Answers
Answer:
a) 82.
b) So a growth factor of 0.025
c) 2.5%.
d) f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.
Step-by-step explanation:
Exponential equation of population growth:
The exponential equation for population growth has the following format:
[tex]f(x) = x(0)(1+r)^x[/tex]
In which x(0) is the initial value and r is the growth factor, as a decimal.
In this question:
In x years after 2021:
[tex]f(x) = 82(1.025)^x[/tex]
a)
This is f(0). So
[tex]f(0) = 82(1.025)^0 = 82[/tex]
So 82.
b)
We have to find r. So
[tex]1 + r = 1.025[/tex]
[tex]r = 1.025 - 1 = 0.025[/tex]
So a growth factor of 0.025.
c)
Growth factor multiplied by 100%.
So 0.025*100% = 2.5%.
d)
f(5) = population in 5 years after January 1st 2021, that is, January 1st 2026.
[tex]f(5) = 82(1.025)^5 = 93[/tex]
f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.
Related Questions
suppose 3 years ago Rose was 24 years older than her daughter at present Rose is 5 times as old as her daughter how old will be the daughter in three years time
Answers
Answer:
Let Rose be R
Let her daughter be D
"3" yrs ago.
Subtract 3 from their ages
Rose was then (R-3) yrs old.
Daughter ..........(D-3)yrs old
So 3yrs ago.... Rose was 24yrs older than D.
Meaning
R=24+D
Which 3yrs ago can be expressed as
(R-3)=24+(D-3)
R - 3 = 24 + D - 3
R - D=24-3 + 3
R-D=24--------1
Now
At present.
R is 5times as old as Daughter
Meaning R = 5D-------2
Substituting into eqn 1
R-D=24
5D-D=24
4D=24
D=6yrs
Substitute D=6 into any equation of choice to get R
R-D=24
R=24+D
R=24+6
R=30yrs
Now we have Roses's age to be 30yrs and Daughter's age to be 6yrs.
We're asked to find the daughter's age in 3yrs time...
Meaning ....D+3
=6+3 = 9yrs
DAUGHTER WOULD BE 9YRS OLD IN 3YRS TIME.
prove that (Cos A +cosB)^2+(SinA+sinB)^2=4cos^2(A-B/2)
Answers
Answer:
[tex](cosA + cos B)^2 + (sin A +sinB)^2 \\\\= cos^2A + cos^2B + 2cosA cosB + sin^2A +Sin^2B +2sinAsinB\\\\=(cos^2A + sin^2 A) + (cos^2B +sin^2B) +2cosAcosB + 2sinAsinB\\\\= 1 + 1 + 2cosAcosB + 2sinAsinB\\\\=2 + cos(A+B)+cos(A-B) + cos(A-B) -cos(A+B)\\\\=2 + 2cos(A-B)\\\\=2(1 + cos(A-B))\\\\=2\times 2 cos^2(\frac{A-B}{2})\\\\=4cos^2(\frac{A-B}{2})[/tex]
Hence proved .
Can somebody help me with this
Answers
Answer:
0.04997916927
Step-by-step explanation:
Answer:
30 degrees
Step-by-step explanation:
arcsin(0.5) deg
= 30
Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. They randomly survey 387 drivers and find that 298 claim to always buckle up. Construct a 84% confidence interval for the population proportion that claim to always buckle up.
Answers
Answer:
The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
They randomly survey 387 drivers and find that 298 claim to always buckle up.
This means that [tex]n = 387, \pi = \frac{298}{387} = 0.77[/tex]
84% confidence level
So [tex]\alpha = 0.16[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.16}{2} = 0.92[/tex], so [tex]Z = 1.405[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.74[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.8[/tex]
The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).
rearrage and solve 4t-s-2t+25
Answers
Answer:
See the image below for the answer:)
Step-by-step explanation:
Question 20
Josh says that has the same quotient as Is this true or false?
O True
O False
Answers
Lin and Claire each threw a rock into a stream. The black graph represents the height of a stone t seconds after it was tossed up by Lin and the purple graph represents the height of a stone t seconds after it was tossed up by Claire.
1) Whose stone hit the water second, and at what time?
2) How long did it take for Claire's rock to reach its maximum? What is the maximum height?
3) Who had the higher initial height? What was it?
