Step-by-step explanation:
Let the initial population of a community be P0 and the population after time t is P(t).
If the population of a community is known to increase at a rate proportional to the number of people present at time t, this is expressed as:
[tex]P(t) = P_0e^{kt}[/tex]
at t = 5 years, P(t) = 2P0
substitute:
[tex]2P_0 = P_0e^{5k}\\2 = e^{5k}\\ln2 = lne^{5k}\\ln2 = 5k\\k = \frac{ln2}{5}\\k = 0.1386[/tex]
If the population is 9,000 after 3 years
at t = 3, P(t) = 9000
a) Substitute into the formula to get P0
[tex]9000 = P_0e^{0.1386\times 3}\\9000 = P_0e^{0.4158}\\9000 = 1.5156P_0\\P_0 = \frac{9000}{1.5156}\\ P_0 = 5938.24[/tex]
Hence the initial population is approximately 5938.
b) In order to know how fast the population growing at t = 10, we will substitute t = 10 into the formula as shown:
[tex]P(10) = 5938.24e^{0.1386(10)}\\P(10) = 5938.24e^{1.386}\\P(10) = 5938.24(3.9988)\\P(10) = 23,745.97[/tex]
Hence the population of the community after 10 years is approximately 23,746
A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process. h)What is the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X)
The probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.
Here,
Since the length of the pipes follows a uniform distribution on the interval [10 feet, 10.57 feet], the probability density function (PDF) for each pipe is:
f(x) = 1 / (10.57 - 10) = 1 / 0.57 ≈ 1.7544 for 10 ≤ x ≤ 10.57
Since the lengths of the pipes are independent, the joint probability density function (PDF) of X and Y is the product of their individual PDFs:
f(x, y) = f(x) * f(y) = 1.7544 * 1.7544 = 3.0805 for 10 ≤ x ≤ 10.57 and 10 ≤ y ≤ 10.57
Now, we want to find the probability that the second pipe (Y) is more than 0.11 feet longer than the first pipe (X).
Mathematically, we want to find P(Y > X + 0.11).
Let's set up the integral to calculate this probability:
P(Y > X + 0.11) = ∬[10 ≤ x ≤ 10.57] [y > x + 0.11] f(x, y) dx dy
We integrate with respect to x first and then with respect to y:
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] ∫[10 ≤ x ≤ y - 0.11] f(x, y) dx dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [∫[10 ≤ x ≤ y - 0.11] 3.0805 dx] dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (x)] from x = 10 to x = y - 0.11 dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (y - (10 - 0.11))] dy
P(Y > X + 0.11) = 3.0805 * ∫[10 ≤ y ≤ 10.57] (y - 9.89) dy
P(Y > X + 0.11) = 3.0805 * [(y² / 2) - 9.89y] from y = 10 to y = 10.57
P(Y > X + 0.11) = 3.0805 * [((10.57)² / 2) - 9.89 * 10.57 - (((10)² / 2) - 9.89 * 10)]
P(Y > X + 0.11) = 3.0805 * [((111.7249 / 2) - 104.9135 - (50 / 2 - 98.9)]
P(Y > X + 0.11) = 3.0805 * [(55.86245 - 104.9135 + 49.9)]
P(Y > X + 0.11) = 3.0805 * [0.84895]
P(Y > X + 0.11) ≈ 2.6092
Therefore, the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.
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What is 3/100 - 1/50 equal?
Answer:
0.01?
Step-by-step explanation:
Video games made up 77.8% of the total revenue for a small specialty store.
A) 0.0778 B) 7.78 C) 77.8
D) 0.778
Timod at home while attending classes
Answer:
D
Step-by-step explanation:
This is saying 77.8% percent out of 100, therefore we right it like D
I hope this helped, please mark Brainliest, thank you!
What is 27 5/6 - 2/7?
Answer:
my calculator says 1159/35
Step-by-step explanation:
Help me plz
8th grade math
Answer
I would say the 3rd one.
Step-by-step explanation:
I do not really remember this but I am in 8th grade math to (Algebra)
Swear no one answers but plz show work ?!
The midpoint of AB is M(3,3). If the coordinates of A are (2, -1), what are the
coordinates of B?
