Answer:
[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]
Step-by-step explanation:
Given that:
A country population at any given time (t) is:
[tex]\dfrac{dP}{dt}= kP+I[/tex]
where;
P = population at any time t
k = positive constant
I = constant rate of immigration into the country.
Using the method of separation of the variable;
[tex]\dfrac{dP}{kP+1}= dt[/tex]
Taking integration on both sides:
[tex]\int \dfrac{dP}{kP+I}= \int \ dt[/tex]
[tex]\dfrac{1}{k} log (kP + I) = t+c_1 \ \ \ here: c_1 = constant \ of \ integration[/tex]
[tex]log (kP + I) =k t+kc_1[/tex]
By applying the exponential on both sides;
[tex]e^{log (kP + I) }=e^{k t+kc_1 }[/tex]
[tex]KP+I = e^{kt} *e^{kc_1}[/tex]
Assume [tex]e^{kc_1 }= C[/tex]
Then:
[tex]kP + I = Ce^{kt}[/tex]
[tex]kP = Ce^{kt}-I[/tex]
[tex]P =\dfrac{ Ce^{kt}-I}{k} \ \ \---- Let \ that \ be \ equation \ (1)[/tex]
When time t = 0, The Total population of the country is also [tex]P_o[/tex]
[tex]P_o = \dfrac{Ce^{0(t)} -I}{k}[/tex]
[tex]P_o = \dfrac{Ce^{0} -I}{k}[/tex]
[tex]P_o = \dfrac{C-I}{k}[/tex]
C - I = kP₀
C = kP₀ + I
Substituting the value of C back into equation(1), we have:
[tex]P =\dfrac{ (kP_o+1)e^{kt}-I}{k}[/tex]
[tex]P =\dfrac{ (kP_o+1)e^{kt}}{k} - \dfrac{I}{k}[/tex]
[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]
Need help geometric sequences see pic for details
Given:
The recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]
[tex]a_1=-3[/tex]
To find:
The explicit formula of the given geometric sequence.
Solution:
We know that, first term of geometric sequence is [tex]a_1=-3[/tex].
Recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\times r[/tex] ...(i)
where, r is common ratio.
We have,
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]r=\dfrac{1}{8}[/tex]
The explicit formula of a geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]
Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get
[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]
Therefore, the correct option is D.
please help me please
A survey showed that 72% of
teens bought new athletic shoes for the
new school year. Based on that survey,
how many teens in a group of 225 bought
new athletic shoes for the new school
year?
Answer:
162
Step-by-step explanation:
225 x 0.72 = 162
PLEASE ANSWER ASAP WILL GIVE 20 POINTS IF CORRECT PLS ANSWER NOW
What is the product of 3.4 × 10^-14 and 1.8 × 10^28?
6.12 × 10^14
9.4 × 10^14
5.2 × 10^42
6.12 × 10^42
Answer:
Its 6.12 × 10^42
Step-by-step explanation:
U have to break it into pieces.. Np Merry Christmas
Need help on this one please and thank you
Answer:
64x64x64=262,144
Step-by-step explanation: mark as brainest plsssssssssssssss
Which expressions are equivalent to 6a(5+d) ?
Select each correct answer.
30a+6ad
30ad
30a+(6a⋅d)
(6a⋅5)+(6a⋅d)
11a + d
Answer: A is correct i think
Step-by-step explanation: 6a x 5 = 30a
6a x d = 6ad
Answer:
A
Step-by-step explanation:
What is the quotient of 4/5 divided by 17/9
Answer:
0.42352941176
Step-by-step explanation:
hope this helps
The value of quotient will be 0.42.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
''4/5 divided by 17/9''
Now,
Since, The expression is,
''4/5 divided by 17/9''
Hence, After solving we get;
⇒ 4/5 ÷ 17/9
⇒ 4/5 × 9/17
⇒ 36/85
⇒ 0.42
Thus, The value of quotient = 0.42
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A local flower shop sells a dozen roses for $12.85. If there is an 8% sales tax, how much in TOTAL will you pay for the roses
Answer:
13.87
Step-by-step explanation:
Y’all know this anything about this?
