The world population was 6.114 billion in 2000 with an estimated growth
rate of 1.9% per year. Assuming the world population follows this exponential
growth mode, find the projected population in 2030.

Answer:

Formula for g(x) is [tex]g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6[/tex]

Step-by-step explanation:

Given - g is a trigonometric function of the form g(x)=a sin (bx+c)+d.  The function intersects its midline at (-1 , 6) and has a minimum point at (-3.5 , 3)

To find - Find a formula for g (x). Give an exact expression.

Proof -

Given that,

g(x)=a sin (bx+c)+d

We know that, Midline is present in between maximum and minimum

Here given that, minimum is present is 3 and midline is present at 6

So, Maximum occurs at 9.

Now,

We know that,

Standard form of sine function is - g(x) = Asin(B(x-C)) + D

Where

A = Amplitude

and Amplitude = (Maximum - minimum) / 2

                         = (9 - 3)/ 2

                         = 6/2 = 3

⇒A = 3

Now,

Period = [tex]\frac{2\pi }{B}[/tex]

⇒B = (2π) / Period

      = (2π) / 10

      = π/5

⇒B = π/5

Now,

Phase Shift : C = -1 ( i.e. 1 to the left)

Vertical Shift : D = 6

So,

We get

g(x) = Asin(B(x-C)) + D

      = [tex]3 sin(\frac{\pi }{5}(x -(- 1))) + 6[/tex]

⇒[tex]g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6[/tex]

∴ we get

Formula for g(x) is [tex]g(x) = 3 sin(\frac{\pi }{5}x + \frac{\pi }{5} ) + 6[/tex]

Answer:

-0.09 x −100 =9

Step-by-step explanation:

brainliest pls

Answer:

X=4, y=5

Step-by-step explanation:

5x + 4y =40 equation 1

6x + 4y =44 equation 2

-1(5x + 4y)=-1(40) multiply equation 1 by -1 so equation will eliminate y

-5x - 4y=-40 modif equation 1

6x + 4y= 44  equation 2

         x=4.     Add above 2 equations

solve for y:

5x + 4y =40

5(4)+4y=40

20+4y =40

4y=20

y=5

check solution ;

6x+4y=44

6(4) + 4(5)=44

24 + 20=44

44=44

Answer:

Option a: m ≠ 0

Step-by-step explanation:

After a small online search, I've found that the complete question is:

If the function f(x) = m*x + b has an inverse function, which statement must be true?

a) m ≠ 0

b) m = 0

c) b ≠ 0

d) b = 0

Ok, if g(x) is an inverse of the function f(x), then:

g( f(x)) = x

f( g(x)) = x

Let's assume that f(x) = m*x + b  has an inverse, and this inverse function is g(x).

Because f(x) is linear, g(x) is also linear, then:

g(x) = n*x + c

Let's find the values of A and B.

We know that:

f( g(x)) = x =  m*(n*x + c) + b

then

x = m*n*x + m*c + b

Then we must have:

m*n = 1

(m*c + b)  = 0

From the first equation m*n = 1

We get:

n = 1/m

The slope of the inverse function is one over the slope of the original function.

Because m is on the denominator, m can not be equal to zero (because a division by zero is not defined)

Then the correct option is the option a, m ≠ 0.          

Answer:

A

Step-by-step explanation:

edge 2021

Answer:

Step-by-step explanation:

Given function in the question is,

[tex]f(x)=\frac{-2x^2-4x}{4x+8}[/tex]

       [tex]=\frac{-2x(x+2)}{4(x+2)}[/tex]

       [tex]=-\frac{1}{2}x[/tex] If [tex]x\neq -2[/tex]

Given function is not defined at x = -2

At x = -2,

[tex]f(-2)=\frac{1}{2}(2)[/tex]

          [tex]=1[/tex]

Therefore, there is a hole in the graph at (-2, 1).

Graph of the function 'f' will be a straight line with a hole at (-2, 1).

Horizontal asymptote → None

Vertical asymptote → None

x-intercept → No x-intercept [Line passes through origin (0,0)]

y-intercept → No y-intercept [Line passes through origin (0,0)]

Hole → (-2, 1)

Answer:

angle 1 is 90

angles 2 and 3 are 65

angle 4 is 25

Answer: uhh idrk bc im taking ur points ok bye <3

Step-by-step explanation:

BAHAHAHAH SORRY IDEK IF U RLLY NEED HELP OR NOT BUT YEAH IM TERRIBLE AT MATH

Answer:

It is 15. Therefore, the coefficient's of the fifth term of binomial expression raised to the power six is 15

Answer:

∠BCD=95°

Step-by-step explanation:

∠B+∠D=127+43=170

360-170=190

∠A=∠C

∠A+∠C=190

∠C+∠C=190

∠C=190/2=95°

Answer:

d

Step-by-step explanation:

100pi

Answer:

250

Step-by-step explanation:

Answer:

B. CPB

Step-by-step explanation:

An acute angle is less than 90°. APE is a right angle. APC and CPE are obtuse angles.

Hope this helps!!

Answer:

B

A is a 90° angle

C and D are obtuse

Answer:

(2x + 15)° = 180°

2x = 180 - 15

2x = 165

x = 165/2

x = 82.5

Answer:

n= 52

Step-by-step explanation:

n= 28+24

n= 52

Hello

Answer:

n=52

Step-by-step explanation:

n-24=28

n=24+28

n=52

You solve n by adding 24 to both sides to get n by itself which is n= 24+28. After you add 24 and 28 together you get 52. So n=52.

Answer:

56.74502 units^2

Step-by-step explanation:

area = pi*radius^2

area = (3.14159265359)(4.25)^2

area = 56.74502 units^2

Answer:

It should be 9ft

Step-by-step explanation:

I hope this helps

Answer:

11

Step-by-step explanation:

hope this helps with the work

Answer:

6 2/7

Step-by-step explanation:

Answer:

are not  

Step-by-step explanation:

it is clear I can explain in the comment section ... because I don not want you to lose time

Answer:

The components of the vector are [tex]x = 2[/tex] and [tex]y = 6[/tex], respectively.

Step-by-step explanation:

The components of the vector is equal to the vector position of the terminal point relative to the initial point ([tex]\vec v[/tex]), that is:

[tex]\vec v = B(x,y) - A(x,y)[/tex] (1)

Where:

[tex]A(x,y)[/tex] - Initial point.

[tex]B(x,y)[/tex] - Terminal point.

If we know that [tex]A(x,y) = (-5,-5)[/tex] and [tex]B(x,y) = (-3,1)[/tex], then the vector is:

[tex]\vec v = (-3,1) -(-5-5)[/tex]

[tex]\vec v = (2, 6)[/tex]

The components of the vector are [tex]x = 2[/tex] and [tex]y = 6[/tex], respectively.

Step-by-step explanation:

Shusil got 8.4 sweets.

Step-by-step explanation:

Gordon share=3/3+5+2×42

3/10×42=12.6

June share=5/3+5+2×42

5/10×42=21

Shusil share=2/3+5+2×42

2/10×42=8.4

Answer:

there is no function I think u forgot to attach it

Answer:

b=4.67ft

Step-by-step explanation:                                                                                    The steps are in the picture below.

Answer:

C or D

Step-by-step explanation:MRK ME BRAINLIEST PLZZZZZZZZ

Answer:

8 in

Step-by-step explanation:

In a cube, the length, width, and height are all the same.

Answer:

8in each

Step-by-step explanation:

A cube has equal sides. Length = 8 in, Width = 8 in and Hight =8 in

Answer:

Slope-intercept form of the line:

Point-slope form of the line:

------------------------------------

Points:

The slope:

The line:

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Points:

The slope:

The line: