Reacting with water in an acidic solution at a particular temperature, compound A decomposes into compounds B and C according to the law of uninhibited decay. An initial amount of 0.40 M of compound A decomposes to 0.37 M in 30 minutes. How much of compound A will remain after 2 hours? How long will it take until 0.10 M of compound A remains? After 2 hours, the amount of compound A remaining will be ? M. (Do not round until the final answer. Then round to thenearest hundredth as needed.)
Answers
The answers to all parts are shown below.
The law of uninhibited decay is a first-order chemical reaction, which means that the rate of the reaction is proportional to the concentration of compound A.
The rate law can be written as:
rate = k[A]
where k is the rate constant and [A] is the concentration of compound A.
From the given data, we can use the following equation to determine the rate constant:
ln([A]t/[A]0) = -kt
where [A]t is the concentration of compound A at time t, [A]0 is the initial concentration of compound A, k is the rate constant, and t is the time.
Using the given data:
[A]t = 0.37 M
[A]0 = 0.40 M
t = 30 minutes = 0.5 hours
ln(0.37/0.40) = -k(0.5)
k = 0.0486 h⁻¹
(a) How much of compound A will remain after 2 hours?
Using the same equation and substituting the known values:
ln([A]t/[A]0) = -kt
ln([A]t/0.40) = -0.0486 x 2
[A]t/0.40 = e⁻(⁹⁷² /¹⁰⁰⁰⁰)
[A]t = 0.25 M
Therefore, after 2 hours, 0.25 M of compound A will remain.
(b) How long will it take until 0.10 M of compound A remains?
Substituting the known values into the equation again:
ln([A]t/[A]0) = -kt
ln(0.10/0.40) = -0.0486t
t = 4.26 hours
Therefore, it will take approximately 4.26 hours until 0.10 M of compound A remains.
(c) After 2 hours, the amount of compound A remaining will be 0.25 M.
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Related Questions
Which of the following tables represents a linear function?
x −2 −1 0 1 2
y 5 2 1 2 5
x −2 −1 0 1 2
y 5 3 1 −1 −3
x 3 3 0 3 3
y −2 −1 0 1 2
x 0 1 2 3 4
y 0 −1 2 −3 4
Answers
The slope at the different sections in table 2 will be constant. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The slope of the linear equation will be constant throughout.
Let's check option B, then we have
m = (3 - 5) / (- 1 + 2) = (- 3 + 1) / (2 - 1)
- 2 = - 2
The slope at the different sections in table 2 will be constant. Then the correct option is B.
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Answer:The answer is b
Step-by-step explanation:B
How many significant figures are in the number
43.6? 43.6 has [?] significant figures.
Answers
Answer:
43.6 has 3 significant figures.
Solve the inequality
X/3+9> 14
Answers
\(\\ \sf\longmapsto \dfrac{x}{3}+9>14\)
\(\\ \sf\longmapsto \dfrac{x}{3}>5\)
\(\\ \sf\longmapsto x>3(5)\)
\(\\ \sf\longmapsto x>15\)
Answer:
the answer is x>15
Step-by-step explanation:
2424 is 75\%75%75, percent of what number?
Answers
im pretty sure its 32 i think
Answer:
32
Step-by-step explanation:
Candy spends £2.65, has 2/3 left, how much money does candy have to start
Answers
Candy spends £2.65, has 2/3 left and Candy has £7.95 money to start with.
Given that Candy spends £2.65 and has 2/3 of the initial amount left, we are required to find how much money Candy has to start with.
Solution:Let the initial amount of money Candy has be x.
Then, the amount of money spent by Candy = £2.65
Amount of money left with Candy = 2/3 of the initial amount
∴ Money left = 2/3 × x
Amount of money spent + money left = initial amount of money
Candy spends £2.65:2/3 of the initial amount left
= £ (x - 2.65)∴ 2/3 × x
= x - 2.65⇒ 2x/3
= x - 2.65⇒ 2x
= 3x - 7.95⇒ 3x - 2x
= 7.95⇒ x = 7.95
Hence, Candy has £7.95 to start with.
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cuanto es 1 mas 1? dende ecuaciones y detalles es para mi examen virtual please
Answers
Answer:
2
Step-by-step explanation:
1+1=2
Help picture below problem 12
Answers
Answer:
124°
Step-by-step explanation:
Not the best at explaining but should be equal to 180 straight across. You have to find the missing angle. You know the right angle is 90° so you will add 34° to get 124°. 180-124 will get you 56°. Straught across you have the angle that you are trying to find which is 124° because 180-56 is 124.