We are given:
Parallelogram CDEF∠C = 13x - 10∠D = 5x + 10To Find: ∠E
Concept Used:
Adjacent angles of a Parallelogram are SupplementaryFinding the value of 'x':
Since adjacent angles of a parallelogram are Supplementary:
∠D + ∠C = 180
5x + 10 + 13x - 10 = 180 [replacing the values of angle C and D]
18x = 180
x = 10 [dividing both sides by 18]
__________________________________________________________
Finding Measure of Angle D:
We are given that:
∠D = 5x + 10
∠D = 5(10) + 10 [since x = 10]
∠D = 60°
__________________________________________________________
Finding the measure of ∠E:
∠D and ∠E are Adjacent angles
Since Adjacent angles are Supplementary:
∠D + ∠E = 180
60 + ∠E = 180
∠E = 120° [subtracting 60 from both sides]
Hence, the measure of ∠E = 120°
will give brainliest!
Answer:
2/1=2
Step-by-step explanation:
can you help me with this question please
Answer:
correct answer it's A
give me a like at least please
please help me with this one :(
Answer:
I can assure you, that this is not that hard. but. I will help you with one of them.
Step-by-step explanation:
audience-look it up in the dictionary
it's basically a crowd of people.
sebtence- I listened to the audio of the audio book.
PLEASE HELP ME I need the answer asap cause my grade is low and this determines my final.
Answer:
i cant see the graph zoom in
Step-by-step explanation:
Answer:
I'm sure it's 2/3
Step-by-step explanation:
the slope is positive and it rises up 2 and over 3
Which statement is true about points located in quadrant Ill in the coordinate
plane?
O A. The x-coordinate is negative, and the y-coordinate is positive.
B. The x-coordinate is positive, and the y-coordinate is negative.
C. The x-coordinate is negative, and the y-coordinate is negative,
D. The x-coordinate is positive, and the y-coordinate is positive.
Please answer TODAY DEC 15
I WILL GIVE 100 POINTS TO THE FIRST PERSON THAT ANSWERS
Answer: C
Step-by-step explanation
I Think Its C
Write the data from greatest to least: 0.8, 0.79, 0.08, 0.81, 0.09, 0.9, 0.89
Answer:
0.9, 0.89, 0.81, 0.8, 0.79, 0.09, 0.08
Step-by-step explanation:
Answer: 0.09 , 0.89 , 0.81, 0.08, 0.79 , 0.9, 0.8
Step-by-step explanation:
First find the greatest
0.09, 0.89,0.81, 0.08, 0,79
Then the least
0.9 .0.8
Now put it all together
0.09, 0.89. 0.81 , 0.08, 0.79 , 0.9, and lastly 0.8
in a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b what is the value of b, if c=13, a=12?
Answer:
5
Step-by-step explanation:
a=12 (height)
c=13 (hypotenous)
b=? (base)
By using Pythagoras theorm
We have, hypotenous sq=base sq+height sq
Let b =base SO, base sq=hypotenous Sq-height Sq
=>base Sq =13sq-12sq
Base Sq =169-144
Base Sq =25
Base =5 (shifting the sq)....
Hope it's helpful
good monke good monke dog
Answer:
very inspirational thanks
Step-by-step explanation:
Answer:
monke
Step-by-step explanation:
-4x+5y-3-11x-y
Does -3 have a like term?
Answer:
nope ❎ ❎ ❎ ❎ ❎ ❎ ❎ ❎
In ΔDEF, if DE ≅ DF and EF is the hypotenuse, then ΔDEF is
a acute and scalene. c. right and isosceles.
b right and scalene. d. obtuse and isosceles.
Answer:
C. Right and isosceles
Explanation:
Since two sides of the triangle are equal in length ([tex]DE[/tex] and [tex]DF[/tex]), this means that the triangle is an isosceles triangle. Since [tex]EF[/tex] is the hypotenuse of this triangle, it also means that the triangle is a right-angle triangle (the hypotenuse refers to the longest side of a right triangle). Therefore, we can conclude that ΔDEF is right and isosceles.
Hope this helps :)
Answer:
It is C.
Step-by-step explanation:
Hope this helped have an amazing day!
the absolute value of 15.3 is the opposite of 15.3?
Answer:
No. The absolute value of 15.3 is 15.3, not the opposite.
Step-by-step explanation:
Absolute value makes any number its positive form. For example -2 in absolute form is 2. So 15.3 in absolute form is still positive 15.3.
