One model of Earth's population growth is P(t)= 64/(1+11e^0.8t)
where t is
measured in years since 1990, and P is measured in years since 1990, and Pis measured in billions of people. Which of the following statements are true? Check all that apply.
Answer: C and D
Step-by-step explanation:
Using the logistic equation, it is found that options C and D are correct.
The logistic equation for population growth is given by:
[tex]P(t) = \frac{K}{1 + Ae^{-kt}}[/tex]
[tex]A = \frac{K - P(0)}{P(0)}[/tex]
In which:
K is the carrying capacity. P(0) is the initial value. k is the growth rate, as a decimal. The population grows exponentially for a while, but as it gets closer to the carrying capacity, the growth slows down.For this problem, the equation is:
[tex]P(t) = \frac{64}{1 + 11e^{-0.08t}}[/tex]
Which means that:
The carrying capacity is of 64 billion people, as [tex]K = 64[/tex].The growth rate is of 8% per year, but it is not steady.The initial population, in millions of people, is of [tex]P(0) = \frac{64}{1 + 11} = 5.3[/tex].Hence, options C and D are correct.
To learn more about the logistic equation, you can check https://brainly.com/question/25697660
Solve the following system of equations. Enter the y-coordinate of the
solution. Round your answer to the nearest tenth.
5x+y=21
- 2x + 61=-34
Answer:
(13.5,-46.5)
Step-by-step explanation:
Since equation 2 is missing y, then x is a constant
-2x + 61 = 34
-2x = 34 - 61
-2x = -27
x = 13.5
Then plug x into the 1st
5x + y = 21
5 * (13.5) + y = 21
67.5 + Y = 21
y = 21 - 67.5
y = -46.5
So the point satisfying both equations is (13.5,-46.5)
Sin(2x+30°)=1
Tìm x
Cảm ơn vì giúp đỡ
Answer:
Step-by-step explanation:
This question is asking us to find where sin(2x + 30) has a sin of 1. If you look at the unit circle, 90 degrees has a sin of 1. Mathematically, it will be solved like this (begin by taking the inverse sin of both sides):
[tex]sin^{-1}[sin(2x+30)]=sin^{-1}(1)[/tex]
On the left, the inverse sin "undoes" or cancels the sin, leaving us with
2x + 30 = sin⁻¹(1)
The right side is asking us what angle has a sin of 1, which is 90. Sub that into the right side:
2x + 30 = 90 and
2x = 60 so
x = 30
You're welcome!
What is the inequality?
Answer:
The best option would be the second one.
Step-by-step explanation:
This is the only option that shows that x can only be greater than -8. The circled dot means x cannot be the number the dot is sitting on, in this case, -8.
find the least number which is exactly divisible by 15 , 20, 25
explain step by step
Answer:
ans is 300Step-by-step explanation:
you need to take LCM of 15,20,25 and their LCM Will be 300I'M NOT PRETTY SURE ABOUT IT. ...Answer:
300
Step-by-step explanation:
5/15,20,25
3,4,5
5*4*3*5
300
Can somebody help me please.
What is the length of line segment SA
Answer:
slalalallalalalalalalalalallapapapqpqpq
Melissa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of 59 and costs an additional 0.15 per mile driven. The second plan has an initial fee of 50 and costs an additional 0.20 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same?
Answer:
Step-by-step explanation:
Let
x = cost per mile
y = Total cost
Plan 1:
y = 59 + 0.15x
Plan 2:
y = 50 + 0.20x
Equate the total cost of the two plans
59 + 0.15x = 50 + 0.20x
59 - 50 = 0.20x - 0.15x
9 = 0.05x
x = 9/0.05
= 180
x = 180 miles
y = 50 + 0.20x
= 50 + 0.20(180)
= 50 + 36
= 86
y = 86
1+2+6+1+4+45+7474747448489
Answer:
7474747448548
Step-by-step explanation:
I hope this helps
Solve the system of equations and choose the correct ordered pair.