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.1 and the probability that the flight will be delayed is 0.11. The probability that it will not rain and the flight will leave on time is 0.88. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.
Answers
The probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.
What is the probability that it is raining and the flight is delayed?Let's use the formula for calculating the probability of the intersection of two events: P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of event B occurring given that event A has occurred.
Let A be the event that it is raining, and B be the event that the flight is delayed. We are looking for P(A and B).
We know that:
P(A) = 0.1 (the probability that it will rain)
P(B) = 0.11 (the probability that the flight will be delayed)
P(not A and not B) = 0.88 (the probability that it will not rain and the flight will leave on time)
We can use the complement rule to find P(A or B):
P(A or B) = 1 - P(not A and not B)
P(A or B) = 1 - 0.88
P(A or B) = 0.12
Now we can use the formula for the intersection of two events:
P(A and B) = P(A) × P(B|A)
We know that P(A) = 0.1, and we need to find P(B|A), the probability of the flight being delayed given that it is raining.
We can use Bayes' theorem to find P(B|A):
P(B|A) = P(A and B) / P(A)
P(B|A) = (P(A) × P(B|A)) / P(A)
P(B|A) = P(B and A) / P(A)
We can rearrange this to get:
P(A and B) = P(B|A) × P(A)
Substituting the values we know:
P(B|A) = P(A and B) / P(A)
0.11 = P(A and B) / 0.1
P(A and B) = 0.11 × 0.1
P(A and B) = 0.011
Therefore, the probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.
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A pet shop is 10 dogs, 15 cats, 6 birds , and 4 snakes . What is the ratio of dogs to pets?
Answers
Answer:
2:7
Step-by-step explanation:
10+15+6+4=35
given dogs=10
10/35=2/7
2:7
Given : XB bisects ABC m < 1 = 4x + 5 m < 2 = 5x - 2
Answers
Mrs. Smith made 6 ¼ dozen cookies for the birthday party. At the end of the party, there were 3 ½ dozen cookies left. How many cookies did the guests eat?
Answers
The guests in the birthday party ate 33 cookies.
How many cookies did the guests eat?We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.
Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.
6 1/4 dozen = 25/4 dozen
3 1/2 dozen = 14/4 dozen
Now we can subtract the number of cookies that were left from the number of cookies that were made:
25/4 - 14/4 = 11/4 dozen
To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.
There are 12 cookies in one dozen, so:
11/4 x 12 = 33
Therefore, the guests ate 33 cookies.
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Which Which expression is equivalent to the 1 below
Answers
Answer:
B
Step-by-step explanation:
(2^6*9^6):18^14
18^6:18^14
18^-8
1:18^8
If a right triangle has a hypotenuse of length 20 units and one leg of length 16 units, find the length of the other leg. A. 12 B. 656 C. 384 D. 36
Answers
Answer:
12
Step-by-step explanation:
Use the Pythagorean theorem which is a^2 + b^2 = c^2
c is hypotenuse and a and b are the legs
we need to find a^2 so
a^2 + 16^2 = 20^2
a^22 + 256 = 400
then subtract 256 from 400
a^2 = 144
square root 144
= 12
Answer:
12 units
Step-by-step explanation:
MULTIPLE CHOICE CALCULUS
1) An object moves along a line so that its position at time t is s(t) = t^4 - 6t^3 - 2t - 1.
At what time t is the acceleration of the object zero?
A. at 3 only
B. at 0 and 3 only
C. at 0 only
D. at 1 only
2) If f(x) = e^x (sin x + cos x), then f'(x) =
A. 2e^x (cos x + sin x)
B. e^x cos x
C. e^x (cos^2x - sin^2x)
D. 2e^x cos x
Answers
Answer:
1) B. at 0 and 3 only
2) D. 2eˣcosx
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringQuadraticsCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Property [Addition/Subtraction]: \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)
Derivative Rule [Product Rule]: \(\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)\)
Trig Derivative: \(\displaystyle \frac{d}{dx}[sinu] = u'cosu\)
Trig Derivative: \(\displaystyle \frac{d}{dx}[cosu] = -u'sinu\)
eˣ Derivative: \(\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'\)
Step-by-step explanation:
*Note:
Velocity is the derivative of position.
