Answer:
D = L/k
Step-by-step explanation:
Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is
dA/dt = in flow - out flow
Since litter falls at a constant rate of L grams per square meter per year, in flow = L
Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow
So,
dA/dt = in flow - out flow
dA/dt = L - Ak
Separating the variables, we have
dA/(L - Ak) = dt
Integrating, we have
∫-kdA/-k(L - Ak) = ∫dt
1/k∫-kdA/(L - Ak) = ∫dt
1/k㏑(L - Ak) = t + C
㏑(L - Ak) = kt + kC
㏑(L - Ak) = kt + C' (C' = kC)
taking exponents of both sides, we have
[tex]L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}[/tex]
When t = 0, A(0) = 0 (since the forest floor is initially clear)
[tex]A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L[/tex]
[tex]A = \frac{L}{k} - \frac{L}{k} e^{kt}[/tex]
So, D = R - A =
[tex]D = \frac{L}{k} - \frac{L}{k} - \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{kt}[/tex]
when t = 0(at initial time), the initial value of D =
[tex]D = \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{k0}\\D = \frac{L}{k} e^{0}\\D = \frac{L}{k}[/tex]
a shopkeeper bought 2 watches for rs 400. he sold them to gain 5% one and loss 5% on other. calculate his final gain or loss percent. if the selling price of both watches is same.
Mickey exercises 1/4 hour every day.
How many hours does he exercise in 8 days?
Answer: You multiply 8 x 3/4=24/4. Then you simplify your answer and it is 6 hours. 24/4 is division 24 divided by 4 equals 6.
Step-by-step explanation: Or, you can change 3/4 to a decimal which is .75. Then you multiply .75 x 8 and the answer is 6.00 which is 6 hours because you do not use the zeros after the decimal point.
Answer:
2 hours
Step-by-step explanation:
You can just multiply 1/4 by 8. You're simply just adding on 1/4 8 times, and that is the same as multiplying.
Review graph I and graph II.
On a coordinate plane, a parabola labeled Graph 2 opens down. It goes through (negative 2, 0), has a vertex at (negative 2, 7), goes through open circle (negative 4, 5), and goes through (negative 6, 0).
On a coordinate plane, a parabola labeled Graph 1 opens down. It goes through (negative 2, 0), has a vertex at (negative 2, 7), goes through open circle (negative 4, 5), and goes through (negative 6, 0). An open circle is at (negative 4, 8).
Which statement compares the limit as x approaches –4 for the two graphs?
In both graph I and graph II, the limit is 5.
In both graph I and graph II, the limit does not exist.
In graph I, the limit does not exist, but in graph II, the limit is 5.
In graph I, the limit is 8, but in graph II, the limit does not exist.
Answer:
A - in both graph I and graph II, the limit is 5
Step-by-step explanation:
:)
Answer:
A - in both graph I and graph II, the limit is 5
Step-by-step explanation:
the guy above me lol
[tex] \frac{5}{8} \div 6[/tex]
I need it in a fraction and a decimal in the simplest form
Answer:
[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{:}\ [/tex]
[tex] \frac{5}{{8}{} } \div 6 = \frac{5}{48} [/tex]
=0.104166=0.1 is your answer
Hallar la altura(h) de un triángulo que tiene una base 12 metros y un área de 96
metros cuadrados. Opción única.
(2 puntos)
16
11
15
Answer:
Height of triangle = 16 meter
Step-by-step explanation:
Given:
Area of given triangle = 96 squares meter
Base length of triangle = 12 meter
Find:
Height of triangle
Computation:
Area of triangle = (1/2)(b)(h)
Area of given triangle = (1/2)(Base length of triangle)(Height of triangle)
96 = (1/2)(12)(Height of triangle)
96 = (6)(Height of triangle)
Height of triangle = 96 / 6
Height of triangle = 16 meter
Can you figure out the answer?
Answer:
1680
Step-by-step explanation:
480x3=1440
480/2=240
1440+240=1680
A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm. He knows that the population standard deviation is 0.83 cm. Assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? State the null and alternative hypotheses for the test.
Answer:
The null hypothesis is [tex]H_o: \mu = 4[/tex].
The alternate hypothesis is [tex]H_a: \mu \neq 4[/tex]
The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.
Step-by-step explanation:
A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.
This means that the null hypothesis is that they are 4.00 cm long, that is:
[tex]H_o: \mu = 4[/tex]
At the alternate hypothesis we test if it is different. So
[tex]H_a: \mu \neq 4[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
4 is tested at the null hypothesis:
This means that [tex]\mu = 4[/tex]
After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.
This means that [tex]n = 196, X = 4.14[/tex]
He knows that the population standard deviation is 0.83 cm.
