lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish in a certain bay after the first year.
Part A: Write the explicit equation for f (n) that represents the number of lionfish in the bay after n years. Show all necessary math work.
Part B: How many lionfish will be in the bay after 6 years? Round to the nearest whole number and show all necessary math work.
Part C: If scientists remove 1,200 fish per year from the bay after the first year, what is the recursive equation for f (n)? Show all necessary math work.
Answer:
There would be 173,535 lionfish after 6 years.
Step-by-step explanation:
Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:
A)
8000 x 1.67 ^ n = f
B)
8000 x 1.67 ^ 6 = X
8000 x 21.691961596369 = X
173,535.692770952 = X
C)
(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f
Therefore, there would be 173,535 lionfish after 6 years.
12. Find all x- and y-intercepts, state the multiplicity of each zero and tell if the graph crosses or
bounces, and state the end behavior Then graph each polynomial by hand,
P(x)=x^2(x-3)^2(x+2)
P(x)=x^4-4x^2
Step-by-step explanation:
12a. To
find x intercepts, set each factor equal to zero
[tex] {x}^{2} = 0[/tex]
[tex]x = 0[/tex]
[tex](x - 3) {}^{2} = 0[/tex]
[tex]x = 3[/tex]
[tex]x + 2 = 0[/tex]
[tex]x = - 2[/tex]
So the x intercepts are( 0,-2,3.)
The multiplicity of 0 and 3 is 2,
The multiplicity of -2 is 1.
The y intercepts are
[tex]0 {}^{2} (0 - 3) {}^{2} (0 + 2) = 0[/tex]
The y intercept is 0.
End Behavior: Since this is a positve 5th root function, as x increases, f(x) increases while as x decreases, f(x) decreases.
The First picture shows the graph of the function. Notice ried the zeroes that have a multiplicity of 2 have a parabolic reflection after thre function reaches their zero.
The zero that have a multiplicity of 1 have just passes through the graph.
12b. We have
[tex] {x}^{4} - 4 {x}^{2} [/tex]
We can easily find y intercept, which is 0.
To find x intercept,
Factor
[tex] {x}^{2} ( {x}^{2} - 4)[/tex]
[tex] {x}^{2} (x + 2)(x - 2) = 0[/tex]
[tex]x = 0[/tex]
[tex]x = 2[/tex]
[tex]x = - 2[/tex]
So the x intercepts are (0,2,-2).
The multiplicity of 0 is 2 while 2 and -2 is 1.
End Behavior: Since this is a positve quartic function, as x increases or decreases , f(x) increases
Look at the second graph,
Answer:
[tex]P(x)=x^2(x-3)^2(x+2)[/tex]
y-intercept is when x = 0:
[tex]\implies P(0)=0^2(0-3)^2(0+2)=0[/tex]
Therefore, y-intercept is at (0, 0)
x-intercept(s) is when P(x) = 0
[tex]\implies x^2(x-3)^2(x+2)=0[/tex]
[tex]\implies x^2=0\implies x=0[/tex]
[tex]\implies (x-3)^2=0\implies x=3[/tex]
[tex]\implies (x+2)=0\implies x=-2[/tex]
Therefore, x-intercepts are:
(0, 0) with multiplicity 2 → bounces(3, 0) with multiplicity 2 → bounces(-2, 0) with multiplicity 1 → crosses x-axisEnd-behavior:
As the lead coefficient is positive and the lead degree is odd,
[tex]P(x) \rightarrow - \infty \textsf{ as }x\rightarrow - \infty[/tex]
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow +\infty[/tex]
-------------------------------------------------------------------------------
[tex]P(x)=x^4-4x^2[/tex]
y-intercept is when x = 0:
[tex]\implies P(0)=(0)^4-4(0)^2=0[/tex]
Therefore, y-intercept is at (0, 0)
x-intercept(s) is when P(x) = 0
[tex]\implies x^4-4x^2=0[/tex]
[tex]\implies x^2(x^2-4)=0[/tex]
[tex]\implies x^2(x-2)(x+2)=0[/tex]
[tex]\implies x^2=0 \implies x=0[/tex]
[tex]\implies (x-2)=0 \implies x=2[/tex]
[tex]\implies (x+2)=0 \implies x=-2[/tex]
Therefore, x-intercepts are:
(0, 0) with multiplicity 1 → crosses x-axis(2, 0) with multiplicity 1 → crosses x-axis(-2, 0) with multiplicity 1 → crosses x-axisEnd-behavior:
As the lead coefficient is positive and the lead degree is even,
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow - \infty[/tex]
[tex]P(x) \rightarrow + \infty \textsf{ as }x\rightarrow +\infty[/tex]
student stands at the edge of a diving board that is 3m high. The student's weight is 350N. What is the student's gravitational potential energy?