What is the temperature if it is 9° colder than 15 F
Answer:
24 Degrees Farinhieght.
Step-by-step explanation:
15 degrees farinhieght added to 9 is 24 degrees.
Find the slope of the line graphed below.
Answer:
-3/2 I believe is the answer,
Step-by-step explanation:
Notice that the (left to right) line is going down, indicating it is negative.
Now do rise over run. Rise Is up and down, so 3, and run is left and right so 2, -3/2 is your answer, Correct me if I am wrong
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} y=-7x+3 \\\\ y=-x-3 \end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
y=−7x+3
y=−x−3
Answer:
(1,-4)
Step-by-step explanation:
Given:
y = −7x+3
y = −x−3
Computation:
y = −7x+3......eq1
y = −x−3.......eq2
Eq 1 - 2
-6x + 6 = 0
x = 1
So,
y = −7x+3
y = −7(1)+3
y = -4
So,
(1,-4)
plz help! will give brainliest!
x^6
When multiplying numbers in exponential form, if the number is the same, you can simply add the exponents:
x^2 * x^4 = x^(2+4) = x^6
The area of rectangle is 35 square feet.the length of rectangle is 5feet what is the width of the rectangle
Answer:
the answer should be 7
Step-by-step explanation:
A car is traveling at a rate of 48 miles per hour. If the car continues to travel at this same rate, how many hours will it take the car to travel 612 miles?
Answer:
12.75
Step-by-step explanation:
If you make a proportion: 48/1=612/x
1(612)= 612
612/48
12.75 hours
At a speed of 48 miles per hour, the car will take approximately 12.75 hours to go 612 miles.
What is the distance?A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.
A car is traveling at a rate of 48 miles per hour.
To determine the number of hours it will take the car to travel 612 miles at a rate of 48 miles per hour, you can divide the distance traveled by the rate at which the car is traveling:
⇒ distance ÷ rate
⇒ 612 miles / 48 miles/hour
Apply the division operation, and we get
⇒ 12.75 hours
Therefore, it will take the car about 12.75 hours to travel 612 miles at a rate of 48 miles per hour.
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How many solutions does this equation have?
-3n = -4n + 7
Answer:
just one: 7 you isolate the numbers by doing -3n + 4n = 7, and u get n = 7
Answer:
2
Step-by-step explanation:
my soulstinos were Solution 1)
3
n
+
7
=
−
1
3
n
+
7
−
7
=
−
1
−
7
3
n
+
0
=
−
8
3
n
=
−
8
3
n
3
=
−
8
3
3
n
3
=
−
8
3
n
=
−
8
3
Solution 2)
3
n
+
7
=
1
3
n
+
7
−
7
=
1
−
7
3
n
+
0
=
−
6
3
n
=
−
6
3
n
3
=
−
6
3
3
n
3
=
−
2
n
=
−
2
The solution is:
n
=
−
8
3
and
n
=
−
2
HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
Which statement best describes a unit rate?
1. John drove 350 miles in 5 hours
2. John drove 10 miles
3. John drove a car and a motorcycle
4. John drove 25 miles in 1 hour
Answer:
4. John drove 25 miles in 1 hour
Step-by-step explanation:
The unit rate is the number of something per unit. There should be a first number and the second number should always be 1.
The statement which best describes a unit rate is John drove 25 miles in 1 hour .
What is unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
According to the question
Best describes a unit rate is that which have second term as 1 unit
So,
Only John drove 25 miles in 1 hour satisfy the condition ,
Hence, The statement which best describes a unit rate is John drove 25 miles in 1 hour .
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g(x)=3x-5 find g(-2)
Answer:
g(2) = -11
Step-by-step explanation:
So, g(-2), basically meaning that x = -2.
Since we know that, we need to plug -2 into all of the x's.
g(2) = 3(-2) - 5
g(2) = -6 - 5
g(2) = -11
The required value of g(2) would be -11.
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The function is given in the question following as:
g(x) = 3x-5
We have to determine the value of g(2) to the given function.
As per the given question, we have
⇒ g(x) = 3x-5
So, g(-2), this meaning that x = -2.
Now, substitute the value of x = -2 in the given function,
⇒ g(2) = 3(-2) - 5
⇒ g(2) = -6 - 5
Apply the addition operation, and we get
⇒ g(2) = -11
Therefore, the required value of g(2) would be -11.
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