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The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expect

Liula [17]

Answer:

After 25 years the population will be:

Australia: 22271200
China: 1580220878
Mexico: 157380127
Zaire: 112794819

Step-by-step explanation:

Growth rate problem that has a growth rate proportional to the population size can be solved using the equation:

P(t) = P₀eʳᵗ

t is your unit of time. It could be days, or hours, or minutes. It changes depending on each problem. In this problem, t is measured in years because you're jumping from 2000 to 2025. Years just makes the most sense to measure that leap in time.

P(t) is the population at time t. An example in this problem could be P(20) would be the population 20 years after the initial count. or maybe P(12) would be the population 12 years after the initial count. or P(0) would be the initial count of the population.

P₀ is the initial population at P(0)
r is the growth rate. Don't forget to convert the percentage to its decimal form

Now that everything is set out, lets use the equation to solve for our answer.

P(t) = P₀eʳᵗ

Australia:

$P(t)=(19169000)e^{(0.006)t}$

after 25 years

$P(25)=(19169000)e^{(0.006)(25)}=22271200.6$

China:

$P(t) = (1261832000)e^{(.009)t}$

after 25 years:

$P(25)=(1261832000)e^{(.009)(25)}=1580220878$

Mexico:

$P(t) = (100350000)e^{(0.018)t}$

after 25 years:

$P(25)=(100350000)e^{(0.018)(25)}=157380127.8$

Zaire:

$P(t) = (51965000)e^{(0.031)t}$

after 25 years:

$P(25)=(51965000)e^{(0.031)(25)}=112794819.9$

6 0

3 years ago

How many ways can a dance instructor send 4 of her 11 students to a summer dance program?

Sedaia [141]

Answer:

d) 330

Step-by-step explanation:

The number of ways can a dance instructor send 4 of her 11 students to summer dance program is C(11 , 4)

That is $11_{C_{4} }$ ways

by using formula $n_{C_{r} } = \frac{n!}{(n-r)!r!}$

now simplification

$11_{C_{4} } = \frac{11!}{(11-4)!4!}$

= $\frac{11X10X9X8X7!}{(7!)4X3X2X1}$

after cancelling 7! and on simplification

= $\frac{11X10X9X8}{4X3X2X1}$

after cancellation we get 330 ways

The number of ways can a dance instructor send 4 of her 11 students to summer dance program is 330

8 0

3 years ago

A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more ar

frutty [35]

Answer:

There is a probability of 76% of not selling the package if there are actually three dead batteries in the package.

Step-by-step explanation:

With a 10-units package of batteries with 3 dead batteries, the sampling can be modeled as a binomial random variable with:

n=4 (the amount of batteries picked for the sample).
p=3/10=0.3 (the proportion of dead batteries).
k≥1 (the amount of dead batteries in the sample needed to not sell the package).

The probability of having k dead batteries in the sample is:

$P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}$

Then, the probability of having one or more dead batteries in the sample (k≥1) is:

$P(x\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{4}{0} p^{0}q^{4}=1*1*0.7^4=0.2401\\\\\\P(x\geq1)=1-0.2401=0.7599\approx0.76$

8 0

2 years ago

Complete the table for y=1/2x-3

Readme [11.4K]

Tables are created by substitute a set of input values into the function to create outputs. The required table is as shown below

x | y

0 -3

1 -2.5

2 -2

<h3>Tables and values</h3>

Tables are created by substitute a set of input values into the function to create outputs

Using x = 0, 1 and 2 as the input values

Given the function

y = 1/2x - 3

If x = 0

y = 1/2(0) - 3

y = -3

If x = 1

y = 1/2(1) - 3

y = -2.5

If x = 2

y = 1/2(2) - 3

y = -2

Hence the required table is as shown below

x | y

0 -3

1 -2.5

2 -2

Learn more on tables and values here: brainly.com/question/12151322

#SPJ1

8 0

1 year ago

3. The bill at a restaurant

meriva

Answer:

$156.86

Step-by-step explanation:

$136.40 + 15% = $20.46

$136.40 + $20.46 = $156.86

3 0

2 years ago

Read 2 more answers