4x - 2y = -2
6x + 3y = 27
A. (2,5)
B. (3,7)
C. (0, -1)
D. (0,9)
Answer:
(2,5)
Step-by-step explanation:
4x - 2y = -2
6x + 3y = 27
Divide the first equation by 2 and the second equation by 3
2x - y = -1
2x + y = 9
Add the equations together
2x - y = -1
2x + y = 9
-------------------
4x = 8
Divide by 4
4x/4 = 8/2
x =2
2x+y = 9
2(2) +y = 9
4+u = 9
y = 9-4
y=5
(2,5)
Use the quadratic formula to find the solutions to the quadratic equation below. Check all that apply. 5x2-X-4 = 0 A. -4/5 B. 5/4C. 2/3 D. 1 E. -1 F.3/2
Hi
5x²-x-4 = 0
Δ= (-1)² - 4*5*(-4)
Δ = 1 -4*-20
Δ = 1 +80
Δ = 81
√Δ= 9
as Δ ≥ 0 , so 2 solutions exist in R
S1 is : ( 1+9) /2*5 = 10/10 = 1
s2 = (1 -9)/2*5 = -8/10 = -4*2 /2*5 = -4/5
Corrects answers are A and D
Answer:
A. -4/5 And D. 1
Step-by-step explanation:
i just got it right
If P(x) = P[tex]_{n}[/tex][tex]x^{n}[/tex] + P[tex]_{n-1}[/tex][tex]x^{n-1}[/tex] + · · · + P[tex]_{0}[/tex] is divided by (x - a), show that the remainder is P(a)
If [tex]P(x) = p_nx^n + p_{n-1}x^{n-1}+\ldots+p_0[/tex] is divided by [tex](x-a)[/tex], then [tex]P(x) = (x-a) \cdot Q(x) + R(x)[/tex] for some polynomials [tex]Q,R[/tex]. Moreover, [tex]\deg R < 1[/tex] (because [tex]\deg (x-a) = 1[/tex]), so there exists [tex]\alpha \in \mathbb{R}[/tex] such that [tex]R(x) = \alpha[/tex] for all [tex]x \in \mathbb{R}[/tex]. But if we calculate [tex]P(a)[/tex], it turns out that [tex]P(a) = (a-a)\cdot Q(a) + \alpha[/tex], so [tex]R(x) = \alpha = P(a)[/tex]. [tex]\blacksquare[/tex]
a(b^2+c^2+bc) + b(c^2+a^2+ca) + c(a^2+b^2+ab)
Answer:
(a-b)(b-c)(a-c)
Step-by-step explanation:
a^2(b - c) + b^2(c-a) + c^2(a - b)
= a^2b - a^2c + b^2c - b^2a + c^2a-c^2b
=a^2b - b^2a - a^2c + b^2c + c^2a -c^2b
= ab(a - b) - c(a^2 - b^2) +c^2(a - b)
=ab(a - b) -c(a - b)(a + b) +c^2(a - b)
=(a - b)(ab - c(a + b) +c^2)
=(a - b)(ab - cb -ca + c^2)
= (a - b)(b(a-c) -c(a-c))
=(a-b)(b-c)(a-c)
what is the square root of 100
The square root of 100 is 10.
To check, solve 10 x 10.
Hope this helps! Please mark me as brainliest!
Have a great day!
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Data should be analyzed using each of the following except:
A. measures of central tendency
B. shape
C. population size
D. spread
A student must find the slope of a line that passes through the points (2.2) and (-1, 3). Which of the statements
below best applies to the sample mathematical work?
Given the points above, I plug these values into the formula y2 -x1/ x2-x1 which yields the expression -1-2/3-2 , which gives a slope of -3.
А. the formula for the slope of the ne is incorrect
B. the student failed to plug in the proper values into the slope formula
C the numeric calculation to find the slope is incorrect
D. the mathematical work shown is correct
Answer:
A
Step-by-step explanation:
the formula of the slope is (y2 - y1)/(x2 - x1)
slope = (3-2)/(-1-2) = 1/(-3) = -1/3
Two sides of a right triangle measure 5 inches and 6 nches, and the third side measures 61 inches.
The length of the third side is about
inches _ . The perimeter of the triangle is about
inches. __
Answer:
The length of the third side is 7.81 inches and the perimeter of the triangle is about 18.81 inches
Step-by-step explanation:
[tex]\frac{3}{2x}[/tex]-[tex]\frac{11}{5}[/tex]=[tex]\frac{7}{8}[/tex].[tex]\frac{64}{49}[/tex]
Answer:
x=35/78
Step-by-step explanation:
3/2x-11/5=(7/8)*(64/49)
3/2x-11/5=8/7
3/2x=8/7+11/5
3/2x=117/35
x=(35*3)/(2*117)
x=35/78
convert 123000000 milligram into gram
Answer:
123,000 grams
Step-by-step explanation:
1000 mg is equivalent to 1 gram.
Answer:
123000g
Step-by-step explanation:
1000mg=1g
123000000mg= xgrams
cross multiplying,
you'll have
[tex] \frac{123000000}{1000} = 123000[/tex]
in a right triangle ABC, C is the right angle. What does Cos B equal
Answer:
not enough information
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!! Determine the Value of K in the diagram ( secant lines to circles).
Answer:
k = 10Step-by-step explanation:
According to intersecting secants theorem we have the following equation:
3x*(3x + 5x) = 2x*(2x + kx)Solve it for k:
3x*8x = 4x² + 2kx²24x² = (4 + 2k)x²24 = 4 + 2k20 = 2kk = 10I need help to find x=
Answer:
x=12
Step-by-step explanation:
Since the polygons are similar, we can write a ratio to solve
red side / yellow side
4 2
--- = ---
x 6
Using cross products
4*6 = 2x
24 = 2x
Divide by 2
24/2 =2x/2
12=x
Answer:
12
Step-by-step explanation:
When two shapes are similar, you need to find the scale factor of two existing corresponding sides.