Acceleration is the derivative of velocity.
Question 1
Step 1: Define
s(t) = t⁴ - 6t³ - 2t - 1
Step 2: Differentiate
[Velocity] Basic Power Rule: s'(t) = 4 · t⁴⁻¹ - 3 · 6t³⁻¹ - 1 · 2t¹⁻¹[Velocity] Simplify: v(t) = 4t³ - 18t² - 2[Acceleration] Basic Power Rule: v'(t) = 3 · 4t³⁻¹ - 2 · 18t²⁻¹[Acceleration] Simplify: a(t) = 12t² - 36tStep 3: Solve
[Acceleration] Set up: 12t² - 36t = 0[Time] Factor: 12t(t - 3) = 0[Time] Identify: t = 0, 3Question 2
Step 1: Define
f(x) = eˣ(sinx + cosx)
Step 2: Differentiate
[Derivative] Product Rule: \(\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x\frac{d}{dx}[sinx + cosx]\)[Derivative] Rewrite [Derivative Property - Addition]: \(\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])\)[Derivative] eˣ Derivative: \(\displaystyle f'(x) = e^x(sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])\)[Derivative] Trig Derivatives: \(\displaystyle f'(x) = e^x(sinx + cosx) + e^x(cosx - sinx)\)[Derivative] Factor: \(\displaystyle f'(x) = e^x[(sinx + cosx) + (cosx - sinx)]\)[Derivative] Combine like terms: \(\displaystyle f'(x) = e^x[2cosx]\)[Derivative] Multiply: \(\displaystyle f'(x) = 2e^xcosx\)Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Prove that the quadratic Sequence 44:52:64; 80: will always have even terms
Answers
The sequence is will always have even numbers, is hence proved.
Given, the quadratic sequence is: 44:52:64:80
Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.
The formula is: Tₙ = 2n² ₊ 2n ₊ 40
take 2 common
Tₙ = 2(n² ₊ n ₊ 20)
in other words n² ₊ n ₊ 20 = y
therefore , Tₙ = 2y
which by definition makes Tₙ an even number at all times.
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HELP PLEASE. I ONLY HAVE 25 MINUTESSS..
Answers
Answer:
D, 42
Step-by-step explanation:
Answer: D) 42
Step-by-step explanation:
What are some key words used to note addition operations?
Answers
Answer:
The correct answer is
For addition, Caulleen used the words total, sum, altogether, and increase. But we could also have used the words combine, plus, more than, or even just the word "and". For subtraction, Caulleen used the words, fewer than, decrease, take away, and subtract. We also could have used less than, minus, and difference.
Step-by-step explanation:
hope this helps u!!!
answer the question correctly for brainliest
Answers
Answer:
15p + 10
Step-by-step explanation:
5 (3p+2)
15p + 10
In a recent survey of 645 working Americans ages 25-34, the average weekly amount spent on lunch as $44.02 with standard deviation $2.81. The weekly amounts are approximately bell-shaped.
a. Estimate the percentage of amounts that were less than $38.40. Round the answer to one decimal place. Approximately % of the amounts were less than $38.40.
b. Estimate the percentage of amounts that are between $41.79 and $47.41.
c. Estimate the percentage of amounts that are at least $38.98.
d. Between what two values will approximately 95% of the amounts be?
Answers
Answer:
use photo math it's great and free
In exercises 1 and 2 use the graph to solve the equation
Answers
The solution:
Exercise 1: x = -1 and 3.
Exercise 2: x = 2 and 4.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The graphs of the two quadratic equation.
So, Exercise 1,
-x² + 2x + 3 = 0.
From the graph,
-1 and 3 are the zeros of the equation.
The solution of the equation is,
x = -1 and 3.
Exercise 2,
x² - 6x + 8 = 0.
From the graph,
2 and 4 are the zeros of the equation.
The solution of the equation is,
x = 2 and 4.
Therefore, the solutions of the both the equation are given above.
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Use the following number line to choose the correct statement. R x P > S S > Q × R Q × R > S
Answers
Answer:
Looking at the number line, we can see that R is to the left of P, and S is to the right of P. Also, Q is to the left of R, and S is to the right of Q.
So, the first statement "R x P > S" is not true, because S is to the right of both R and P.
