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]
11th Grade And Algebra
4g + 13 =54
Answer:
g = 41⁄4
Step-by-step explanation:
4g + 13 = 54
=> 4g = 54 - 13
=> 4g = 41
=> g = 41⁄4
∴ g = 41⁄4
if lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then find lim (fg)(x)
a.1
b.0
c.3
d.does not exist
Answer:
0
Step-by-step explanation:
Assuming the problem is:
"lim x-> 4 f(x)=5 lim x-> 4 g(x)=0 and lim x-> 4 h(x)=-2, then find lim x->4 (fg)(x)"
lim x->4 (fg)(x)
Since we know the limits of f and g at x=4 exist we can write the limit as:
lim x->4 f(x) lim x->4 g(x) (since fg(x) means f times g of x.)
5(0)
0
if lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then lim (fg)(x) 0
What is inequality?inequality the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Assuming the problem is:
"lim x-> 4 f(x)=5 lim x-> 4 g(x)=0 and lim x-> 4 h(x)=-2, then find lim x->4 (fg)(x)"
lim x->4 (fg)(x)
Since we know the limits of f and g at x=4 exist we can write the limit as:
lim x->4 f(x) lim x->4 g(x) (since fg(x) means f times g of x.)
=5(0)
=0
Hence the lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then lim (fg)(x) 0
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Is the graph increasing , decreasing or constant
Answer: Constant.
The graph does not have an incline and therefore has a slope of 0. This means that the graph is constant.
If
you had 2 angles that equal 180 degrees and you was given a angle of
55 degrees What degree is the missing angle? *
Answer:
125 degrees for 540 degrees total
Step-by-step explanation:
Answer:
125° is the missing angle.
Step-by-step explanation:
Sum of all angles in a quadrilateral is 360°.
180°+55°+X°= 360°
235° + x = 360°
x = 360°-235°= 125°
x = 125°
Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Suppose a screening program for the early detection of breast cancer was started in order to increase the survival rate p of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were screened by the program and who were diagnosed to have the disease. Let x represent the number of those in the sample who survive the disease.
Required:
a. If you wish to determine the community screening program has been effective, state the alternative hypothesis that should be tested.
b. State the null hypothesis.
c. If 164 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using αα=.05 and explain the practical conclusion from your test.
d. Find the p-value for the test and interpret it.
Answer:
A) Alternative hypothesis; Ha: p_o > ⅔
B) Null hypothesis;
H0: p_o = ⅔
C) There is sufficient evidence to support the claim that the community screening programme was effective
D) p-value = 0
Its less than the significance value and so we will reject the null hypothesis and conclude that the community screening programme was effective
Step-by-step explanation:
A) We are told that ⅓ of those diagnosed eventually die of the disease. Thus, ⅔ is the fraction that will survive the disease.
Thus, the null hypothesis is;
H0: p_o = ⅔
We are told that a screening programme was started to increase the survival rate. Thus,the alternative hypothesis is;
Ha: p_o > ⅔
B) null hypothesis is;
H0: p_o = ⅔
C) 164 out of the 200 women selected survived the disease.
Thus sample proportion is;
p^ = 164/200
p^ = 0.82
For the z-score value, we will use the formula;
z = (p^ - p_o)/√((p_o(1 - p_o)/n)
Now, p_o = ⅔ = 0.67
Thus;
z = (0.82 - 0.67)/√((0.67(1 - 0.67)/200)
z = 4.51
From online p-value from z-score calculator, we have p-value ≈ 0
This is less than the significant level of 0.05 and therefore we will reject the null hypothesis and conclude that the community screening program was effective.
D) p-value ≈ 0
Reject the null hypothesis
A teepee in the shape of a cone has a
radius of 7 feet and a height equal to
its diameter. What is the volume of the
teepee? Use 3.14 for .
The volume of the given cone is 718.01 square feet. Therefore, option H is the correct answer.
What is the volume of a cone?The volume of a cone is the amount of space occupied by a cone in a three-dimensional plane. A cone has a circular base, which means the base is made of a radius and diameter. The volume of a cone formula is 1/3 πr²h.
