MATHEMATICS HIGH SCHOOL

If the population of Centerville in 1910 was 4,200 and 5,000 in 1920, assuming exponential growth, what would the population be in 2020?​

Answers

Answer 1
Answer:

The exponential equation is solved and the population in 2020 is given by the relation P ( A ) = 27,369

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population be P ( 0 ) = 4,200

Let the population in 10 years be P ( 1 ) = 5,000

Now , the population in 100 years is P ( 100 ) =

The exponential growth formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

r = ln(5,000/4,200) / 10 = 0.017

Now we can use this value of r to predict the population in 2020, which is 100 years after 1920:

P(100) = 5,000 × e^(0.017 × 100) = 27,369

Hence , the predicted population of Centerville in 2020, assuming exponential growth, is 27,369

To learn more about exponential growth factor click :

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Answer 2
Answer:

Answer:

the real answer is 28588

Step-by-step explanation:

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C- legs and arms
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Answers

 The correct answer A. 

What is the scale factor of the dilation? Help please

Answers

Imagine A'V' is part of the dilated figure, and AV is part of the original figure.

A'V' = 3.2

AV = 3.2 + 4.8 = 8

A'V'/AV = 3.2/8 = 2/5

Answer: First choice, 2/5.

The sides of a triangle are in the ratio of 6:8:10 and its perimeter is 720 cm. Find its area.​

Answers

216m²

Given that the sides of a triangle are in the ratio of 6:8:10 and their perimeter is equal to 720cm.

To find the area, we would use heron's formula which says area = √[s(s-a)(s-b)(s-c)] ,where a,b,c are the respective sides of the triangle and s = perimeter/2 but before that,we would need to find out the sides , for that , let's say the sides are equal to 6x ,8x & 10 x.

Then,

ATQ,

6x + 8x +10x = 720cm

24x = 720cm

x = 720cm/24

x = 30cm

therefore,

6x = 6*30cm = 180cm

8x = 8*30cm = 240cm

10x = 10*30cm = 300cm

and

s = 720cm/2 = 360cm

Now,

using heron's formula,

area = √[s(s-a)(s-b)(s-c)]

area = √[360cm(360cm-180cm)(360cm-240cm)(360cm-300cm)

area = √[360cm*180cm*120cm*60cm]

area = √(466,560,000cm⁴)

area = 21,600cm² or 216m²

The minimum fine for driving in excess of the speed limit is $25. An additional $6 is added to the minimum fine for each mile per hour (mph) in excess of the speedlimit. Rachel was issued a $103 fine for speeding in a 55-mph speed limit zone. For driving at what speed, inmph, was Rachel fined?

Answers

Let the excess speed limit be y.

According to your question,

25 + 6y = 103

6y = 103 - 25 = 78

y = 78/6 = 13

Thus, the excess speed was 13 mph.

Thus, speed of Rachel = 55 + 13 = 68mph

Thus, Rachel was driving at 68 mph.

2. Solve for x. SHOW YOUR WORK.

Answers

Answer:

x=9

Step-by-step explanation:

The two labelled angles are equal, so we can construct an equation. Then, we solve the equation for x.

4x+2=7x-25\n2=3x-25\n3x=27\nx=9

First, we subtract 4x from both sides. Next, we add 25 to both sides. Finally, we divide both sides by 3.

The diameter of a soccer ball is 8.65 inches what is the volume of the ball rounded to nearest hundredth

Answers

A soccer ball is an icosahedron with curved faces that is why it can be regarded as spherical. The volume of a sphere is calculated through, 

                                        Vs = 4πr^3/3

  where Vs is the volume and r is radius. From the given, 8.65 in is the diameter which is 4.325 in in radius. 

                                        Vs = 4π(4.325^3)/3 = 338.88 in cubed.

Thus, the volume of the ball is 338. 88 in cubed. 
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