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4 years ago

GCF of 15x^2y^3 and -20x^3yz

1 answer:

4 0

$15x^2y^3=3\cdot\boxed{5}\cdot\boxed{x}\cdot\boxed{x}\cdot\boxed{y}\cdot y\cdot y\\\\-20x^3yz=-2\cdot2\cdot\boxed{5}\cdot\boxed{x}\cdot\boxed{x}\cdot x\cdot\boxed{y}\cdot z\\\\GCF(15x^2y^3,\ -20x^3yz)=\boxed{5}\cdot\boxed{x}\cdot\boxed{x}\cdot\boxed{y}=5x^2y$

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The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. A) Estimate how lo

VLD [36.1K]

Answer:

A) 63.36 years.

B) 100.42 years.

Step-by-step explanation:

We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.

A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.

$P(t)=7.1(1.011)^{t}$

$7.1 \times 2=7.1(1.011)^{t}$

$\frac{7.1 \times 2}{7.1} =(1.011)^{t}$

$2 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(2) =ln (1.011)^{t}$

$ln(2) =t \cdot ln(1.011)$

$0.6931471805599453 =t \cdot 0.0109399400383344$

$t=\frac{0.6931471805599453}{0.0109399400383344}$

$t=63.3593217267282743049\approx 63.36$

Therefore, it will take 63.36 years the population to be double.

B) Now we will find the number of years it will take the population to be triple of its size.

$7.1 \times 3=7.1(1.011)^{t}$

$\frac{7.1 \times 3}{7.1} =(1.011)^{t}$

$3 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(3) =ln (1.011)^{t}$

$ln(3) =t \cdot ln(1.011)$

$1.0986122886681097 =t \cdot 0.0109399400383344$

$t=\frac{1.0986122886681097}{0.0109399400383344}$

$t=100.4221490079915311298\approx 100.42$

Therefore, it will take 100.42 years the population to triple of its size.

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3 years ago

Identify the error by providing a brief description. Then, complete the problem correct

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Answer:

True answer: -24

Step-by-step explanation:

Showing the error

-16-2(-2) – 12 First you need to multiply

8(-2) - 12 The error here is that the wrong numbers are multiplied together

-16-12 Add the negatives together

-28 Your answer (the incorrect one)

The correct way of solving it

-16 -2(-2) - 12 Multiply into the parenthesis

-16 + 4 -12 Add the first two numbers

-12 - 12 Add the numbers together

-24 The answer

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3 years ago

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Reptile [31]

Answer:

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Step-by-step explanation:

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3 years ago

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This is an example of the commutative property of multiplication.

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