The kinetics of some phase transformations obey the Avrami relationship. Using the fraction transformed-time data given below, determine the total time required for the transformation to go to 92% completion. Fraction transformed Time (s) 0.2 12.6 0.7 25.7 Enter your answer in accordance to the question statement s
Solution :
Avrami relationship
[tex]$1-y=exp(-kt^n)$[/tex]
[tex]$\ln(1-y)=-kt^n$[/tex]
[tex]$-\ln(1-y)=kt^n$[/tex]
[tex]$\ln\left[\ln\left(\frac{1}{1-y}\right)\right]=\ln k + n \ln t$[/tex]
The fraction transformed is 0.2 at 12.6 s,
[tex]$\ln\left[\ln\left(\frac{1}{1-0.2}\right)\right]=\ln k + n \ln (12.6)$[/tex]
[tex]$-1.5 = \ln k + 2.533 n$[/tex] .........(i)
The fraction transformed is 0.7 at 25.7 s,
[tex]$\ln\left[\ln\left(\frac{1}{1-0.7}\right)\right]=\ln k + n \ln (25.7)$[/tex]
[tex]$0.5 = \ln k + 3.24 n$[/tex] ..............(ii)
Subtract (ii) from (i),
-2 = -0.71 n
n = 2.81
Therefore, from (i),
[tex]$-1.5 = \ln k + 2.533 (2.81)$[/tex]
k = 0.000181
Now if the fraction transformed is 0.92, then
[tex]$kt^n=-\ln (1-y)$[/tex]
[tex]$t=\left[\frac{-\ln (1-y)}{k}\right]^{\frac{1}{n}}$[/tex]
[tex]$t=\left[\frac{-\ln (1-0.92)}{0.000181}\right]^{\frac{1}{2.81}}$[/tex]
t = 29.8528 s
Which of the following formulas does not represent finding The height of a rectangular prism with a volume of 200 in.³, a length of 4 inches, and a with of 5 inches?
Which statement is false?
A. Negative numbers are always less than positive numbers.
B. The sum of two negative numbers is always negative.
O C. The difference between two negative numbers is sometimes positive.
D. The product of two negative numbers is always negative.
E. The quotient of two negative numbers is always positive.
Answer:
So, the option (D) is the answer.
Step-by-step explanation:
A. The negative numbers are always less than positive numbers.
It is true.
For example, - 2 < + 2
B. The sum of two negative numbers is always negative.
It is true.
For example, - 3 + (- 3) = - 6
C. The difference between two negative numbers is sometimes positive.
It is true.
For example, (- 3) - (-4) = 1
D. The product of two negative numbers is always negative.
It is false.
For example, (-3)(-3) = 9
E. The quotient of two negative numbers is always positive.
It is true.
For example, (-3)/(-1) = 3
solve the equation s - 12 equals 20
ASAP pls
Answer:
s = 32
Step-by-step explanation:
s - 12 = 20
s (- 12 + 12) = 20 + 12
s = 32
Step-by-step explanation:
s-12=20
s=20+12
s=32
Hope it helps.
What is 234.506 rounded to the nearest hundredth
Answer:
Rounded to the nearest hundredth, 234.506 becomes 234.51.
PLEASE HELP!!! CALCULUS ASSIGNMENT
Answer:
(d) [tex]\displaystyle 12x^3 - 15x^2 + 2[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 3x^4 - 5x^3 + 2x - 1[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = 4(3x^{4 - 1}) - 3(5x^{3 - 1}) + 2x^{1 - 1} - 0[/tex]Simplify: [tex]\displaystyle y' = 4(3x^3) - 3(5x^2) + 2[/tex]Multiply: [tex]\displaystyle y' = 12x^3 - 15x^2 + 2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
( d ) 12x³ - 15x² + 2
Step-by-step explanation:
y = 3x⁴ - 5x³ + 2x - 1
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of axⁿ is nax^{n-1}.[tex] \small \sf \: y = 4\times 3x^{4-1}+3\left(-5\right)x^{3-1}+2x^{1-1} [/tex]
multiply 4 × 3.[tex] \small \sf \: y = 12x^{4-1}+3\left(-5\right)x^{3-1}+2x^{1-1} [/tex]
Multiply 3 × -5[tex] \small \sf \: y = 12x^{3}-15x^{3-1}+2x^{1-1} [/tex]
subtract the exponentsy = 12x³ - 15x² + 2⁰
For any term t except 0, t⁰ = 1.y = 12x³ - 15x² + 2 × 1
y = 12x³ - 15x² + 2
Hence, option ( d ) is the correct answer.
