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]
message
Isabella, Marcus, Carl, Devon, and Taylor are to be seated together in a row. If Carl and Devon must sit next to each other, how many different ways can the five people be arranged?
Answer:
24
Step-by-step explanation:
4 numbers can be arranged that many times and Carl and Devon count as one since they need to sit next to one another!
Nadine's curtain company is making curtains for a local hotel. She wants each curtain to be 48 inches long. At the fabric store, fabric is sold by the foot. If Nadine's curtain company wants to make 52 curtains, how many feet of fabric will she need? 1 inch = 1 12 foot
Find the median and mean of the data set below: 39, 22, 14, 9, 1, 11
Answer:
mean is 16
Step-by-step explanation:
Which statement can you conclude is true from the given information?
Answer:
angle IJA is a right angle
Solve the equation for x. 25x = 275
x =
Answer:
x = 11
Step-by-step explanation:
So the equation is 25x = 275. In order for us to find out what x is we need to get rid of 25 that is next to x, so we are going to have to divide 25x by 25. What you do to one side you do to the other so the equation will look like this:
25x/ 25 = 275/ 25
25x/25 = x
275/25 = 11
so x = 11
PLSSSSSS I NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Simplify the Expression:
[tex]\sqrt{9a^{2} }[/tex], if a<0
Answer: -3x
Step-by-step explanation: If you separate out each term on its own, 9 and x², and do the square root of each one, you are left with 3x. This is also coincidentally what the right side of this graph looks graphically. However, the line of 3x does continue past x=0, so the other side of this graph, -3x, fits this better.
Thats my best guess, either way, hope it helps!
A 20 ft tall ladder standing next to a statue casts a 12 ft shadow. If the statue casts a shadow that is 9 ft long then how tall is it?
Given that,
Length of the ladder = 20 ft
It casts a 12 ft shadow
To find,
If the statue casts a shadow that is 9 ft long then how tall is it?
Solution,
Let the ladder be x ft tall.
20 ft tall ladder = 12 ft shadow
9 ft tall ladder =
[tex]\dfrac{20}{12}\times 9\\\\=15\ ft[/tex]
Hence, the required length is 15 ft.
4(x-6y) i really need help on this!
Answer:
you should simply distribute it 4x -24y that mean you should × 4 by x and 4by 6y then you will get the answer
if the point (6,3) lies on the graph of a direct variation, what is the constant of variation?
Answer:
[tex]k = 0.5[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (6,3)[/tex]
Required
Determine the constant of variation
Since it is a direct variation, the following relationship exists:
[tex]y = kx[/tex]
Where k represents the constant.
Substitute 6 for x and 3 for y
[tex]3 = k * 6[/tex]
[tex]3 = 6k[/tex]
Make k the subject
[tex]k = \frac{3}{6}[/tex]
[tex]k = 0.5[/tex]
Hence, the constant of variation is 0.5
Solve for u .
-24 = u ÷ 6
u =
Answer:
[tex]u = - 144[/tex]
Step-by-step explanation:
[tex] - 24 = u \div 6[/tex]
[tex] - 24 \times 6 = u[/tex]
[tex] - 144 = u[/tex]
to be sure
[tex] - 24 { = }^{?} - 144÷6[/tex]
[tex] - 24 = - 24[/tex]
Answer:
u = -144
Step-by-step explanation:
-24 = u ÷ 6
Multiply both side by 6.
-24 × 6 = u ÷ 6 × 6
-144 = u
Verification:-
-24 = -144 ÷ 6
-24 = -24
LHS = RHS
5 divided by 3/12 equals
Answer:
= 20
Step-by-step explanation:
Turn it into multiplication by doing keep, switch, flip. Keep 5. Switch division to multiplication. Flip 3/12 to 12/3 or 4.
5 x 4 = 20.
please help asap i dont understand at all
Answer:
Reflect shape A over the y-axis and vertically translate shape A downward 1 unit.
any one here in LISD district
Answer:
I'm not, but free points?
Step-by-step explanation:
PLZ HELP ME WITH THIS!?!? I WILL MARK BRAINLIEST!!!
Answer: can it be a bit clearer pls?
Step-by-step explanation:
What does "(-2)(6)" mean
Answer:
Step-by-step explanation:
it means that you do negative 2 times 6. That is -2 x 6, which is -12
Answer:
implied multiplication
Step-by-step explanation:
(-2)(6)
When two parentheses are next tow each other, there is implied multiplication
-2 * 6
-12
How can u find the perimeter in a graph
Item Measured Scale Reading (tons) Number of Items on the Scale Weight per Item (tons)
Raul and his friends
1
20
4
cars
7
8
2
baby elephants
ما | ط
001
goats
4
cow NIP
desks
1
32
Answer:
Plato Answer
Step-by-step explanation:
PLEASE HELP!!! (20 POINTS)
Is it true that [20+(−1)0]0=1? Explain.
A.No, because the negative sign will cancel the values, resulting in zero.
B.Yes, because the negative sign will cancel the values, resulting in one.
C.No, because any number raised to the zero power is zero.
D.Yes, because any number, except zero, raised to the zero power is one.
HELP URGENT !!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
Help please.....its due today
.) Mr. Leonard is saving his money for a new Jeep toy. If 30% of the toy Jeep
is $6.00, how much is the toy?
Answer:
i think its 20 dollars
Step-by-step explanation:
hope its right
Helppp... last question on the test lol
(Will mark brainliest)
Answer:
A. Y=1.4x
Step-by-step explanation:
What are the answers pls?
Answer:
B)
Step-by-step explanation:
I believe the answer is B).
Hope this helps! Do you give brainlliest?
A computer store buys a computer system at a cost of 357.60$. The selling price was first at 596$ , but then the store advertised a 40% markdown on the system. Answer parts a and b.
Answer:
i not know what you need me to help you
Step-by-step explanation:
What is the equation of this line
Answer:
Y= 2x
Step-by-step explanation:
Two points in that graph are (1,2) and (2,4). you have to do rise over run so 4-2 over 2-1 and the answer is 2/1 or just two.
If the equation 5(3x + 7) – 1 = 3(52 + k) + 4 has infinitely many solutions, what is the value of k?
Answer:
k = 5x - 42
Step-by-step explanation:
can u pls help me with this question
Answer:
3 miles per hour
Step-by-step explanation:
his speed is 12/4 (or 3) miles an hour. What you do, is you have to multiply 15 by four to go from 15 min to one hour, and you also have to multiply 3/4 by four.
1
What is the y-intercept of a line that has a slope of 4 and passes through point (8, 3)?
3
Ο Ο Ο Ο
11
Answer:
The slope-intercept form: y = mx + b
m - a slope
b - y-intercept
We have a slope m = 1/4. Substitute: y = 1/4 x + b
We know, the line passes through point (8, 3) → x = 8, y = 3.
Put the values of x and y to the equation of the line:
1/4 · 8 + b = 3
2 + b = 3 |-2
b = 1
Answer: y-intercept is (0, 1)
Step-by-step explanation:
whats 1 + 1? brainly to who could answer
Answer:
i think its 4
Step-by-step explanation:
4. Charles claims that he can distinguish between beer and ale 75 percent of the time. Ruth bets that he cannot and, in fact, just guesses. To settle this, a bet is made: Charles is to be given ten small glasses, each having been filled with beer or ale, chosen by tossing a fair coin. He wins the bet if he gets seven or more correct. Find the probability that Charles wins if he has the ability that he claims. Find the probability that Ruth wins if Charles is guessing.
Answer: Probability that Charles gets 7 or more correctly = 0.776
Probability that Ruth wins = 0.827
Step-by-step explanation:
Given data:
Probability that Charles distinguishes between beer and ale = 0.75
no of glasses = 10
no required to win the bet = 7 or more.
Solution:
a) probability of success p=0.75.
This is a binomial probability problem, what we need to solve for is the probability that ( X >=7 ) this can be gotten as
P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)
where k=7,8,9,10
Probability that he gets 7 correctly.
P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)
Substitute k = 7 into the equation
= 0.250
Probability that he gets 8 correctly.
P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)
substitute k = 8 into the equation
= 0.282
Probability that he gets 9 correctly.
P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)
Substitute k = 9 into the equation
= 0.188
Probability that he gets 10 correctly.
P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)
Substitute the k= 10 into the equation.
= 0.0563
Probability that Charles gets 7 or more correctly
= 0.250 + 0.282 + 0.0563 + 0.188
= 0.776
b) Probability that Ruth wins
K = 1,2,3,4,5,6
p=0.5
P(X < 7)
P(X < 7) = (10Ck) (.5)^k (1-.5)^(10-k)
Probability that he gets one correctly
P(X = 1 ) = (10Ck) (.5)^k (1-.5)^(10-k)
substitute k= 1 into the equation.
= 0.0098
P(X=2) = (10Ck) (.5)^k (1-.5)^(10-k)
Substitute k= 2 into the equation
= 0.0439
P(X =3) = (10Ck) (.5)^k (1-.5)^(10-k)
Substitute k=3 into the equation.
=0.117
P(X=4) = (10Ck) (.5)^k (1-.5)^(10-k)
Substitute k= 4 into the equation
= 0.2051
P(X=5) = (10Ck) (.5)^k (1-.5)^(10-k)
Substitute k =5 into the equation
= 0.246
P(X= 6 ) = (10Ck) (.5)^k (1-.5)^(10-k)
Substitute k = 6 into the equation
= 0.205
Probability that Ruth wins
= 0.205 + 0.246 + 0.2051 + 0.117 + 0.0439 + 0.0098
= 0.827