For example, you can do 6 and 2.
Divide:
6/2 = 3
The scale factor: 3
Now multiply 4 and the scale factor (3):
4 × 3 = 12
So, x = 12.
Hope this helped.
The perimeter of a rectangle is given by the formula P=2w+2l,where w is the width and l is the length.Rearrange the formula for the length ( ).
Answer:
l = (p - 2w)/2
Step-by-step explanation:
applying the distributive property to the expression, 24x+18y will produce which equivalent expression.
1. 6(4+3y)
2. 6(4x+3y)
3. 3xy(8+6)
4. 3(8x+6y)
Answer:
6(4x + 2y)
Step-by-step explanation:
24x = 2 * 2 * 2 * 3 * x
18y = 2 * 3* 3 * y
Common factors = 2 * 3 = 6
24x + 18y = (6*4x) + (6*2y) {6 is common in both terms}
= 6*(4x + 2y)
What is the value of the exponential expression below?
I don’t understand how to solve this
Answer:
42.1
Step-by-step explanation:
The height of the main triangle is,
h = 47√3/2 (since it's an 30-60-90 triangle)
so to find x,
tan(44) = h/x
x = h/tan(44)
x = 42.1 (rounded to the nearest tenth)
Answered by GAUTHMATH
Classify the following polynomials according to the number of terms. Combine any like terms first.
x^2 + 3x + 2x
x^2 + 5x = Binomial
x^3 + x + 3x^2 - x
x^3 + 3x^2 = Binomial
4x^3 + x + x^2 - 2x
4x^3 + x^2 - x = Trinomial
3x^4 + x - 3x^4 - x
0 = No Polynomial/Zero Polynomial
Hope this helps!
The first given polynomial is binomial.
The second given polynomial is binomial.
The third given polynomial is binomial.
The fourth given polynomial is monomial.
What is polynomial?Polynomials are algebraic expressions that consist of variables and coefficients.
What is monomial?A monomial is an algebraic expression that has only one term.
What is binomial?Binomial is an algebraic expression that contains two different terms connected by addition or subtraction.
What is trinomial give?A trinomial is an algebraic expression that has three non-zero terms.
According to the given question.
We have some polynomials.
If we take the polynomial:
[tex]x^{2} +3x+2x[/tex]
The above polynomial can be written as
[tex]x^{2} + 5x[/tex]
Since, the above polynomial has only two terms therefore it is a binomial.
[tex]x^{3} +x+3x^{2} -x = x^{3} +3x^{2}[/tex]
The above polynomial has only two terms. Hence, the given polynomial is binomial.
[tex]4x^{2} + x + x^{2} -2x\\=5x^{2} -x[/tex]
The given polynomial has only two terms therefore it is binomial.
[tex]3x^{4} + x - 3x^{4} -x\\= 0[/tex]
The given polynomial has only one term therefore it is monomial.
Find out more information about classification of polynomials here:
https://brainly.com/question/12677239
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Inverse proportion
it takes 3 hrs for two people to clean six identical rooms.
how long would it take 5 people to clean 20 of the same rooms at the same k rate
i know answer need explan.
Answer:
Hello,
4 hours
Step-by-step explanation:
Let say w the work clean one room.
h the number of hours worked
p the number of people who works
k is a constant
6w=k*h*p
3 h, 2 p==> 6w
6w=k*3*2 ==> k=w
5 p, 20 w ==>
20w=k*h*p
20w=w*h*5
20=h*5
h=20/5
h=4
It will take 4 hours.
Find a recursive rule for the nth term of the sequence.
-8, 3, 14, 25, ...
Answer:
Step-by-step explanation:
a1=-8
a2=3
D=11
n=-8+11(n-1)
Find the value of x and y
[tex]\\ \rm\Rrightarrow \dfrac{x}{2}=3[/tex]
[tex]\\ \rm\Rrightarrow x=2(3)[/tex]
[tex]\\ \rm\Rrightarrow x=6[/tex]
And
[tex]\\ \rm\Rrightarrow \dfrac{y}{2}+1=3[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{y}{2}=3-1=2[/tex]
[tex]\\ \rm\Rrightarrow y=2(2)[/tex]
[tex]\\ \rm\Rrightarrow y=4[/tex]
Answer:
x=6 y=4
Step-by-step explanation:
Equating corresponding terms , we get
x/2=3
or, x=6
Also,
y/2+1=3
or, (y+2/2)=3
or, y+2=6
or, y=6-2
y=4
Therefore, x=6 and y=4.