A photograph measures 3 inches tall and 5 inches wide. Becky wants a larger print of the photograph that is 25 inches wide. How many inches tall should the larger print be if it is to be in proportion to the smaller photograph?
Answer:
15 inches tall
Step-by-step explanation:
every 3 inches increased, the width increases by 5.
Jerome purchased a 4-year old car for $12,000. He was told this make a model depreciates exponentially at a rate of 5.7% each year. What was the original price to the nearest hundred dollars?
Group of answer choices
$19,300
$15,200
$12,500
$17,500
-2x +9y=8
x=y+3
Step by step
Kyle is studying migration patterns of birds. Specifically, he is comparing the distance travelled by geese and the distance travelled by pelicans in a year. Do geese travel significantly more distance than pelicans do?
Geese Pelicans
M = 191 miles M = 190 miles
n = 61 n = 61
s = 1.429 s = 1.355
Required:
a. State the null and alternative hypotheses in words.
b. Locate the critical value that defines the critical region.
c. Calculate your statistic.
d. Make a decision with respect to the null.
e. Write a concluding statement in everyday language.
Answer:
H0 : μ1 - μ2 = 0
H0 : μ1 - μ2 > 0
Test statistic = 3.96
Critical value = 1.67
Reject H0
We can conclude that there is significant evidence to support the claim that geese do travel more Than pelicans
Step-by-step explanation:
M= xbar1 = 191 ; M = xbar2 = 190 miles
n1 = 61 n2 = 61
s = 1.429 ; s2 = 1.355
Hypothesis :
H0 : μ1 - μ2 = 0
H0 : μ1 - μ2 > 0
Test statistic :
(x1 - x2) ÷ √[(s1²/n1) + (s2²/n2)]
(191 - 190) ÷ √[(1.429²/61) + (1.355²/61)]
1 ÷ √[(0.0334760) + (0.0300987)]
1 ÷ √0.0635747
1 ÷ 0.2521402
= 3.966
Degree of freedom :
df = n - 1
df = 61 - 1 = 60
Critical value :
Tcritical at 0.05%, df = 60
Tcritical = 1.67
Decision region:
Reject H0 if Tstatistic > Tcritical
Since ;
3.96 > 1.67 ; We reject H0
We can conclude that there is significant evidence to support the claim that geese do travel more Than pelicans
13 +22
if r = -3 and s = 4
35 is the answer
have a wonderful day
which comprison is correct?
a. 3/2 < 1/3
b. 3/8 > 1/6
c. 11/6 < 3/4
d. 3/5 = 5/8
Answer:
The second one
Step-by-step explanation:
USE THE BUTTERFLY TECHINQUE
3/8 O 1/6
18 3/8 O 1/6 8
18 > 8
3/8 > 1/6
Answer:
B is correct
3/8> 1/6 = 3 · 3/8 · 3 > 1 · 4/6 · 4 = 9/24 > 4/24 = 9 > 4 = Yes
Does y= x represent a function
Please HELPP with this question
9514 1404 393
Answer:
551.07 yd²
Step-by-step explanation:
For radius r and height h, the total surface area of the cylinder is given by ...
SA = 2πr(r +h)
Here, the radius is 4.5 yards (half the diameter) and the height is 15 yards. That makes the surface area ...
SA = 2(3.14)(4.5 yd)(4.5 +15 yd) = 551.07 yd²
What’s the area of this rectangle
Answer:
49/5 mm
Step-by-step explanation:
7/2×14/5
multiply the numerator and denominator
98/10
simplify
49/5 or
9 4/5 mm
Each (hypothetical) data set below represents some readings on span gas. Assume the Gauss model, with errors following the normal curve. However, bias may be present. In each case, make a t-test to see whether the instrument is properly calibrated or not. In one case, this is impossible. Which one, and why?
a. 71, 68, 79
b. 71, 68, 79, 84, 78, 85, 69
c. 71
d. 71, 84
Answer:
71 ( C ).
