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Paraphin [41]
2 years ago
13

The table gives estimates of the world population, in millions, from 1750 to 2000. (Round your answers to the nearest million.)

Mathematics
1 answer:
BaLLatris [955]2 years ago
3 0

Answer:

A.) 1508 ; 1870

B.) 2083

C.) 3972

Step-by-step explanation:

General form of an exponential model :

A = A0e^rt

A0 = initial population

A = final population

r = growth rate ; t = time

1)

Using the year 1750 and 1800

Time, t = 1800 - 1750 = 50 years

Initial population = 790

Final population = 980

Let's obtain the growth rate :

980 = 790e^50r

980/790 = e^50r

Take the In of both sides

In(980/790) = 50r

0.2155196 = 50r

r = 0.2155196/50

r = 0.0043103

Using this rate, let predict the population in 1900

t = 1900 - 1750 = 150 years

A = 790e^150*0.0043103

A = 790e^0.6465588

A = 1508.0788 ; 1508 million people

In 1950;

t = 1950 - 1750 = 200

A = 790e^200*0.0043103

A = 790e^0.86206

A = 1870.7467 ; 1870 million people

2.)

Exponential model. For 1800 and 1850

Initial, 1800 = 980

Final, 1850 = 1260

t = 1850 - 1800 = 50

Using the exponential format ; we can obtain the rate :

1260 = 980e^50r

1260/980 = e^50r

Take the In of both sides

In(1260/980) = 50r

0.2513144 = 50r

r = 0.2513144/50

r = 0.0050262

Using the model ; The predicted population in 1950;

In 1950;

t = 1950 - 1800 = 150

A = 980e^150*0.0050262

A = 980e^0.7539432

A = 2082.8571 ; 2083 million people

3.)

1900 1650

1950 2560

t = 1900 - 1950 = 50

Using the exponential format ; we can obtain the rate :

2560 = 1650e^50r

2560/1650 = e^50r

Take the In of both sides

In(2560/1650) = 50r

0.4392319 = 50r

r = 0.4392319/50

r = 0.0087846

Using the model ; The predicted population in 2000;

In 2000;

t = 2000 - 1900 = 100

A = 1650e^100*0.0087846

A = 1650e^0.8784639

A = 3971.8787 ; 3972 million people

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Dennis_Churaev [7]

Answer:

a) quotient = 2,  remainder = 5

b) quotient = -10,  remainder = -1

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d) quotient = 77,  remainder = 0

e) quotient = 0,  remainder = 0

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g) quotient = 0,  remainder = -1

h) quotient = 4,  remainder = 0

Step-by-step explanation:

The relationship between the quotient, remainder and divisor is that the product of the quotient and divisor added to the reminder gives the dividend.

Based on this, when

a)19 is divided by 7 = 19/7

= 2\frac{5}{7}

Hence the quotient is 2, the remainder is 5

Applying the same principle, when

b) −111 is divided by 11

= -10\frac{1}{11}

Hence the quotient is -10, the remainder is -1

c) 789 is divided by 23

=34\frac{7}{23}

Hence the quotient is 34, the remainder is 7

d) 1001 is divided by 13

= 77

Hence the quotient = 77, the remainder is 0

e) 0/19 = 0

Hence the quotient is 0, the remainder is 0

f) 3/5

Hence the quotient is 0, the remainder is 3

g) -1/3

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h) 4/1

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3 0
2 years ago
If ray JG is an angle bisector of ∠FJH, find m∠FJH.
miss Akunina [59]

Answer:

m∠FJH=60°

Step-by-step explanation:

The complete question is

JG bisects FJH, FJG= (2x + 4)° and GJH = (3x -9)°  

What is FJH

we know that

m∠FJH=m∠FJG+m∠GJH -----> equation A

If ray JG is an angle bisector of ∠FJH

then

m∠FJG=m∠GJH -----> equation B

substitute the given values in equation B and solve for x

(2x + 4)°=(3x -9)°

3x-2x=4+9

x=13

Find the measure of angle FJH

m∠FJH=(2x + 4)°+(3x -9)°

substitute the value of x

m∠FJH=(2(13) + 4)°+(3(13) -9)°

m∠FJH=(30)°+(30)°

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2 years ago
In a random sample of 8 people with advanced degrees in biology, the mean monthly income was $4744 and the standard deviation wa
eimsori [14]

Answer: u= ( 4342.08, 5145.92).

Step-by-step explanation: the population mean is estimated using the sample by the formulae assuming a 95% confidence level

u = x' + Zα/2 * (√σ/n) or x' - Zα/2 * (√σ/n)

u = estimated population mean

x' = sample mean = 4744

n = sample size =8

σ = sample standard deviation. = 580

α = level of significance = 1- confidence level = 1-0.95= 0.05

Zα/2 = z score from the normal distribution table for a 2 tailed test = 1.96

First boundary value for interval

u = 4744 + 1.96 ( 580/√8)

u = 4744 + 1.96 * (205.0609)

u = 4744 + 401.92

u = 5145.92

Second boundary value for interval

u = 4744 - 1.96 ( 580/√8)

u = 4744 - 1.96 * (205.0609)

u = 4744 - 401.92

u = 4342.08

Thus the confidence interval for population mean is

u= ( 4342.08, 5145.92).

3 0
2 years ago
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Helga [31]
Hi there
1) b
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2) a
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3)d
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4) c
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