Answer:
(4, 7)
Step-by-step explanation:
Given that:
Midpoint of AB = M(3, 3)
Coordinate of A = (2, - 1)
Let coordinates of B = (x, y)
Recall :
Midpoint of AB = [(Ax + Bx) / 2, (Ay + By) / 2]
Mx = (Ax + Bx) / 2
My = (Ay + By) / 2
Mx = 3
Mx = (Ax + Bx) / 2
3 = (2 + x) / 2
2*3 = 2 + x
6 = 2 + x
6 - 2 = x
4 = x
My = 3
My = (Ay + By) / 2
3 = (-1 + y) / 2
2*3 = - 1 + y
6 = - 1 + y
6 + 1 = y
7 = y
Hence,
B = (4, 7)
0.8 kg is more or less than 0.6 kg
Answer:
More than
Step-by-step explanation:
Answer:
More
Step-by-step explanation:
Can you help me i wil give you a branlist and please help me
Answer:
i love free points dont you
Since there are no exponents in this problem, the next step is
✔ (- 2)2.2
.
Simplify the previous step and you get
.
The final answer is
Anwers:
22 is the answer
during his vacation, dalyn rents a small boat from a rental service that charges a flat fee of $40 plus $10 per hour (including taxes). The total charge comes to $100. Which equation can be used to calculate the number of hours, x, that Dalyn rents the boat?
Answer:
(100 - 40) ÷ 10 = amount of hours
= 6 Hours
Step-by-step explanation:
HOPE THIS HELPS
PLZ MARK BRAINLIEST
Which equation BEST demonstrates the associative property of multiplication?
(5 + 6) x 7 = 7 x (6 + 5)
(5 x 6) x 7 = 5 x (6 x 7)
5 x 7 = 5 x 7
5 x 7 = 7 x 5
Answer:
c
Step-by-step explanation:
A line passes through (2, 7) and has a slope of -4. What is its equation in point-slope form?
Sorry I'm bad
Answer:
y= (-4/1)x -1
Step-by-step explanation:
A baseball diamond is a square with sides 90 ft long. A batter is at bat, with runners at first and second base. At the moment the ball is hit, the runner at first base runs to second base at 25 ft/s. Simultaneously, the runner on second base runs to third base at 15 ft/s. How fast is the distance between these two runners changing 2 s after the ball is hit?
Answer:
It is changing at -11 ft
Step-by-step explanation:
The distance d is given by
d = √x²+(90-y)²
We have to differentiate
dy/st = 25ft
dx/dt = -15ft
The question says after 2 seconds
Y = 25x2 = 50ft
X = -15x2 = -30ft
Then we calculate rate of change of distance. From the calculations I did, I arrived at
(1/2√900+1600).[900-2000]
= -1100/2x50
= -1100/100
= -11ft
Please check attachment to help you understand the answer better as it is more detailed.
The distance between these two runners changing 2 s after the ball is hit 11 ft
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A baseball diamond is a square with sides 90 ft long.
A batter is at bat, with runners at first and second base.
At the moment the ball is hit, the runner at first base runs to second base at 25 ft/s.
Simultaneously, the runner on second base runs to third base at 15 ft/s.
The distance d is given by
[tex]\rm d = \sqrt{x^{2} +(90-y)^2}[/tex]
We have to differentiate
[tex]\rm \dfrac{dy}{st} = 25 \ ft\\\\\dfrac{dx}{dt} = -15 \ ft[/tex]
The question says after 2 seconds
[tex]\rm Y = 25x ^2 = 50 \ ft\\\\X = -15x^2 = -30 \ ft[/tex]
Then we calculate the rate of change of distance will be
[tex]\rm \dfrac{1 }{2\sqrt{900 + 1600}} * (900 - 2000) = \dfrac{-1100}{2*50} = \dfrac{-1100}{100} = -11\ ft[/tex]
More about the differentiation link is given below.
https://brainly.com/question/24062595
Find the remainder when
f(x) = 8x^3 + 4x^2 – 13x + 3
is divided by 2x + 5.
A. 1241/125
B. -129/2
C. 69/125
D. 183
Dividing f(x) by 2x + 5 leaves the same remainder as division by x + 5/2. By the remainder theorem, it is equal to f (-5/2), so the remainder here is
f (-5/2) = 8 (-5/2)³ + 4 (-5/2)² - 13 (-5/2) + 3 = -129/2
Can you help me please
Answer this please and thank you
Answer:
The Answer is x^2/2
Step-by-step explanation:
The ^ is the power of _
In this case ^ is the power of 2.