Step-by-step explanation:
The impossible case is the third case i.e.71
because there is only one reading on the span gas hence it is impossible to carry out a t-test on just one valid reading in an experiment.
Simplify (4a to the fifth power b to the sixth power) to the fourth power
Answer:
(4a^5b^6)^4 = 256a^20b^24
Step-by-step explanation:
You are trying to figure out how many license plates can be created from the digits 0 through 9. The license plate has 6 numbers, and none can be repeated. How many license plates can be created?
Answer:
1
Step-by-step explanation:
Need help with this question. 20 points
9514 1404 393
Answer:
3
Step-by-step explanation:
For x > 0, the function f(x) is ...
f(x) = 3x -4 . . . . . . . . for x > 0
Translating this down 1 unit makes it ...
g(x) = f(x) -1 = 3x -5
The rate of change for any interval such that x > 0 in the whole interval is the coefficient of x: 3.
The rate of change on the interval is 3.
__
If you like, you can find the rate of change from ...
m = (g(5) -g(2))/(5 -2) = (10 -1)/3 = 9/3 = 3
The rate of change is 3.
If you subtract 13 from an even number, the answer will be odd.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
Even numbers are divisible by 2 with no remainder. 13/2 = 6.5 so yes.
uppose you are performing a hypothesis test with H subscript 0 superscript blank space colon space mu equals 10 and H subscript A colon mu greater than 10, using a sample size of 50 observations. You sample data has a mean of 10.7, with a standard deviation of 3.1. Compute the test statistic for this hypothesis test
Answer: The test statistic for this hypothesis test =1.597
Step-by-step explanation:
When population standard deviation is unknown, we use t-test statistic:
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]\overline{x}[/tex] = sample mean, [tex]\mu[/tex] = population mean , s= sample standard deviation, n = sample size.
As per given,
[tex]t=\dfrac{10.7-10}{\dfrac{3.1}{\sqrt{50}}}\\\\=1.59669273171\approx1.597[/tex]
Hence, the test statistic for this hypothesis test =1.597
Find 35% of a number is 70 find the number
Answer:
200.
Step-by-step explanation:
35% = 0.35 so
0.35x = 70
x = 70 / 0.35
= 200.
Answer:
200
Step-by-step explanation:
Let the number = x
35% of x = 70
35/100 * x = 70 Multiply by 100
35x = 70 * 100
35x = 7000 Divide by 35
x = 7000/35
x = 200
Similar Triangles
Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.
a. 14/27 = 21/28 = 14/27
b. 14/18 = 21/27 = 7/9
c. 14/21 = 18/27 = 2/3
d. 27/14 = 28/21 = 27/14
Please select the best answer from the choices provided
Answer:
B. 14/18 = 21/27 = 7/9
Step-by-step explanation:
I calculated it logically
leo le debe 15.00 pesos. Si su madre le da 60.00 pesos de paga y se gasta 20.00 con sus amigos
¿cuanto dinero le queda?
¿tendrá pendiente alguna deuda?
Answer:
Le quedan 25 pesos
No tendrá pendiente ninguna deuda
Step-by-step explanation:
60-15-20=25
Which choice below could represent the distance jake walked?
Answer:
50 yard South, 40 yard east 60 yard northwest
x^2log2x+secx differential equation plz solve the question and give ans
Answer:
only 5 points
Step-by-step explanation:
if the marked price of a gift item is Rs .300 and sold it for Rs.210. find the discount percent .
Answer:
original price - new price
300- 210=90
discount/ original price ×%
90/300×100
=30%
The discount percent is 30%
Tina wrote 2 equivalent expressions that could be used to calculate the number of books on her shelves. Which pair of expressions is equivalent?
4+(9+8) and 4−(9−8)
3(9+8) and 9(3+8)
(4×9)×8 and 9×(4×8)
(5+4)+1 and 5(4+1)
Answer:b
Step-by-step explanation:
Not D
Answer:
(4×9)×8 and 9×(4×8)
Step-by-step explanation:
please help lolz ty besties
Simplify the expression. Write your answer as a power.
(3.8^3)^4
The simplified expression is