Answer:
1050 J
Step-by-step explanation:
GPE = Weight x height
= 350 x 3
= 1050 J
Help me and show work because I don't understand this one
Step-by-step explanation:
[tex]4 {}^{2x + 3} = 1[/tex]
In order for exponents to be equal, they must have the same base and same power.
So what exponet can we raise 4 to in order to get 1.
Remeber that
[tex]a {}^{0} = 1[/tex]
so
[tex]4 {}^{0} = 1[/tex]
,So we finally have
[tex]4 {}^{2x + 3} = 4^{0} [/tex]
Set the exponents equal to each other
[tex]2x + 3 = 0[/tex]
[tex]2x = - 3[/tex]
[tex]x = - \frac{3}{2} [/tex]
What is the equation of the line in slope-intercept form?
Answer:
y=4/3x+4
Step-by-step explanation:
solve by completing the square:
x^2+3x-70=0 (Answer: -10, 7)
x^2=-10x-30 (Answer: { })
help and with explanation; will give brainliest
Answer:
Step-by-step explanation:
x² + 3x - 70 = 0
x² + 3x = 70
x² + 3x + (3/2)² = 70 + (3/2)²
(x + 3/2)² = 70 + 9/4 = 289/4 = (17/2)²
so
x + 3/2 = ±17/2
x = ±17/2 - 3/2
x₁ = 17/2 - 3/2 = 14/2 = 7
x₂ = -17/2 - 3/2 = -20/2 = -10
x² = -10x - 30
x² + 10x = -30
x² + 10x + (10/2)² = -30 + (10/2)²
x² + 10x + 25 = -30 + 25 = -5
(x + 5)² = -5
[tex]x+5 = \pm\sqrt{-5}\\x + 5 = \pm i \sqrt{5}\\x = -5\pm i \sqrt{5}\\\\x_1 = -5+ i \sqrt{5}\\\\x _2= -5- i \sqrt{5}\\[/tex]
A one-celled, aquatic organism called a dinoflagellate is 1000 micrometers long. A microscope magnifies the dinoflagellate 100 times. What is the magnified length of the dinoflagellate in meters? (1 micrometer is 10^-6 meter) Write your answer as a power
A shop in the mall is 8 yards by 12 yards. How much would it cost to recarpet the shop with carpet that costs $2.69 per square yard?
Answer:
Step-by-step explanation:
You will first have to find the area to find the price of each square yard.
Area is 8*12 = 96. Multiply this by 2.69.
It will cost 258.24 dollars to recarpet the shop.
Let me know if this helped
Answer:
A shop in the mall is 8 yards by 12 yards. How much would it cost to recarpet the shop with carpet that costs $5.00 per square yard?
Step-by-step explanation:
If I have a 97% in one of my classes what do I have to get on my final project, which is 30% of my grade, to pass with at least a C or 70%.
Answer:
you will need at least a 94 on your final project
Step-by-step explanation:
hope it helps!
6. From a 5-pound bag of flour, Maura used 2 3/16 pounds to bake
cakes. Find the weight of the flour left in the bag.
What is the scale factor the smaller rectangle to the larger rectangle?
A
6
B
2
C
48
D
1/2
Answer:
scale factor is larger larger length over the smaller length.
Using PEMDAS
1.) 10 - 8 ÷ 4 + (7 - 2)
2.) 3² + 2 (6) - 3
2.) 18
P - arenthesisE - xponents M - ultiplication D - ivisionA - ddition S - ubtractionSOLUTION1:10 - 8 ÷ 4 + (7 - 2)10 - 8 ÷ 4 + 510 - 2 + 58 + 513SOLUTION2:3² + 2 (6) - 39 + 2 (6) - 39 + 12 - 321 - 318#LearningWithMath
please help fast!!!!!!!!!!!!!
Answer:
a. 6+y b. 5- (10x c)
C. 14 +(6 x c) d. x +y=18 f. x - 12 = 7
Step-by-step explanation:
a Japanese giant salamander can weigh 140 lb what is the weight in ounces
five more than thrice a certain number x
50 PTS. Solve the given equation by completing the square.
r2 + 8 = 38
Fill in the values of a, b, and c to complete the solutions.
Answer:
r = 15
Step-by-step explanation:
That's my answer hope it helps brainliest my answer please that's correct
Answer:
r=15
Step-by-step explanation:
hope it helps you bro
Please help!
Part A and part B please
Answer:
39
Step-by-step explanation:
Given:1st grade:
19%2nd grade:
14%3rd grade:
22%4th grade:
26%5th grade:
19%TOTAL : 205 students.To find -Since the total students have been given, we just have to find the percentage of the 205 students that are 5th graders (19%).