This means that [tex]\sigma = 0.83[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}[/tex]
[tex]z = 2.36[/tex]
Pvalue of the test and decision:
The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.
Looking at the z-table, z = -2.36 has a pvalue of 0.0091
2*0.0091 = 0.0182
The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.
write 770000 and round it to the nerest lakh
Step-by-step explanation:
Seven lakh and seventy thousand.
This is your answer.
2 3/4 + 12 6/8 = answer
Answer:
15 1/2
Step-by-step explanation:
Answer:
15 1/2
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!
Answer:
half of 11:
5.5^2 x 3.14
30.25 x 3.14 = 94.985
round
94.99
In triangle ABC, m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘.
What is the value of x?
Answer:
x = 23
Step-by-step explanation:
A triangle contains 180°. So, simply create the equation m∠A + m∠B + m∠C = 180° and solve for x.
2x + 3x + 1 + 3x - 5 = 180
8x - 4 = 180
8x = 184
x = 23
The value of x in triangle ABC, where m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘ is 23.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.
In triangle ABC,
m∠A=(2x)∘, m∠B=(3x+1)∘, m∠C=(3x−5)∘.As, the sum of all the angles of triangle is equal to the 180 degree. Thus,
[tex]m\angle A+m\angle B +m\angle C=180^o\\(2x)+(3x+1)+(3x-5)=180\\2x+3x+3x=180+5-1\\8x=184\\x=\dfrac{184}{8}\\x=23^o[/tex]
Thus, the value of x in triangle ABC, where m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘ is 23.
Learn more about the triangle angle sum theorem here;
https://brainly.com/question/7696843
#SPJ2
Identify the terminal point for a 60° angle in a unit circle.
A.
22
B. (1,1)
c. (7)
D. (5.)
Answer:
it's A
Step-by-step explanation:
i hope this helps :D
Identify the terminal point for a 60° angle in a unit circle.
What is the terminal angle?
Terminal point definition the final destination or station of a bus or rail journey | Meaning, pronunciation, translations, and examples.
for the terminal point for a 60-degree angle in a unit circle.
Therefore the correct option is D.
Therefore, the 1/3 and root(3)/2.
To learn more about terminal angle visit:
https://brainly.com/question/1982296
#SPJ2
Please explain how you got this
Answer:
area = 68 ft²
Step-by-step explanation:
area = 1/2(b1 + b2)(h) = 1/2(9 + 8)(8) = 68 ft²
Answer:
68
Step-by-step explanation:
First find the internal square area (64) then calculate the outer triangles (2 each) to get 68 plz thx, 5 str and mark brainliest
Please help (no links) or i will report you i just need answers
1. b=117°
2.c=67°
have an amazing day <3
How many ways can three people be selected from a group of seven people if order DOES matter?
Answer:
no it doesnt matter unless you do this The fundemetal principle of counting.
7 ways 3 people = 21 ways
Step-by-step explanation:
What is the part of the steam engine that does the work?
the flywheel
the piston
the turbine
the cylinder
Answer:
Piston
Step-by-step explanation:
Because i took the test ..................................
78% of all laboratory mice can make it through a maze. If 600 randomly selected mice attempt the maze. Write out the formula to calculate the confidence interval
36’s square root is what??? This is literally due in 15 minutes!
Answer:
square root of 36 is 6
Step-by-step explanation:
because 6 x 6 =36
Answer:
the square root is of 36 is 6
free 100 pointssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
Thank you for the points man I really need them to ask a huge question
Step-by-step explanation:
I answer your question, I get the points, I make the question, someone elce gets the points.
what is the unit price of 12 cupcakes for 25 dollars
Answer:
Unit price of 12 cupcakes for 25 dollars = 25/12
= 2.08 dollars
Answer:
The unit price would be $2.08 for a cupcake because if you divide 12 and 25, you would get 2.08.
Step-by-step explanation:
help pleaseeeeee? omggggg
ILL MARK BRAINLIEST OF CORRECT AND GIVE 25 POINTS
This figure was broken into a triangle and a parallelogram as shown.
Use the figures to complete the statements.
The height of the triangle h is
in. 10 12 22
The area of the triangle is
in.2.40 48 80 96
The area of the parallelogram is
in.2 40 48 80 96.
The area of the irregular figure is
in.2. 88 128 144 176
Step-by-step explanation:
The height of the triangle H is 12
The area of the triangle is 48
The area of the parallelogram is 80
The area of the irregular figure is 128
I think
:)
pls help its due soon
Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions. (a) How many ways can the letters of the word DANCER be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with elements. So the answer is . (b) How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit? (c) How many ways can the letters of the word DANCER be arranged in a row if the letters NCE must remain together (in order) as a unit?
Answer:
(a) 720 ways
(b) 120 ways
(c) 24 ways
Step-by-step explanation:
Given
[tex]Word = DANCER[/tex]
[tex]n =6[/tex] --- number of letters
Solving (a): Number of arrangements.
We have:
[tex]n =6[/tex]
So, the number of arrangements is calculated as:
[tex]Total =n![/tex]
This gives:
[tex]Total =6![/tex]
This gives:
[tex]Total =6*5*4*3*2*1[/tex]
[tex]Total =720[/tex]
Solving (b): DA as a unit
DA as a unit implies that, we have:
[DA] N C E R
So, we have:
[tex]n = 5[/tex]
So, the number of arrangements is calculated as:
[tex]Total =n![/tex]
This gives:
[tex]Total =5![/tex]
This gives:
[tex]Total =5*4*3*2*1[/tex]
[tex]Total =120[/tex]
Solving (c): NCE as a unit
NCE as a unit implies that, we have:
D A [NCE] R
So, we have:
[tex]n = 4[/tex]
So, the number of arrangements is calculated as:
[tex]Total =n![/tex]
This gives:
[tex]Total =4![/tex]
This gives:
[tex]Total =4*3*2*1[/tex]
[tex]Total =24[/tex]
What is the slope of a line perpendicular to y=-7/4x?
O A. - 4
O B. - 7
O c.
7
4
O D. 4
If a varies inversely with b, and a=20 when b=1/4, find the equation that relates a and b
Answer:
Step-by-step explanation:
280ora
what is the domain of y=log5x?
A. all real numbers less than 0
B. all real numbers greater than 0
C. all real numbers not equal to 0
D. all real numbers
I'm sorry to rush but I need the answer kinda quickly
PLEASEI BEG U ALL PLEASE 26 POINTSPLEASE JUST HELP ME ON THIS I DONT HAVEMUCH TIMELEFT
Answer:
a) 14
b) 7/45
Step-by-step explanation:
a) 12 are male and studied chemistry
b) There are 14 male Biologists and 90 in total which is 14/90 which = 7/45
(I'm not 100% sure but if I'm wrong I'm very sorry)
I read the question wrong 3 times I'm blind
A city hosted a music festival that included three concerts. According to the sales database, 28% of the audience attended the first concert, 42% attended the second one, 30% attended the third one, 80% attended at least one of the three concerts, 10% attended the first and second ones, 8% attended the first and third ones, and 7% attended the second and third ones. Find the probability that a randomly selected audient attended all the concerts
Answer:
[tex]P(X\cap Y\cap Z)=0.05[/tex]
Step-by-step explanation:
From the question we are told that:
Percentage of audience in first concert [tex]P(X)=0.28[/tex]
Percentage of audience in second concert [tex]P(Y)=0.42[/tex]
Percentage of audience in third concert [tex]P(Z)=0.30[/tex]
Audience Percentage at at-least one concert [tex]P(X \cup Y \cup Z)=0.80[/tex]
Percentage of audience at first & second concert [tex]P(X \cap Y)=0.10[/tex]
Percentage of audience in first & third concert [tex]P(X \cap Z)=0.08[/tex]
Percentage of audience in second & third concert [tex]P(Y\cap Z)=0.07[/tex]
Generally the equation for probability of attending all concerts [tex]P(X\cap Y\cap Z)[/tex]is mathematically given by
[tex]P(X \cup Y \cup Z)=P(X)+P(Y)+P(Z)-P(X \cap Y)-P(X \cap Z)-P(Y\cap Z)+P(X\cap Y\cap Z)[/tex]
[tex]P(X\cap Y\cap Z)=P(X \cup Y \cup Z)-P(X)-P(Y)-P(Z)+P(X \cap Y)+P(X \cap Z)+P(Y\cap Z)[/tex]
[tex]P(X\cap Y\cap Z)=0.80-0.28-0.42-0.30+0.10+0.80+0.70[/tex]
[tex]P(X\cap Y\cap Z)=0.05[/tex]
Therefore the probability that a randomly selected audient attended all the concerts
[tex]P(X\cap Y\cap Z)=0.05[/tex]
Gavin went on 24 runs last month that totaled 100 miles. Each run was a distance of either 3 miles or 5 miles. Which system of equations can be used to determine the number of 3-mile runs, x, and the number of 5-mile runs, y, that Gavin went on last month?
A.
x + y = 100
3x + 5y = 24
B.
x + y = 100
5x + 3y = 24
C.
x + y = 24
3x + 5y = 100
D.
x + y = 24
5x + 3y = 100
Answer:
d
Step-by-step explanation: