Cho has 5 students in the play. If Mrs. Gardner has 4 more than that, she has 9 students in the play in her class. We now need to figure out the number of student in her class.
The total students are Cho's, Logan's, and Gardner's classes added together. We know that Logan's class is 23 students, so if we subtract that from the total, we can see that Cho's and Gardner's class have 47 students. If Mrs. Cho has 24 students in her class, we can subtract that from the 47, so we know that Mrs. Gardner has 23 students in her class.
What is the height of the cone below?
Answer:
Where's the cone at and I might be able to help
Step-by-step explanation:
Answer: Please put a picture of the cone underneath the question!
Step-by-step explanation:
Please help if you can!!!!!!
Answer:
Perpendicular
Ms. Hagan invested twice as much money in an account that pays 7% interest as she did in an account that pays 6% in interest. Her total investment pays her $1,000 a year in interest. How much did she invest at each rate?
Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.
Step-by-step explanation:
Let P be the initial amount she invested in an account that pays 6% interest.
Then, amount invested in other account = 2P
Simple interest = Principal x rate x time
After one year, for the first account,
Interest = P(0.06)(1) = 0.06P
For second account,
Interest = (2P)(0.07)(1)=0.14P
Total interest = [tex]0.06P+0.14P=1000[/tex]
[tex]\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000[/tex]
2P = 2(5000)=10000
Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.
At the interest rate of 6%, amount invested is; $5000
At interest rate of 7%, amount invested is; $10000
Let P be the initial amount that Ms. Hagan invested in the 6% interest account that
Since she invested twice as much in the 7% interest account as in the 6% interest account, then;
Initial amount invested in the 7% interest account = 2P
Formula for Simple interest is;
I = Principal × rate × time
Interest after 1 year for the 6% interest account is,
I_1 = P × 0.06 × 1
I_1 = 0.06P
Interest after 1 year for the 7% interest account is,
I_2 = 2P × 0.07 × 1
I_2 = 0.14P
Total investment pays her $1000 after a year. Thus;
0.06P + 0.14P = 1000
0.2P = 1000
P = 1000/0.2
P = $5000
Then amount initially invested in the 7% interest account = 2P = $10000
Read more about simple interest at; https://brainly.com/question/1873210 at;
4+8= 2 x (6-3)
Can somebody help me ASAP
Answer: 12≠6
False
Step-by-step explanation:
If it is completely impossible to put a contract in writing, which of the following would be the best substitute?
a. having a friend witness the verbal agreement
a video or audio recording of the verbal agreement
the words "I promise" spoken in a verbal recitation of the contract
d. a firm hand-shake between all those involved in the contract
C.
Please select the best answer from the choices provided
Answer:
B
Step-by-step explanation:
Because the the contract will be in verbal form. no matter if it is videotaped or recorded or both a "videoed verbal contract" not just written. so like paper thst is notarized or not this is still the same bc the the same rules apply the contract is still valid. the rest of the options are more like what they call gentlemens agreements which would be the handshake type of thing. and no matter what any agreement someone has to witness the transaction or contract. so definitely the answer is B
The area of the square above is 36. What is the value of x?
A) 2
B) 4
C) 6
D) 9
I think it is A)2 because 3^2 = 9 and 9×4 = 36
7. Write an equation of the line that passes through the points (1, 4) and (-2, 10), in point-slope form.
Answer:
y = -2x + 6
Step-by-step explanation:
This has sort of the same concept as your earlier question
Use the equation y = mx + b
To find the slope, take the second y value and subtract the first y value. Then take the second x value and subtract the first x value. Divide the answers. You'd get -2 in this case. -2 would be your slope (m).
The substitute any set of x and y values (either (1, 4) or (-2, 10)) and the slope into y = mx + b. You'd get 6 as your y-intercept (b).
How many births occur among women under the age of 20?
Answer:
what do you mean?
Step-by-step explanation:
Write an equation in slope intercept form that is perpendicular to 3x + 2y equals 12 and passes through the point (1,2)
Answer:
The equation is y = (2/3)x + (4/3).
Step-by-step explanation:
First, you have to change the equation into slope-intecept formula to find its gradient (slope) :
[tex]3x + 2y = 12[/tex]
[tex]2y = - 3x + 12[/tex]
[tex]y = - \frac{3}{2}x + 6[/tex]
Given that when a line is perpendicular to the other line, their slope value multiplied, will form -1. Next, we have to find the slope for line :
[tex]m1 \times m2 = - 1[/tex]
[tex] - \frac{3}{2} \times m2 = - 1[/tex]
[tex]m2 = - 1 \div - \frac{3}{2} [/tex]
[tex]m2 = \frac{2}{3} [/tex]
Lastly, we have to subatitute the x and y values into the equation, to find its intercept value :
[tex]y = \frac{2}{3}x + b[/tex]
[tex]let \: x = 1,y = 2[/tex]
[tex]2 = \frac{2}{3} (1) + b[/tex]
[tex]b = 2 - \frac{2}{3} [/tex]
[tex]b = \frac{4}{3} [/tex]
[tex]y = \frac{2}{3} x + \frac{4}{3} [/tex]
Can I get help on C plz
Answer:
the answer would be 6...
WORTH 30 POINTS *will give you brainliest*
Answer:
x = 3
Step-by-step explanation:
MN is exactly half of 6x + 2 (midpoint theorem)
2(2x + 4) = 6x + 2
4x + 8 = 6x + 2
-2x + 8 = 2
-2x = -6
x = 3
Evaluate the expression 6x for x 6.
6x = blank when x=6
Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}} : [/tex]
x = 6[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
Value of 6x[tex] \underline{ \underline{ \text{Solution}}} : [/tex]
~ Plug the value of x and then multiply !
⇾ [tex] \tt{6x = 6 \times 6 \times = \boxed{36}}[/tex]
[tex] \red{ \boxed{ \boxed{ \text{Our \: final \: answer : \boxed{ \tt{36}}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
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Factor the expression. d2 + 10d + 25
Answer:
(d+5)^2
Step-by-step explanation:
How much water do you add to make 12% sugar syrup using 5g sugar.
Answer:
You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then
5 g - 12%,
x+5 g - 100%.
mathematically you can write a proportion;
5/x+5=12/100
=>500=12(x+5)
,500=12x+60
,12x=400,
x=440/12
=110/3
=36 2/3g of water36.66 grams of water is added to make 12% sugar syrup using 5g sugar.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Let the amount of water is added be 'x'.
Amount of sugar = 5 g
We need to make 12% of sugar syrup.
x grams of water is added to 5 g of sugar, to 12% of sugar syrup.
5/5+x=12/100
Apply cross multiplication
5×100=12(5+x)
500=60+12x
Subtract 60 from both sides
440=12x
Divide both sides by 12
x=36.66
Hence, 36.66 grams of water is added to make 12% sugar syrup using 5g sugar.
To learn more on Ratios click:
https://brainly.com/question/1504221
#SPJ2
Someone please help and thank you
Answer:
8:3
Step-by-step explanation:
The GCF of each of them is 8. Divide both of them by it you'll get the ratio
in equivalence the answer is 8 3
Can someone please help
Answer:
340
Step-by-step explanation:
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
There is a line that includes the point (-5, 2) and has a slope of -3. What is its equation in slope-intercept form?
Answer:
y=-3x-13
Step-by-step explanation:
Answer:
1 .
Step-by-step explanation:
Derrick needs to sell a minimum of 100 orders each month to make it into the sales winners circle. He has already sold 45 orders this month. He still needs to sell s more orders.
Which inequality can be used to find the possible values for s?
PLEASE ANSWER THIS QUESTION RIGHT.What do we call the graph of a quadratic?
Answer:
parabola
Step-by-step explanation:
A group of friends hiked 7 miles in 2 hours at this same rate what is the total number of miles they can hike in 8 hours