I need help figuring out this equation

Answer:

5% annual population growth rate

Step-by-step explanation:

Let the percent the population grows by be [tex]X\%[/tex]. The total population, [tex]f(x)[/tex], after [tex]t[/tex] years can be modeled by the function:

[tex]f(x)=40,000\cdot (\frac{X}{100}+1)^t[/tex]

Why?

Let's take a look at a simple example. If we said a number [tex]n[/tex] grew by 10%, we could represent the number after it grew by multiplying [tex]n[/tex] by [tex]1.10[/tex]. This is because growing by 10% is equivalent to taking [tex]100\%+10\%=110\%[/tex] of that number and we convert a percentage to a decimal by dividing by 100.

Therefore, if the population grew [tex]X\%[/tex], we would divide it by 100 to convert it to a decimal, then add 1 (100%) and raise to the power of [tex]t[/tex] (number of years) to multiply by the initial population of 40,000 to get the total population after [tex]t[/tex] years.

Since the population of the town after two years is 44,100, substitute [tex]f(x)=44,100[/tex] and [tex]t=2[/tex] into [tex]f(x)=40,000\cdot (\frac{X}{100}+1)^t[/tex]:

[tex]44,100=40,000\cdot (\frac{X}{100}+1)^2,\\\\(\frac{X}{100}+1)^2=\frac{44,100}{40,000},\\\\(\frac{X}{100}+1)^2=1.1025,\\\\(\frac{X}{100}+1)^2=\pm \sqrt{1.1025},\\\\\begin{cases}\frac{X}{100}+1=1.05,\frac{X}{100}=0.05, X=\boxed{5\%},\\*\text{negative case is extraneous since X must be positive}\end{cases}[/tex]

Therefore, the city has an annual population growth rate of 5%.

Answer:

26 and 2

Step-by-step explanation:

Given,

Sum of two even numbers = 54

let one number be x

another number be x +2

x + x +2 = 54

2x + 2 = 54

2x = 54 - 2

2x = 52

x = 52/2

x = 26

Therefore, the numbers are 26 and 26 + 2 = 28..

Answer:

D. Vertical translation of 4 units.

Step-by-step explanation:

This transformation keeps x the same but shifts y up 4 units (adding 4 to it). This is a vertical shift up 4, which we can also call a vertical "translation."

Answer:

Step-by-step explanation:

x - 5 < 2 (y - 8) • 1/4

x - 5 < (y - 8) / 2

2 (x - 5) < y - 8

2x - 10 < y - 8

2x - 10 + 8 < y

y > 2x - 2

graph 2x - 2 and shade the section above

The graph of (y - 8)² > 4x - 20 is the same as the graph of x - 5 < 1/4(y - 8)²

The inequality of the graph is given as:

x - 5 < 1/4(y - 8)²

Multiply both sides by 4

4x - 20 < (y - 8)²

Rewrite the inequality as:

(y - 8)² > 4x - 20

Hence, the graph of (y - 8)² > 4x - 20 is the same as the graph of x - 5 < 1/4(y - 8)²

See attachment for the graph

Read more about graphs at:

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Answer:

221.61

Step-by-step explanation:

First we need to put 73% into decimal form.

73%= 0.73.

0.73 * 220= 160.6

Sales tax is 0.161.

After rounding its $1 and 61 cents.

220 + 1.61 = 221.61.

Hope that helped.

9514 1404 393

Answer:

  all of them (A, B, C, D)

Step-by-step explanation:

Two unique points define a line. Any pair of unique points will always be collinear (reside on the same line).

Each of the points listed, together with (2, 1), will define a line. The two points will be collinear.

