Answer:
3,240
Step-by-step explanation:
The computation of the population of rabbits in the year 2003 is shown below:
Given that
In the year 1995, the population of the rabbits was 1000
And, in 1999 the population of the rabbits grown to 1,800
So there is an increase of
= (1800 - 1000) ÷ 1000
= 80%
So for 2003, the population of the rabbits is
= 1800 + (1800 × 0.80)
= 3,240
Given:
The population of rabbits on an island is growing exponentially.
In the year 1995, the population of rabbits was 1000, and by 1999 the population had grown to 1800.
To find:
Expected population of rabbits in the year 2003, to the nearest whole number.
Solution:
The exponential growth model is:
[tex]y=ab^t[/tex]
Where, a is the initial value, b is the growth factor, t is the number of years.
Let y be the population of rabbits t years after 1995.
In the year 1995, the population of rabbits was 1000, it can be written as (0,1000) and by 1999 the population had grown to 1800, it can be written as (4,1800).
For (0,1000),
[tex]1000=ab^0[/tex]
[tex]1000=a(1)[/tex]
[tex]1000=a[/tex]
For (4,1800) and a=1000, we get
[tex]1800=1000b^4[/tex]
[tex]\dfrac{1800}{1000}=b^4[/tex]
[tex]1.8=b^4[/tex]
[tex](1.8)^{\frac{1}{4}}=b[/tex]
[tex]b\approx 1.1583[/tex]
The required exponential model is:
[tex]y=1000(1.1583)^t[/tex] ...(i)
in year 2003, the number of years since 1995 is 8.
Putting t=8 in (i), we get
[tex]y=1000(1.1583)^8[/tex]
[tex]y=3240.1748[/tex]
[tex]y\approx 3240[/tex]
Therefore, the population of rabbits in the year 2003 is 3240.
The weights in pounds of five cats are 12, 14, 12, 16, and 16. Find the mean, median, mode, and range of the data set.
Answer:
Mean: 14
Median: 14
Mode: 12, 16
Good luck!
When calculating the discriminant if your answer was 16, what does that say about your roots?
Answer:
Your roots are equal to 16
What is the equation of the midline of the graph of y=2cos(x/4)−3
Answer:
y = -3
Step-by-step explanation:
y=2cos(x/4)−3
range of cos α : -1 ≤ cos α ≤ 1
-2 ≤ 2cos(x/4) ≤ 2
-5 ≤ 2cos(x/4)−3 ≤ -1 (-2-3= -5 and 2-3= -1) ....Range ( 2 x Amplitude)
midline: midline of y = -1 and y = -5 y = -3
1.What is the principal which would amount to $6 900 in 3 years at 5% simple interest per annum?Required to answer. Single choice.
(1 Point)
a.) $6 885
b.) $6 555
c.) $6 000
d.) $5 865
Answer:
c
Step-by-step explanation:
I just looked up the question
The answer choices are 11 1 2.48 6
Answer:
The ball reached its maximum height of ([tex]11\ yards[/tex]) in ([tex]1\ second[/tex]).
Step-by-step explanation:
This question is essentially asking one to find the vertex of the parabola formed by the given equation. One could plot the equation, but it would be far more efficient to complete the square. Completing the square of an equation is a process by which a person converts the equation of a parabola from standard form to vertex form.
The first step in completing the square is to group the quadratic and linear term:
[tex]h(t)=-5t^2 + 10t + 6\\\\h(t) = (-5t^2 + 10t) + 6[/tex]
Now factor out the coefficient of the quadratic term:
[tex]h(t)=-5(t^2 -2t) + 6[/tex]
After doing so, add a constant such that the terms inside the parenthesis form a perfect square, don't forget to balance the equation by adding the inverse of the added constant term:
[tex]h(t) = -5(t^2 -2t) + 6\\\\h(t) = -5(t^2 -2t + 1 -1 ) + 6[/tex]
Now take the balancing term out of the parenthesis:
[tex]\\\\h(t)=-5(t^2 -2t + 1) + 6 + ((-1)(-5))[/tex]
Simplify:
[tex]h(t) = -5(t^2 -2t + 1) + 6 + 5\\\\h(t) = -5(t-1)^2 + 11[/tex]
The x-coordinate of the vertex of the parabola is equal to the additive inverse of the numerical part of the quadratic term. The y-coordinate of the vertex is the constant term outside of the parenthesis. Thus, the vertex of the parabola is:
[tex](1, 11)[/tex]
help me pleaseeeeeeeeee
Answer:
The diameter is related because it helps find the circumference.