In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was
determined that 20% of all stock investors are retired people. In addition, 40% of all U.S. adults invest in mutual funds. Suppose a random sample of 25 stock investors is taken What is the probability that fewer than 4 are retired people
Answer:
a) 0.1108
(b) 0.0173
Step-by-step explanation:
We are given that 20% of all stock investors are retired people. A random sample of 25 stock investors is taken.
Firstly, the binomial probability is given by;
where, n = number of trails(samples) taken = 25
r = number of successes
p = probability of success and success in our question is % of
retired people i.e. 20%.
Let X = Number of people retired
(a) Probability that exactly seven are retired people = P(X = 7)
P(X = 7) =
= = 0.1108
(b) Probability that 10 or more are retired people = P(X >= 10)
P(X >= 10) = 1 - P(X <= 9)
Now, using binomial probability table, we find that P(X <= 9) is 0.98266 at n = 25, p = 0.2 and x= 9
So, P(X >= 10) = 1 - 0.98266 = 0.0173.
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 9 percent, has a YTM of 7 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7 percent, has a YTM of 9 percent, and also has 13 years to maturity. The bonds have a $1,000 par value.
What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years?
Answer:
Bond Xcurrent market price:
PV of face value = $1,000 / (1 + 3.5%)²⁶ = $
PV of coupon payments = $45 x 16.89035 (PV annuity factor, 3.5%, 26 periods) = $760.07
current market price = $408.84 + $760.07 = $1,168.91
price in 1 year:
PV of face value = $1,000 / (1 + 3.5%)²⁴ = $437.96
PV of coupon payments = $45 x 16.05837 (PV annuity factor, 3.5%, 24 periods) = $722.63
market price = $437.96 + $722.63 = $1,160.59
price in 3 years:
PV of face value = $1,000 / (1 + 3.5%)²⁰ = $502.57
PV of coupon payments = $45 x 14.2124 (PV annuity factor, 3.5%, 20 periods) = $639.56
market price = $502.57+ $639.56 = $1,142.13
price in 8 years:
PV of face value = $1,000 / (1 + 3.5%)¹⁰ = $708.92
PV of coupon payments = $45 x 8.31661 (PV annuity factor, 3.5%, 10 periods) = $374.25
market price = $708.92 + $374.25 = $1,083.17
price in 12 years:
PV of face value = $1,000 / (1 + 3.5%)² = $933.51
PV of coupon payments = $45 x 1.89969 (PV annuity factor, 3.5%, 2 periods) = $85.49
market price = $933.51 + $85.49 = $1,019
price in 13 years:
market price = $1,000 + $45 = $1,045
Bond Ycurrent market price:
PV of face value = $1,000 / (1 + 4.5%)²⁶ = $318.40
PV of coupon payments = $35 x 15.14661 (PV annuity factor, 4.5%, 26 periods) = $530.13
current market price = $318.40 + $530.13 = $847.53
price in 1 year:
PV of face value = $1,000 / (1 + 4.5%)²⁴ = $347.70
PV of coupon payments = $35 x 14.49548 (PV annuity factor, 4.5%, 24 periods) = $507.34
market price = $347.70 + $507.34 = $855.04
price in 3 years:
PV of face value = $1,000 / (1 + 4.5%)²⁰ = $414.64
PV of coupon payments = $35 x 13.00794 (PV annuity factor, 4.5%, 20 periods) = $455.28
market price = $414.64+ $455.28 = $869.92
price in 8 years:
PV of face value = $1,000 / (1 + 4.5%)¹⁰ = $643.93
PV of coupon payments = $35 x 7.91272 (PV annuity factor, 4.5%, 10 periods) = $276.95
market price = $643.93 + $276.95 = $920.88
price in 12 years:
PV of face value = $1,000 / (1 + 4.5%)² = $915.73
PV of coupon payments = $35 x 1.87267 (PV annuity factor, 4.5%, 2 periods) = $65.54
market price = $915.73 + $65.54 = $981.27
price in 13 years:
market price = $1,000 + $35 = $1,035
The base area of a right circular cone is 1/4 of its total surface area. What is the ratio of the radius
to the slant height?
Given:
The base area of a right circular cone is [tex]\dfrac{1}{4}[/tex] of its total surface area.
To find:
The ratio of the radius to the slant height.
Solution:
We know that,
Area of base of a right circular cone = [tex]\pi r^2[/tex]
Total surface area of a right circular cone = [tex]\pi rl+\pi r^2[/tex]
where, r is radius and l is slant height.
According to the question,
[tex]\pi r^2=\dfrac{1}{4}(\pi rl+\pi r^2)[/tex]
Multiply both sides by.
[tex]4\pi r^2=\pi rl+\pi r^2[/tex]
[tex]4\pi r^2-\pi r^2=\pi rl[/tex]
[tex]3\pi r^2=\pi rl[/tex]
Cancel out the common factors from both sides.
[tex]3r=l[/tex]
Now, ratio of the radius to the slant height is
[tex]\dfrac{r}{l}=\dfrac{r}{3r}[/tex]
[tex]\dfrac{r}{l}=\dfrac{1}{3}[/tex]
Therefore, the ratio of the radius to the slant height is 1:3.
What isthmus solution to the equation 2x+2=10
Answer:
addition
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
10-2=8
8/2=4
Hope this helps!
$75 dinner; 18% tip
Explained step by step pls
Answer: $13.50
Step-by-step explanation:
Answer:
$13.5
Step-by-step explanation:
Everything you do is multiply 75 by 0.18 ( 0.18 represents 18%)
which gives you 13.5, so the tip would be $13.50
If sqrt 16 = x, then x2 =
Answer:
The square root of 16=4, 4x2=8, x2=8.
Step-by-step explanation:
You are creating bracelets and then selling them to your friends at a 85% markup rate. If it costs you $1.80 to create the bracelet, how much of a markup will you add to the bracelet?
Answer:
you will add $1.53 to every bracelet you make
Step-by-step explanation:
figure out what 85 percent of 1.80 is and then add that to 1.80 for the total price
85% x 1.8 = 1.53 (markup ammount)
1.80 + 1.53 = 3.33 (total cost)
Plizzz helppp I don't know how to do it helpp
Answer:
Lol I'll help you. So for the 1st problem, you need to subtract 7x from 4x but if your looking for and answer then x=2. For the 2nd problem subtract 3x-5x and 7 + 9 which brings you to -2x - 16 which means you would have to find x in this problem which means x has to be a negative. The negative answer is x= -32 since a negative x a negative is a positive. Which brings you to 16-16 and then 0. For the third one, you need to change the problem. Turn it into 5x - x = 4 + 8 which brings you to 4x = 12 making x =3. and for number 4 you need do the same as we just did and do 11x - 6x - 3x and then do 20 - 6 which brings you to 2x = 14 which makes x=7.
Step-by-step explanation:
Question
An amount of $290,000 is borrowed for a period of 25 years at an interest rate of 4%. The amortization schedule for this
loan is below. Payments of $1,530.73 are made monthly.
Payment #
1
2
Payment Interest
1,530.73 966.67
1, 530.73964.79
1.530.73 962.90
Debt Payment
564.06
565.94
567.83
Balance
289, 435.94
288, 870.00
288, 302.17
3
4
X
5
Calculate x,the balance on the loan at the end of month 4. Give your answer to the nearest dollar. Do not include commas
or the dollar sign in your answer.
Provide your answer below:
The Answer is
$287732
I wish you all the best of luck
help needed please answer asap
34 full. He uses 16 of a full tank’s gas per day driving to and from work.
How many days can Drew drive to work with the gas he has in the tank?
How much smaller is x−3 than x+4?
Answer: bsf google
Step-by-step explanation: go to google look it up and find the answer
Answer:
x-3
Step-by-step explanation:
It's x-3 because if you put 12-3 it will be 9 but if you add x+4 it will be 16
The Sweet Shoppe sells a half-dozen cupcakes for $16.50. The Cupcake Factory sells a dozen cupcakes for $30.00. Jameska purchases two cupcakes from each shop. What is the difference in the purchases?
The difference in the purchases is $
.
Answer:
$1.50
Step-by-step explanation:
The cost of half of dozen of cupcakes at Sweet Shoppe = $16.50.
The cost of a dozen cupcakes at Cupcake factory = $30.00. Therefore the cost of half a dozen cupcakes at Cupcake factory = $30.00 / 2 = $15.00
The difference in purchases = cost of half a dozen cupcakes at Sweet Shoppe - cost of half of dozen of cupcakes at cupcake factory
The difference in purchases = $16.50 - $15.00 = $1.50
This means that their is a difference of $1.50 for half a dozen cupcakes between the Sweet Shoppe and cupcake factory.