Answer:

x=−5+√29 or x=−5−√29

Step

Let's solve your equation step-by-step.

x2+10x+10=14

Step 1: Subtract 14 from both sides.

x2+10x+10−14=14−14

x2+10x−4=0

For this equation: a=1, b=10, c=-4

1x2+10x+−4=0

Step 2: Use quadratic formula with a=1, b=10, c=-4.

x=

−b±√b2−4ac

2a

x=

−(10)±√(10)2−4(1)(−4)

2(1)

x=

−10±√116

2

x=−5+√29 or x=−5−√29

Answer:

703.7 in²

Step-by-step explanation:

SA = 2πrh+2πr²

= 2×π×7×9+2×π×7²

= 224π

= 703.7 in² (rounded to the nearest tenth)

Answer:

224π

in²

Step-by-step explanation:

Answer:

~~314.16

Step-by-step explanation:

lol i dont have 100000000 points. anyways

you can find the area of a sphere with the formula 4πr^2 with r being the radius

this sphere's radius is 5 as shown in the image

so

4π*r^2

4π*(5)^2

=4π*25

=100π

put into calculator

~~314.16cm^3

hope this helps

Answer:

try 91.78, 91.58, 91.26, 363.4

Step-by-step explanation:

9514 1404 393

Answer:

  (a)  a^4/(4b^2)

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  a^-b = 1/a^b

__

Your expression simplifies as follows.

  [tex]\dfrac{3a^2b^{-4}}{12a^{-2}b^{-2}}=\dfrac{3}{12}\cdot\dfrac{a^{2-(-2)}}{b^{-2-(-4)}}=\boxed{\dfrac{a^4}{4b^2}}[/tex]

Answer:

first... You think and Conceptualize

A diameter divides a circle into equal halves

We're given the end points of the Diameter.

With this we can fine the Center of the circle.

The End Points are

(-6, -1) and ( 2, 3)

Half-way through the diameter gives the center of the circle

So We'd apply the Mid-Point formula to get the co-ordinate of the center.

X= x₁ + x₂/2 , Y = y₁ + y₂/2

X = -6 + 2/2, Y = -1 + 3/2

X= -2. Y = 1

The Midpoint is (-2, 1)

The Radius would be the distance between the center and a point on the circumference.

We already have 2 points of the circumference (Which are the endpoints of the diameter).

So we can pick any of them arbitrarily.

I'd go with (2,3)

So We'd apply the distance between Points formula to get the magnitude of the radius

(-2,1) (2,3)

D = √(x₁ - x₂)² + (y₁ - y₂)²

D = √(-2-2)² + (1-3)²

D=√(-4)² + (-2)²

D=√20.

Our Radius is √20.

Equation of Circle =

(x-h)² + (y-k)² = r²

Where h and k are the center of the circle(-2,1)

(x-(-2))² + ( y - 1 )²= (√20)²

(x + 2)² + ( y - 1)² = 20

Our Answer

(x + 2)² + (y - 1)² = 20.

This should be it.

Have a great day!

Answer:

boat speed 79 kph

stream speed 16kph

Step-by-step explanation:

Let v be the still water velocity

Let s be the stream velocity

3(v - s) = 189

3v - 3s = 189

   v - s = 63

        v = 63 + s

         5(v + s) = 475

         5v + 5s = 475

5(63 + s) + 5s = 475

315 + 5s + 5s = 475

               10s = 160

                  s = 16 km/hr

v = 63 + 16

v = 79 km/hr

Answer:

Does the answer help you

Answer:

The new price is 66% off the original not 75% off

Step-by-step explanation:

Let x be the original price

First take 60 percent off

x - x*60% = new price

x- .60x = .40x

The new price is .40x

Then take 15 % off

(.40x) - (.40x)*15%

.40x - .40x*.15

.40x - .06x

.34x

100 -.34 =.66

The new price is 66% off the original not 75% off

9514 1404 393

Answer:

  -1

Step-by-step explanation:

We notice that we want term a1 and have terms a17 and a33. These terms (every 16-th term) form an arithmetic sequence. The middle term (a17) is the average of the other two, so we have ...

  a17 = (a1 +a33)/2

  2a17 -a33 = a1 = 2(10) -21 = -1

  a1 = -1

_____

Additional comment

You could go to the trouble to find the general term of the sequence.

  an = a1 +d(n -1)

  a17 = a1 + d(17 -1) = 10

  a33 = a1 + d(33 -1) = 21

Subtracting the first equation from the second, we have ...

  16d1 = 11

  d1 = 11/16

Using the first equation, we find ...

  a1 +(11/16)(17 -1) = 10

  a1 = 10 -11 = -1 . . . . same as above.

Answer:

Here is the answer

I hope it xa helping u

Answer:

Its the 3 one

Step-by-step explanation:

Answer:

117.8

Step-by-step explanation:

surface area = πr²+πrl, where r = radius and l = slant height

so,

πr²+πrl

= π×3²+π×3×9.5

= 75π/2

= 117.8 (rounded to the nearest tenth)

Step-by-step explanation:

1 day = 24 hrs

so, 20 days = 20 × 24 = 480 hours

mark me as brainliest

Answer:

480 hours

Step-by-step explanation:

Explanation:

I used GeoGebra to determine that the approximate solutions in (x,y) form are

(0.00333, 0)

(9.59682, 3.45925)

These are the locations where the two graphs cross or intersect.

When rounding to the nearest tenth, we end up with (0, 0) and (9.6, 3.5) which is why the answers are D and E.

Be careful to keep in mind that x = 0 is not in the domain of g(x) since log(0) is undefined. So it's fairly misleading to say that (0,0) is an intersection point when it's not even on the graph of g(x). This is one big issue with rounding numbers that we lose crucial information like this.

Answer:

Hello,

x=9.59682

Step-by-step explanation:

Using Excel with the methode of "dichotomie" (divide by 2)

Just modifiy value in A2(start value)  and E1 (precision)

9514 1404 393

Answer:

  a) not a function

  b) is a function

  c) not a function

  d) is a function

Step-by-step explanation:

If the graph passes the "vertical line test," then the relation is a function.

Choices B and D are linear equations. Their graph is a straight line, so each x-value corresponds to exactly one y-value. (Every non-vertical line passes the vertical line test.)

Choices A and C are equations of parabolas that open horizontally. It is easy to draw a vertical line that intersects the graph twice, so these relations fail the vertical line test.

__

  B, D -- functions

  A, C -- not functions

Answer:

(g÷f) (x) (1.8) ³x²+⁷x+2

Step-by-step explanation:

Im glad to help you

Answer:

5 - ? = 4

5- 1 = 4

➪5 - 4 = ?

➪1 = 5-4

➪ 5- 1 = 4

hopes its helps you ..

Answer:

106.25km

Step-by-step explanation:

8.5cm = 0.000085km

map:real life

1:1250000

0.000085km : 0.000085km * 1250000 = 106.25km

Answer:

15 units

Step-by-step explanation:

Point D is at 8

Point A is at -7

D - A

8 - -7

8+7

15 units

Answer:

the answer is 15

you can just count the number of steps going forward from -7 to 8.

Answer:

120

Step-by-step explanation:

There are 10 possible toppings to choose from, you choose 7.

Using combinatorics, it's 10!/(7! 3!), or 120.

The formula is (total amount to choose from )! divided by (amount you choose)!(amount you don't choose)!

Or search up combination formula

A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

The formula for combination.

= [tex]^nC_r[/tex]

= n! / r! (n -r)!

The number of possible 7-toppings for the pizza is 120.

A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

We have,

The total number of toppings = 10.

n = 10

The number of required toppings = 7.

r = 7

The formula for combination.

= [tex]^nC_r[/tex]

= n! / r! (n -r)!

The possible number of possible 7-toppings pizzas.

= [tex]^{10}C_7[/tex]

= (10 x 9 x 8) / (3 x 2)

= 120

Thus,

n = 10 and r = 7

[tex]^{10}C_7[/tex] = 120

The number of possible 7-toppings for the pizza is 120.

Learn more about combination here:

https://brainly.com/question/14355408

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