PLEASE HELP!
Hello! I'm having a lot of trouble figuring out these problems. I'm not asking for all of the answers but, just a better understanding. Thank you!
Answer:
1) 4
2)I think 2
3)4
4)3
5)2
6)1
7)3
Step-by-step explanation:
1) since the x is to squared it is a quadratic equation
3) A and D have same slope=0.5
others were solved using Excel
what is x? plz help :)
Answer:
13
Step-by-step explanation:
using the Pythagorean theorem a²+b²=c²
or the two shorter sides square added together equal the longest side squared
5²+12²
5²=25
12²=144
144+25=169
then we just have to take the square root of 169
√169=12
have a great day :D
7/8 ÷ 7/16 = Reduce your answer to the lowest terms.
HELP PLS!!
If the sequence 4, 8, 12, 16 continues, what will be the 7th
term?
Answer:
28
Step-by-step explanation:
In order to find the seventh term in this arithmetic function, you need to find its function; in order to do this, you must first identify the common difference by finding the difference between two consecutive terms:
16 - 12 = 4; the common difference is 4
Now, you need to find the 0th term, which is the 1st term minus the common difference:
4 - 4 = 0
At this point, you can write out the function (where f(n) = [0th term] + [common difference]n:
f(n) = 4n
Finally, you can plug 7 into this function:
f(n) = 4(7)
f(n) = 28, so the 7th term is 28
Paul wants to visit his aunt who lives 300 miles away from his house. He drives his car at about 50 miles an hour. If X represents the time spent driving and why represents the distance from his aunts house which scatterplot could represent the situation
Answer:
It would take 6 hours.
An equation for that could be: 50x = 300 (X is how long it would take)
So 50 mph• X (time spent) = 300 miles
You didn't give me any scatterplots to look at so I can't help you with that sorry
Find the missing sides of each triangle. Leave your answers in radical form
Answer:
youbhave give me more information.
Answer:
incomplete question
please write the whole question or diagram of the question
What factor is represented by the yellow shading in the model? [Hint: Include the overlapping area.]
Answer:
[tex]Fracton = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
See attachment
Required
The fraction of yellow
From the attached image:
[tex]Yellow = 5[/tex]
[tex]Total = 30[/tex]
So, the fraction is:
[tex]Fracton = \frac{Yellow}{Total}[/tex]
[tex]Fracton = \frac{5}{30}[/tex]
Divide by 5/5
[tex]Fracton = \frac{1}{6}[/tex]
Answer: 4/5
Step-by-step explanation:
Which of these statements is true? Sin 18° = cos 72°, sin 55° = cos 55°, sing 72° = cos 18°c both a and c
Answer:
Sin 18° = cos 72° and sin 72° = cos 18°
Step-by-step explanation:
According to trigonometry identity;
sin Ф = cos(90 - Ф)
for Sin 18° = cos 72
Ф = 18°
Substitute into the expression
sin Ф = cos(90 - Ф)
sin 18 = cos(90 - 18)
Sin 18 = cos 72
Hence the statement id true
For sin 72° = cos 18
Ф = 72°
Substitute into the expression
sin Ф = cos(90 - Ф)
sin 72 = cos(90 - 72)
Sin 72 = cos 18
Hence this statement too is correct
The two correct statements are Sin 18° = cos 72° and sin 72° = cos 18°
(8.64 × 10^6) × (1.334 × 10^10)
Answer:
8.64x1.334x10^16
11.52576x10^16
simplify (2x+1)(x+8) - (x-3)(2x+1)
Answer:
22x+11 is your answer
Step-by-step explanation:
(2x+1)(x+8) - (x-3)(2x+1)
(2x+1)(x+8-x+3)
(2x+1)(11)
=22x+11
4x−4<8 AND9x+5>23 thank u for your help
Answer:
x < 3 AND x > 2
Step-by-step explanation:
4x − 4 < 8
4x < 8 + 4
4x < 12
x < 3
9x + 5 > 23
9x > 23 - 5
9x > 18
x > 2
PLEASE HELP FAST !!
3/2+19/3
Answer:
28/6 yeah thats right wasp
Answer:
Step-by-step explanation:
Is 17/34 and 32/64 proportional why or why not?
Answer:
Yes
Step-by-step explanation:
Both equals to 1/2
That's the answer
Please help I’m struggling
Karley added 14 bottle caps to her collection. She
now has 54 boule caps. Write and solve an equation to
find the number of bottle caps she originally had.
PLEASE ANSWER !!
Answer:
54 - 14 = 30
Step-by-step explanation:
10 minutes to answer
Write an expression equivalent to
4 - (-7)
help
What is the area of a triangle that has a height of 6 ft and a base length of 7 feet?
Answer: 21ft
Step-by-step explanation:
Answer:
the area of triangle is height ×base
6×7=42
i think this is the answer
1. Given the tax table below, write a piecewise function to represent the situation. Let x equal the taxable income and T) equal the income tax. Sample Income Tax Table Tax rate Taxable income reported Over Not over 15% $0 $32,450 28% $32,450 $78,400 33% $78,400 $155,800 38% $155,800
A silk worm grows twice asd long as it was the day before .If the worm measures v40 mm on the 10 th day, on which day was it 2.5 mm long
Answer:
On the sixth day (10 - 4), the worm was 2.5mm long.
Step-by-step explanation:
Giving the following information:
Future Value= 40mm
Present Value= 2.5mm
Number of periods (n)= ?
Growth rate= 100% per day
First, we need to calculate the number of days it will take to grow from 2.5mm (PV) to 40mm (FV):
n= ln(FV/PV) / ln(1+i)
n= ln (40 / 2.5) / ln (2)
n= 4
It will take 4 days.
On the sixth day (10 - 4), the worm was 2.5mm long.
Answer this question to get marked as brainliest!!!!!
Answer:
A) 80 degrees
Step-by-step explanation:
100-20=80
1
The rate of population decline of Seaside
Harbor is modeled by the equation
-0.00810
P(t)=15000e
where t is the time
in years and 15,000 is the current
population. In approximately how many
years will the population of Seaside
Harbor be 9,000?
(−0.0081p)(t)=(15000)(2.718282)
Step 1: Divide both sides by -0.0081t.
−0.0081pt
−0.0081t
=
40774.227427
−0.0081t
p=
−40774.227427
0.0081t
Answer:
p=
−40774.227427
0.0081t
Write the equation(y=mx) for the line that contains the points (6,6) and (10,14). No picture
Answer:
y = 2x - 6
Step-by-step explanation:
14-6/10-6 = 8/4 = 2 = slope
6 = 2(6) + b
6 = 12 + b
b = -6
Engineers are designing a rollercoaster that at one point goes underground. The rollercoaster’s path underground is a large curve. The engineers use the function shown to model the elevation, ܧ ,in feet and ݐ , time, in seconds, of the rollercoaster’s path while it is underground.
Answer:
One way to solve the quadratic equation x2 = 9 is to subtract 9 from both sides to get one side equal to 0: x2 – 9 = 0. The expression on the left can be factored:
(x + 3)(x – 3) = 0. Using the zero factor property, you know this means x + 3 = 0 or x – 3 = 0, so x = −3 or 3
Step-by-step explanation:
One way to solve the quadratic equation x2 = 9 is to subtract 9 from both sides to get one side equal to 0: x2 – 9 = 0. The expression on the left can be factored:
(x + 3)(x – 3) = 0. Using the zero factor property, you know this means x + 3 = 0 or x – 3 = 0, so x = −3 or 3
What is the formula for total surface area of
cylinders?
Thanks in advance
Answer:
For a cylinder there is 2 kinds of formulas the lateral and the total. the lateral surface area is just the sides the formula for that is 2(pi)radius(height). the formula for the total surface area is 2(pi)radius(height) + 2(pi)radius squared.
Step-by-step explanation: