This question is about exponential growth and the rabbit population on an island.
Explanation:The subject of this question is Mathematics. Specifically, it involves exponential growth and a function that represents the rabbit population on the island over time. Let's define the function f(x) to represent the population of rabbits at year x.
Based on the information given, the initial population is 20 rabbits. The population triples every year, which means that for each year x, the population is f(x) = 20 * 3^x.
For example, after 1 year, the population would be f(1) = 20 * 3^1 = 60 rabbits. After 2 years, the population would be f(2) = 20 * 3^2 = 180 rabbits, and so on.
Learn more about Exponential growthhttps://brainly.com/question/34350466
#SPJ2
Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of α if α < β. sin(2x − 8) = cos(6x − 6)
Answer:
The value of angle α is 18 degree.
Step-by-step explanation:
Given information: Angles α and β are the two acute angles , α < β.
Given equation is
[tex]\sin (2x-8)=\cos (6x-6)[/tex]
[tex]\cos (90-(2x-8))=\cos (6x-6)[/tex] [tex][\because \sin (90-x)=\cos x][/tex]
Equating both sides.
[tex]90-2x+8=6x-6[/tex]
[tex]98+6=6x+2x[/tex]
[tex]104=8x[/tex]
[tex]13=x[/tex]
The value of x is 13.
The measure of angles is
[tex]2x-8=2(13)-8=18[/tex]
[tex]6x-6=6(13)-6=72[/tex]
Since 18<72, therefore the value of angle α is 18 degree.
Answer:
A
Step-by-step explanation:
A 4-foot tall person standing with her back to the sun casts an 6-foot long shadow. To the nearest degree, what angle does the sun make with the ground?
width = (b - a)/n = (8 - 0)/4 = 2
2(f(0) + f(2) + f(4) + f(6))
2(-1 - 2.5 - 1.5 - 0.5)
2(-5.5)
-11
Is my answer C, -11? The question says four subintervals, so I used f(0), f(2), f(4), and f(6). I want to make sure that I am NOT supposed to be using f(8), because f(8) would give me a final answer of D. -13.5
The lenght of a rectangle is twice its width. The area of the rectangle is 18 square centimeters. Find the perimeter of the rectangle?
The figure below shows a shaded circular region inside a larger circle:
A shaded circle is shown inside another larger circle. The radius of the smaller circle is labeled as r and the radius of the larger circle is labeled as R. On the right side of the image is written r equal to 4 inches and below r equal to 4 inches is written R equal to 5 inches.
What is the probability that a point chosen inside the larger circle is not in the shaded region?
24%
36%
50%
64%
Points earned on this question: 0
Answer:
36%
Step-by-step explanation:
How do you find the lateral area of the prism
A rectangle measures 12cm by 7cm. What is its area
Jill recorded the average number of gallons of water that she used on her garden each day during different months. The chart below displays her records.
Month
Gallons Per Day
March
35
April
37
May
42
June
55
July
65
August
34
September
24
When does Jill’s chart show the greatest increase in the gallons used per day?
A.
May to June
B.
June to July
C.
July to August
D.
March to April
For one History test, John had to answer 45 questions, John answered 33 of them correctly. What percent did John get on his history test? Round your answer to the nearest tenth if necessary.
PLEASE SHOW WORK!!!
A barn is an atomic unit of area equal to 10–28 m2. what is the surface area of the earth expressed in units of barn? assume the earth is a sphere with a radius of km. (the surface area of a sphere is 4πr2.)
Determine whether the triangles are similar. If so, what is the similarity statement and the postulate or theorem used?
Answer:
DGH~DFE; SAS~
Step-by-step explanation:
A plane is flying at an altitude of 32,000 feet. The distance between the plane and a radio tower on the ground is 50,000 feet. What is the angle of depression between the plane and radio tower (round to 1 decimal place)?
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) + 3?
A.
It is the graph of f(x) translated 3 units up.
B.
It is the graph of f(x) translated 3 units to the right.
C.
It is the graph of f(x) where the slope is decreased by 3.
D.
It is the graph of f(x) translated 3 units down.
The statement correctly describes the graph of g(x) if g(x) = f(x) + 3, it is the graph of f(x) translated 3 units down. The correct option is D.