Given that, radius of a base of cone is 7 feet.
A height of a cone equal to its diameter = 7×2 = 14 feet
Here, volume of a cone = 1/3 ×3.14×7²×14
= 718.01 square feet
Therefore, option H is the correct answer.
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Find the perimeter of triangle round nearest tength
This is the answer. I hope it helps!
A student rounds a number to 12.9. Which of the following is a possible value of the original number?
Answer:
12.85, 12.86, 12.87, 12.88, 12.89, 12.90, 12.91, 12.92, 12.93, and 12.94
Step-by-step explanation:
there is none
pls help me waaaaaaa
Answer:
lol lol lol lol lol lol lol lol
Step-by-step explanation:
PLEASE HELP ME GIVING LOTS OF POINTS AND BRAINLIEST TO THE FIRST LEGIT ANSWER!!!
A group of students were surveyed to find out if they like building snowmen or skiing as a winter activity. The results of the survey are shown below:
60 students like building snowmen
10 students like building snowmen but do not like skiing
80 students like skiing
50 students do not like building snowmen
Make a two-way table to represent the data and use the table to answer the following questions.
Part A: What percentage of the total students surveyed like both building snowmen and skiing? Show your work. (5 points)
Part B: What is the probability that a student who does not like building snowmen also does not like skiing? Explain your answer. (5 points)
Answer: 45.4% of students like both building snowmen and skiing
18.1% of students who do not like building snowmen also do not like skiing
Step-by-step explanation:
__________________________________________________
likes snowmen doesn't like snowmen total
__________________________________________________
likes skiing 50 30 80
__________________________________________________
doesn't like skiing 10 20 30
_________________________________________________
total 60 50 110
what is 7.09 Divided by 101
Answer:
0.070198..
Step-by-step explanation: its an on going number so make sure to put the line on top on the 0198
(2a + 3b + 1) - (3a + 5b) - (2a - 2b – 3)
Answer:
4- 3a .............................
Write the number six and a half thousand in figures
Answer:
Step-by-step explanation:
6500 is the correct answer
Find the greatest common factor of 6c^3 and 10c^4
Answer:
2c^3
Step-by-step explanation:
The greatest common divisor of 6 and 10 are 2
The factors that are common to 6c^3, 10c^4 would be 2ccc
Simplify that and you have 2c^3
which is the smallest integers, please answer, -9, 0, -2, -4, -11
Answer:
-11 :)
Step-by-step explanation:
Answer: 0
Step-by-step explanation:
A researcher was interested in knowing whether the mean weight of the second baby is higher, lower, or about the same as the mean weight of the first baby for women who have at least two children. She selected a random sample of 20 women who had at least two children and asked for the weights of the first two at birth. She found that the mean of the differences (first - second) was 5 ounces, and the standard deviation of the differences was 7 ounces.
Required:
a. Why was the researcher's study design better than taking independent samples of mothers and asking the first sample about the weight of their first baby and the sec_ and sample about the weight of their second baby?
b. Define the parameter of interest. Use appropriate notation.
c. Write the mean of 5 ounces and the standard deviation of 7 ounces using appropriate statistical notation.
d. Find a 90% confidence interval for the parameter that you defined in part (b). Write a sentence or two interpreting the interval.
Name an interior angle that is supplementary to <7.
Will give BRAINLIEST!!!!
Answer:
2, 4, and 6
Step-by-step explanation:
Supplementary angles are angles that add to 180°.
We can see that the angles that make a straight line/straight angle with ∠7 are supplementary to it, because a straight line is 180°.
Those numbers would be be 2, which equals to 4, which equals to 6 and also 8, but that number isn't one of the answers
2,4, and 6
find the volume if the figure
Answer:
there aint no figure
Step-by-step explanation:
Answer:
yea there ain't no figure
Step-by-step explanation:
lololololololololol
Help me out!!!! ASAP!!!!
Answer:
226 feet
Step-by-step explanation:
264^2 + 900^2= c^2
879696= c^2
938= c
900+ 264= 1164
1164- 938= 226
I think this is right
A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 167?
put in a new
A rectangular garage is 11 yards long and 5 yards wide. It costs $2.00 per square yard
concrete floor. How much would it cost to put a new concrete floor in the garage?
Answer:
$110
Step-by-step explanation:
The first step would be to multiply 11 and 5 to get the result of 55.
Then, you would multiply 55 by whatever the cost per square yard is, which in this case is $2.
Finally after multiplying 55 and 2 you would get the answer of $110.
Hope this helped! Have a great day! :)
RT and UW are parallel lines.
Which angles are corresponding angles?
Sade used the two blocks pictured to build a tower. What is the TOTAL VOLUME of the two blocks for this entire tower? *
Answer: V=120
have an amazing day <3
Answer:what is the answer i dont understand
plz help
Describe the trend in the scatter plot . Explain your answer
From the given scatter plot it is a positive trend.
We need to describe the trend of given scatter plots.
How to identify the trend of the scatter plots?A scatter plot shows a positive trend if y tends to increase as x increases. A scatter plot shows a negative trend if y tends to decrease as x increases. A scatter plot shows no trend if there is no obvious pattern.
Here, from the given graph it is a positive trend.
Hence, from the given scatter plot it is a positive trend.
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L
2.8
K
Solve AJKL. Round the answer to the nearest tenth.
A. J = 42.2°, K = 110.70, L = 27.1°
B. J = 110.70, K = 42.20, L = 27.1°
C. J = 42.2°, K = 27.1°, L = 110.70
D. J= 27.1°, K = 110.7°, L = 42.2°
Please select the best answer from the choices provided
Answer:
Result = 124.6
Step-by-step explanation:
If the digit after tenth is greater than or equal to 5, add 1 to tenth. Else remove the digit. Example
124.58
The first number of right of decimal point is 5
The second digit after decimal point is 8 which is greater than 5
So add 1 to 5
Result = 124.6
A shoe string is cut in to equal pieces that measure 0.50 of an inch. If the shoe string measures 7.50 inches, how many equal pieces can be cut?
There are 64 teams in a basketball tournament. All teams play in the
first round but only winning teams move on to subsequent rounds.
Write an explicit rule for T(n), the number of games in the nth round of
the tournament. State the domain:
The domain of this function is n ≥ 1, where n is the round of the tournament.
What is domain and range of the function?The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.
The explicit rule for T(n), the number of games in the nth round of the tournament is 2ⁿ⁻¹. The domain of this function is n ≥ 1, where n is the round of the tournament.
Since all teams play in the first round, the number of games in the first round (n = 1) is 2¹⁻¹, which is equal to 1. As the rounds progress, the number of games in each round is doubled. T
herefore, the number of games in the second round (n = 2) is 2²⁻¹, which is equal to 2. The number of games in the third round (n = 3) is 2³⁻¹, which is equal to 4.
This pattern continues for each round, as the number of games in the nth round is 2ⁿ⁻¹.
Therefore, the domain of this function is n ≥ 1, where n is the round of the tournament.
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Find the distance between the pair of points (2,-1) and (-5,-5)?
Answer:
down 4 and over 7 so 11
Step-by-step explanation:
Convert 400 meters (m) to feet (ft). Round your answer to two decimal places. (1 metre = 3.28084 feet)
Answer:
1m----------3.28084ft
400m---------xft
x=(400*3.28084)/1
x=1,312.33 ft
Step-by-step explanation:
Phil needs to run at least 30
miles this week for his
training, If he has already run
18 miles this week, then how
mary miles should he run on
each of the 3 remaining days
this week?
I NEED THE INEQUALITIES SOLUTION AND THE GRAPH OF EACH QUESTION
Please please please give me all to each question not just the answer please
IF YOU GIVE ME A LINK I WILL REPORT YOU!
Answer:
The answers to these equations are 4 for the left math problem, 4 for the middle math problem, and 10 for the right math problem.
Step-by-step explanation:
Answer above.