The second statement "S > Q x R" is also not true, because Q is to the left of R, and S is to the right of both Q and R.
The third statement "Q x R > S" is true, because Q is to the left of R, and S is to the right of both Q and R. Therefore, the correct statement is:
Q x R > S
Select the point that satisfies ys x2 - 4x + 2.
O A. (2, 2)
O B. (1,1)
C. (5,5)
O D. (4,4)
Answers
Answer:
A
Step-by-step explanation:
PLEASE HELP !! suppose that F(x)=x^2 and G(x)=3x^2+8.which statement best compares the graph of G(x) with the graph of F(x)
Answers
Answer:
The graph of g(x) is the graph of f(x) stretched by 3 and shifted 8 units up
Step-by-step explanation:
Given
\(f(x)=x^2\)
\(g(x) =3x^2 + 8\)
Required
Compare g(x) and f(x)
We have:
\(g(x) =3x^2 + 8\)
Rewrite as:
\(g(x) =3[x^2] + 8\)
Substitute:\(f(x)=x^2\)
\(g(x) =3f(x) + 8\)
This means that:
3f(x)
f(x) is stretched vertically by a factor of 3
+8
Then shifted upwards by 8 units to give g(x)
General form of
Y= 1/3x +3 and has an x intercept of 3
Answers
Answer:
Step-by-step explanation:
y
=
1
3
x
−
3
Use the slope-intercept form to find the slope and y-intercept
Slope:
1
3
y-intercept:
(
0
,
−
3
)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
x
y
0
−
3
3
−
2
Graph the line using the slope and the y-intercept, or the points.
Slope:
1
3
y-intercept:
(
0
,
−
3
)
x
y
0
−
3
3
−
2
image of graph
The volume of a box is 9cm³ and its base area is 20cm². What is the height of the whole box
Answers
Answer:
0.45 cm
Explanation:
In order to find the height of any shape given the volume and base area.
Simply divide the volume by the base area.
Here given:
Volume: 9 cm³Base area: 20 cm²Height:
volume ÷ base area = 9 ÷ 20 = 0.45 cmA store purchased baseball bats for $26 and sold them for $28.86. What percentage is the mark-up?
Answers
Step-by-step explanation:
Markup percentage = (Sold price - Cost price)/Cost price × 100
=> (28.86 - 26)/26 × 100
=> 2.86/26 × 100
=> 11%
i need help with this one plz! (marking BRAINLIST) :)
Answers
Answer: (a) = 110 degrees, (b) = 8
If I understand the picture correctly, (a) wants you to find the angle K. It first shows us that both J to K, and L to K are equal in length of 11, thus there is no deviation in angle 35 degrees with L (so they both equal each other). Therefore, the angle K will equal 180 degrees subtracted by the sum of J and L, which is 110 degrees.
For (b), it appears that all the angles have the same singular mark at the edges, so all sides will equal 8.
I hope this helped!
A=4,B=7,C=11,D=13. Given the number line, AB=
Answers
Step-by-step explanation:
AB=28 !... .......hope this helps..
Can you help me with these 2 articles? pls
Answers
Answer:
no jooopoooopooopoopoo
Jane has been practicing sewing, and she wants to make a rectangular blanket to give as a gift to her best friend. So that the blanket is not too small, Jane decides the blanket will have an area of approximately 40 square feet, or 5,760 square inches. She also wants the blanket to be 18 inches longer than it is wide to have room to embroider her friend's name along one edge.
To the nearest tenth of an inch, what is the width of the blanket?
Answers
The width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.
What is width in rectangle ?
In a rectangle, the width refers to the measurement of the shorter side of the rectangle, which is perpendicular to its length.
Let x be the width of the blanket in inches. Then the length of the blanket is x + 18 inches.
The area of the blanket is given by:
Area = Length x Width
5760 sq inches = (x + 18) inches * x inches
Expanding the right-hand side and solving for x, we get:
\(x^2 + 18x - 5760 = 0\)
We can solve this quadratic equation using the quadratic formula:
\(x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a\)
where a = 1, b = 18, and c = -5760. Plugging in these values, we get:
\(x = (-18 \pm \sqrt{(18^2 - 4(1)(-5760))}) / 2(1)\)
\(x = (-18 \pm \sqrt{(18^2 + 23040)}) / 2\)
x ≈ 67.42 or x ≈ -85.42
Since the width cannot be negative, the width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.
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