What is transformation of graph?When an existing graph is modified to produce a new variation of the existing graph.
Let y = f(x) then f(x)-3 means y-3. Subtracting 3 from the y coordinate of each point will move the entire curve down 3 units.
Thus, the correct option is D.
Learn more about transformation of graph
https://brainly.com/question/10059147
#SPJ2
what’s a transversal angle
Mark placed a pool in his backyard which is enclosed by a triangular fence the radius of the pool is 20.5 feet. How backyard is not covered by the pool
At a carnival, Brian bought 9 packs of 16 tickets each. He uses 39 tickets so far . how many tickets does he have left
The number of tickets left after using 39 tickets is 105.
What is multiplication?Multiplication is the process of adding a number up to a given number
Given that, there are 9 packs and there are 16 tickets in each pack.
Therefore, the total number of tickets is:
16 × 9
= 144
Now, the number of available tickets after using 39 tickets:
144 - 39
= 105
Hence, the number of tickets left after using 39 tickets is 105.
To learn more about multiplication, click here:
https://brainly.com/question/11527721
#SPJ5
1)
At 1 pm the shadow of a tree is 14 feet long. At the same time the shadow of a 18 foot telephone pole is 21 feet long. What is the height of the tree?
A) 9 feet
B) 12 feet
C) 18 feet
D) 22 feet
Find the first derivative?
y = 1/(x - 2) - 3
y' = d(x - 2)^-1 / dx The three is a constant and will disappear.
y' = d(x - 2)^-1 -1 d(x - 2)/dx
y' = -1*(x - 2)^-2 * 1
The minus comes from bringing down the original power down and reducing the power by one of the question. The 1 at the end comes from differentiating what is inside the brackets. It is called the chain rule
d(x - 2) / dx = d(x) / dx which is 1. The two, being a constant, disappears. The final answer is
y' = - (x - 2)^-2
Answer:
[tex]\displaystyle y' = \frac{-1}{(x - 2)^2}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{1}{x - 2} - 2[/tex]
Step 2: Differentiate
Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{1'(x - 2) - 1(x - 2)'}{(x - 2)^2}[/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle y' = \frac{-1(1)}{(x - 2)^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{-1}{(x - 2)^2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
AB is dilated by a scale factor of 3 to form A'B' . Point O, which lies on AB , is the center of dilation. The slope of AB is 3. The slope of A'B' is . through point O.
The slope will remain the same, So the slope of [tex]A'B'[/tex] will be [tex]3[/tex].
Step-by-step explanation:
Given: [tex]AB[/tex] is dilated by a scale factor of [tex]3[/tex] to form [tex]A'B'[/tex] . Point [tex]O[/tex], which lies on [tex]AB[/tex], is the center of dilation. The slope of [tex]AB[/tex] is [tex]3[/tex].
As mentioned in question:
Given that [tex]AB[/tex] has been dilated by scale factor [tex]3[/tex] to form [tex]A'B'[/tex].
So using laws of dilation, the image is congruent to the pre image.
This implies that the image will not change in any way whatsoever apart from the size.
Hence, the slope will remain the same, So the slope of [tex]A'B'[/tex] will be [tex]3[/tex].
Learn more about laws of dilation here: https://brainly.com/question/15868300?referrer=searchResults
PLEASEEE PLEASSE HELP!! BRANLIEST!!!PLEASEEE
Triangle XYZ is formed by the three squares J, K, and L:
Which statement best explains the relationship between the sides of triangle XYZ?
XY + YZ = ZX, because 144 + 256 = 400
(XY)2 + (YZ)2 = (ZX)2, because 144 + 256 = 400
(XY)2 + (YZ)2 = (ZX)2, because 202 + 122 = 162
XY + YZ = ZX, because 202 + 122 = 162
Triangle XYZ is formed by the three squares J, K, and L
So it is a right triangle.
Pythagorean Theorem: a^2 + b^2 = c^2
Answer:
(XY)^2 + (YZ)^2 = (ZX)^2, because 144 + 256 = 400
ank’s teacher asked him to verify that the product (y – 3)(y2 + 3y + 9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3 + 3y2 + ay – 3y2 – ay – 27. What is the value of a in the polynomial?
A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Roun
When a parabola represented by the equation y - 2x 2 = 8 x + 5 is translated 3 units to the left and 2 units up, the new parabola has its vertex at
Using 125 words or more, write a short paragraph discussing the reasons why someone should make a wil
A will tells everyone what will happen to your money, possessions, and property when you die. There are many reasons to make a will. First, it will be easier for your family and friends to sort everything out. Without a will, it can be very stressful and time consuming to figure out how to allocate everything. Plus, if you don't have a will the law will decide how to allocate it and this might not be the way you want it. It can be especially important to write a will if you have children or other family that depend on you financially. This way, you can leave them the most possible to help them even when you are no longer alive. By writing a will, you can decrease the amount of inheritance tax that might need to be paid on any property and money that you will leave behind. Ultimately, by writing a will you will be able to decide who you leave your money, possessions, and property to when you die which can be very important to some individuals.
Ill Mark Brainliest if you answer correctly. The figure below shows a shaded circular region inside a larger circle:
A shaded circle is shown inside another larger circle. The radius of the smaller circle is labeled as r and the radius of the larger circle is labeled as R. On the right side of the image is written r equal to 4 inches and below r equal to 4 inches is written R equal to 5 inches.
What is the probability that a point chosen inside the larger circle is not in the shaded region?
24%
36%
50%
64%
First we have to find the areas of both circle using the formula
[tex] Area = \pi r^2 [/tex]
For larger circle,
[tex] Area= \pi(5)^2 = 25 \pi [/tex]
For smaller circle,
[tex] Area = \pi (4)^2 = 16 \pi [/tex]
Required probability
[tex] = \frac{25 \pi -16 \pi}{25 \pi} *100 = \frac{9}{25}*100 = 36% [/tex]
Correct option is the second option .
Answer:
the other person is correct
Step-by-step explanation:
give them brainliest
find the probability that a student chosen at random plays football or cricket or both
4. Find the diameter of the circle for BC = 10 and DC = 23. Round to the nearest tenth. The diagram is not drawn to scale. (1 point) 62.9 52.9 7.7 42.9
An electrician can wire a house in 20 hours. if she works with an apprentice, the same job can be completed in 12 hours. how long would it take the apprentice, working alone, to wire the house?
It would take the apprentice 30 hours to wire the house alone.
Explanation:Let's assume that the work done by the electrician alone in 1 hour is represented by E, and the work done by the apprentice alone in 1 hour is represented by A. According to the given information, the electrician can wire the house in 20 hours, so E = 1/20. When the electrician and the apprentice work together, they can wire the house in 12 hours, so their combined work in 1 hour is represented by (E + A) = 1/12.
To find out how long it would take the apprentice to wire the house alone, we can subtract the work done by the electrician in 1 hour (E) from the combined work done by both the electrician and the apprentice in 1 hour (E + A), which gives us A = (E + A) - E. Substitute the values:
A = (1/12) - (1/20) = (20 - 12) / (12 x 20) = 8 / 240 = 1/30.
So, the apprentice can wire the house alone in 30 hours.
A class's test scores are normally distributed. If the average score is 60 and the standard deviation is 7, choose the spots where the students scoring below 46 and above 74 lie.
Answer with Step-by-step explanation:
We are given that a class's test scores are normally distributed with the average score 60.
We know that the curve of a normal distribution is symmetric about its mean.
60-14=46
60+14=74
Hence, the point 46 lies to the left of the mean and 74 lies to the right of mean and the two points have the same function value
(since the graph is symmetric to the left and right of mean i.e. points which are equidistant from the mean have same values)
Answer:
One of the answers I got that was correct was the box on the furthest left.
Step-by-step explanation:
HELP IM GIVING 20 POINTS AND BRAINLY
What is the correlation coefficient r for the data set?
Enter your answer to the nearest hundredth in the box.
r =
x y
25 240
26 242
27 230
28 229
28 220
28 219
29 200
30 202
31 184
32 180
we know that
using a excel tool
see the attached table
the correlation coefficient r for the data set is
r=-0.96
the answer is
-0.96