So this can be found out:
19% of 205
Solution:
Always use this formula to find a percentage:
% / 100 = Part / Whole replace the given values:
19 / 100 = Part / 205
Cross multiply:
19 x 205 = 100 x Part, or
3895 = 100 x Part
Now, divide by 100 and get the answer:
Part = 3895 / 100 = 38.95
Since decimal cant be a whole number round to nearest tenth:
First note that 38.95 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:
Integer Part: 38Fractional Part: 95To round 38.95 to nearest tenth means to round the numbers so you only have one digit in the fractional part.
We use the following rules to round 38.95 to the nearest tenth:
A) If the last digit in the fractional part of 38.95 is less than 5, then simply remove the last the digit of fractional part.B) If the last digit in the fractional part of 38.95 is 5 or more and the first digit in the fractional part is less than 9, then add 1 to the first digit of the fractional part and remove the second digit.C) If the last digit in the fractional part of 38.95 is 5 or more and the first digit in the fractional part is 9 then add 1 to the Integer part and make the fractional part 0.With 38.95, rule C applies and the answer is:
39.0
8-109. Solve each equation.
.
a. 6x+12=-x-2
Answer:
x = -2
Step-by-step explanation:
6x+12 = -x-2
7x+12 = -2(bring x to the left)
7x = -14(bring constants to the right)
x = -2
Karl is putting a frame around a rectangular photograph. The photograph is 12 inches long and 10 inches wide, and the frame is the same width all the way around. What will be the area of the framed photograph?
write a pair of equivalent fractions for 2/5?.
Step-by-step explanation:
4/10
6/15
8/20
10/25
these were some
Find the slope of the line through the pair of points: ( − 3 , 4 ) and ( 0 , 2 ) .
Answer:
[tex]-\frac{2}{3}.[/tex]
Step-by-step explanation:
1) the required slope can be calculated if to use the ratio:
slope=(y(B)-y(A))/(x(B)-x(A)), where x(A)=-3; y(A)=4; x(B)=0 and y(B)=2;
2) according to the formula above:
s=(2-4)/(0+3)=-2/3.
The slope of the line through the given points is: -2/3.
What is the Slope of a Line?Slope of a line= change in y / change in x = rise/run.
Given the points:
(-3, 4) = (x1, y1)
(0, 2) = (x2, y2)
Slope = (4 - 2)/(-3 - 0)
Slope = 2/-3
Slope of the line = -2/3
Learn more about slope of a line on:
https://brainly.com/question/20848
#SPJ6
The function G(x) = sin(x) is the result of the application of transformations
on the original function F(x) = cos(x). Which of the following options
correctly describes the transformations applied to F(x)?
A. A phase shift of n radians
B. A vertical shift of -1 unit
T
C. A phase shift of radians
2
a
D. A vertical shift of 1 unit
Sell
Answer: shifted by π/2 radians
Step-by-step explanation:
The function sine of 'x' can be equated to the function cosine of 'x' by shifting cosine by 180 degrees. In math words:
[tex]sin(x)=cos(x-180)[/tex]
The value 180 degrees in radians would be π/2. Therefore, in radians:
[tex]sin(x)=cos(x-\pi /2)[/tex]
The 'x' inside of the functions is called the argument, and the value added or subtracted to the argument is the phase. The correct answer would be that sine is equal to cosine shifted by a phase of π/2 radians
How do I find the ordered pair with an x-value of 2, for the equation f(x)=4x-1? What is the ordered pair? urgent please
Step-by-step explanation:
f(2)=4(2)-1 = 7
the ordered pair is (4,7)
At a certain college, there were 700 science majors, 300 engineering majors, and 500 business majors. If one student was selected at random, the probability that the student is an engineering major is
Answer:
300/1500, 1/5, or 20%
Step-by-step explanation:
There are 1500 students total, but only 300 engineering students. We can represent this as a fraction: 300/1500. When reduced it comes out to 20%.
Utilize graphing to find the solution to
the following system of equations.
y = 2x + 1 AND y = x - 3
(-4, [?])
What’s the answer that goes in the green box picture below:
If WX is tangent to circle y, find wx
that statement is very true
a car travels at a speed of 300km per hour in 3 hours,what is the distance covered
(2x – 4) and ( 5x²-2x+6)
Answer:
2(x-2)(5x^2+4)
maybe i am wrong sorry if i am
Find the slope and the y-intercept of the graph of the linear equation.
y = 4x-7
The slope is (Answer here)
and the y-intercept is (Answer here)
Answer:
The slope is 8.000/2.000 = 4.000
The y-intercept is -7/1 = -7.00000
Step-by-step explanation:
^^
Matt is carpeting his bedroom. The room measures 12 feet by 14 feet. If carpet costs $2.29 per square foot, then how much will Matt spend to carpet his bedroom?