Answers
Answer:
1) claire's stone at 1.25 seconds
2) 0.5 seconds and its max height was 9
3) lin at 8ft
Step-by-step explanation:
the intercepts tell you the first and third question and then the max height is the highest point on the graph
not sure what measurements you were supposed to use so I used seconds and feet and if that's not it then it's the same numbers just different words
Can someone explain to me the Laws of Sine and Cosine. Will mark brainliest.
Answers
Answer:
here you are
i hope it helps! :)
Step-by-step explanation:
What is the M.A.D. of this data set? 3,6,6,7,8,11,15,16
Answers
the answer is 8 because it was in the middle
it's 8
The spread of a rumor in a town can be modeled as , where N is the number of people who have heard of the rumor, and t is time (in days). How long will it take until 2000 people know about the rumor?
Answers
Answer:
the time is 16 days
Step-by-step explanation:
The computation of the time period is given below:
N = 500 √t
2000 = 500 √t
√t = 4
Now do the square on both the sides
SO,
t = 16
Hence, the time is 16 days
We simply applied the above method to determine the time period
Determine how many people will fit in a building with a width of 105 feet and a length of 250 feet, if we use a standard of 16 people per 25 square feet.
Answers
Answer:
16,800 people
Step-by-step explanation:
105 * 250 = 26,250
p = 26250ft² * (16 people / 25ft²)
p = 16,800 people
Answer:
16800
Step-by-step explanation:
105 x 250 = 26250 and then divide it by 25 which is 1050 then multiply by 16 which is 16800
Hope this helps!
PLS HELP ASAP! WILL GIVE U BRAINLIEST
Valid or Invalid: If a number is even, then it is a multiple of 4.
A. Invalid
B. Valid
Answers
Answer:
valid
Step-by-step explanation:
it's valid because for example here are some even numbers, 0, 2, 4, 6, 8, they're are all multiples of four.
hope that helped :)
mark me brainliest pls
The diameter of a circle is 2 meters. What is the circles circumftance
Answers
Answer:
2π or 6.284 meters
Step-by-step explanation:
Circumference = πd
= 2π
Solve the following equation for x: 6( 4X +5) = 3( X +8) +3
Answers
Answer:
x= -1/7
Step-by-step explanation:
Order from least to greatest
1/8, 11/12, 9/8
Answers
Answer:
Step-by-step explanation:
First make the denominators the same.
Take the LCM of (8, 12 , 8) = 24
So,
[tex]\frac{1}{8}, \frac{11}{12}, \frac{9}{8} \ becomes \ \frac{3}{24}, \frac{22}{24}, \frac{27}{24}[/tex]
[tex]Order \ from \ least \ to \ greatest \ \\\\\frac{3}{24} < \frac{22}{24} < \frac{27}{24}[/tex]
That is,
[tex]\frac{1}{8}, \frac{11}{12}, \frac{9}{8}[/tex]
Helpppppppp me plzzzzzzz
Answers
Answer:
Length of Line AC = 26 units
Step-by-step explanation:
Given:
Line AC = [3x + 1] + 8
Line BC = [x - 2] + 2
Find:
Length of Line AC
Computation:
Line AB ║ Line L
So,
Using Mid-Point theorem;
[3x + 1] / 8 = [x - 2] / 2
2[3x + 1] = 8[x - 2]
6x + 2 = 8x - 16
8x - 6x = 16 + 2
2x = 18
x = 9
So,
Line AC = [3x + 1] + 8
Line AC = [3(9) + 1] + 8
Line AC = [27 + 1] + 8
Line AC = 28 + 8
Length of Line AC = 26 units
You start at (2, -1). You move down 3 units and left 3 units. Where do you end?
Answers
Answer:
(-1,-4)
Step-by-step explanation:
(2, -1)
Moving down 3 means subtract 3 from the y value
Left 3 means subtract 3 from the x value
(2-3, -1-3)
(-1,-4)
A die is rolled 2 times. What is the probability of getting a 2 on the first roll and a 5 on the second roll?
Answers
Answer:
1/36
Step-by-step explanation:
the chance of rolling a 2 on a 6-sided die is 1/6 and rolling a 5 on a 6-sided is also 1/6.
So, 1/6 * 1/6 = 1/36
Hope this is helpful
Answer:
Step-by-step explanation:
six sided die gives you 6 possibilities
probability of rolling a 2 is 1/6
probability of rolling a 5 on the second roll is 1/6
What is the fraction of 100 and 3,000
Answers
[tex]\huge \bf{Question:-}[/tex]
What is the fraction of 100 and 3,000.
[tex]\huge\bf{Answer:-}[/tex]
[tex] \bf{ \frac{100}{3000} } \: simplified \: to \: lowest \: term \: is : - [/tex]
[tex] \bf \pink{ \frac{1}{30}} [/tex]
=1/30
=0.0333333333
Find the slope on the line?
Answers
Answer:
slope=0
Step-by-step explanation:
Hi there!
We're given a graph with a line and two marked points on the graph: (-1,3) and (3,3)
the formula given for slope calculated from two points is (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are points
we have our two points: (-1,3) and (3,3) and we can label them:
x1=-1
y1=3
x2=3
y2=3
now substitute into the formula
note: Remember the formula shows SUBTRACTION, even though we have NEGATIVE numbers. When we simplify, we'll add the numbers.
slope=(3-3)/(3--1)
simplify
slope=0/4
divide
slope=0
Hope this helps!
(t+5)(t+2),make t the subject of the formula
Answers
Answer:
t= 2p+5/p-1
Step-by-step explanation:
The question is not well writen
Assume p = t+5/t-2
We are to make t the subject of the formula
Cross multiply
p(t-2) = t+5
pt - 2p = t+5
pt - t = 2p+5
t(p-1) = 2p+5
t= 2p+5/p-1
Hence the value of t is 2p+5/p-1
WORTH 20 POINTS
Use the volume formula to find the volume of the prism.
A. 9 cubic units O
B. 18 cubic units
C. 4 cubic units O
D. 7 cubic units
Answers
9514 1404 393
Answer:
A. 9 cubic units
Step-by-step explanation:
We interpret the smudges in your attachment to be dimensions of 1 1/2, 4, and 1 1/2. The volume is the product of these.
V = LWH
V = (4)(1.5)(1.5) = 9 . . . . cubic units
The volume of the prism is 9 cubic units.
What is m∠A?
Help plz
Answers
Answer:
66
Step-by-step explanation:
180 - 57-57
Can someone please help?
Answers
divide k800. in the ratio of 5:3
Answers
Answer:
k500: k300
Step-by-step explanation:
5 parts :3 parts
there are 5+3=8 parts in total
800 divide by 8 parts = 100 in each part
k800 is 5:3 is k500: k300
6x-5
Step-by-step explanation:
4/5÷4/10
12×2 -64×-11,×+1
×3-×2+7×
___________
6x-5 answer
If the above cube is a container with an inside length of 25cm, how many
3.3.3
litres will it hold?
Answers
Answer:
Capacity of cube in liter = 15.625 liter
Step-by-step explanation:
Given:
Side of cube = 25 cm
Find:
Capacity of cube in liter
Computation:
Volume of cube = Side³
Volume of cube = 25³
Volume of cube = 15,625 cm³
We know that
1 cm³ = 0.001 liter
Capacity of cube in liter = Volume of cube in cubic cm x 0.001
So,
Capacity of cube in liter = 15,625 x 0.001
Capacity of cube in liter = 15.625 liter
Oscar bought 12 lunches for 30$ what was the unit cost
Answers
$30 / 12 = 2.5
10 points will give brainliest
Answers
Answer:
A. 9/2 × 3/8
Step-by-step explanation:
______________
hope this helps
How does the distance traveled and time elapsed compare for Carrie and Kevin as they traveled from mile marker 225 to mile marker 230?
Answers
Answer:
This implies that they traveled the same distance and they spend the same amount of time from 225 to 230 mile marker
Step-by-step explanation:
Given
See attachment for graph
Required
Compare the distance and time travel
From the attached graph, we have the origin to be (0,0).
This represents the mile marker 225
Mile marker 230 is represented by point 5 on the y-axis.
Kevin's line at point 5 is represented as: (16,5)
Carrie's curve at point 5 is represented as: (16,5)
Both points are equal; i.e.
[tex](16,5) =(16,5)[/tex]
This implies that they traveled the same distance and they spend the same amount of time from 225 to 230 mile marker
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
5t+t–2t
Answers
Answer:
4t
Step-by-step explanation:
Note that teach term has the variable t in it. Also, note that if t is by itself, it actually means 1t. Combine the given constants:
5t + 1t - 2t
= (5t + 1t) - 2t
= (6t) - 2t
= 4t
4t is your answer.
~