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Natasha2012 [34]
3 years ago
9

The current population of a town is 10,000. If the population, P, increases by 20% each year, which equation could be used to fi

nd the population after T years?
Mathematics
1 answer:
frozen [14]3 years ago
7 0

Answer:

<u>The equation would be:</u>

<u>p = 10,000 * (1 + 0.2)∧ t</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Current population of a town = 10,000 inhabitants

Growth rate of the population = 20% annually

2. Which equation could be used to find the population after T years?

p = Population of the town after t years

t = Number of years

We will use the following equation:

<u>p = 10,000 * (1 + 0.2)∧ t</u>

For example, let's calculate the population after 6 years, replacing with the real values, we have:

p = 10,000 * (1 + 0.2)⁶

p = 10,000 * 2.986

p = 29,860 inhabitants

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What would be the correlation coefficient (r) of the following scatter plot?
luda_lava [24]

Answer:

-0.89 (i think)

Step-by-step explanation:

Since the graph seems to be going downwards from the right, it has a negative correlation. And since the data seems to be pretty close together, the correlation must be strong. That narrows the answer down to -0.89

If its wrong then i'm not a smart person, and it's -0.15

8 0
2 years ago
You offer to do the dishes for your family for the next month. You suggest that they can pay you in one of three ways.
Sophie [7]

Answer:

I say number 2

Step-by-step explanation:

0.02 is 2 cents while 0.20 is twenty sense. That would make more sense

5 0
3 years ago
Read 2 more answers
The perimeter of the scalene triangle is 54.6 cm. Which equation can be used to find the value of b if side a measures 8.7 cm?
77julia77 [94]

A scalene triangle is a triangle that has 3 sides that are all different lengths.

Let these letters represent the problem:

a = 8.7

b = side 2

c = side 3

P = 54.6

To find the perimeter, we just need to add all the sides [ P = a + b + c ]

So, put what we have in the formula above.

54.6 = 8.7 + b + c

Best of Luck!

7 0
3 years ago
Read 2 more answers
An urn contains n white balls andm black balls. (m and n are both positive numbers.) (a) If two balls are drawn without replacem
Genrish500 [490]

DISCLAIMER: Please let me rename b and w the number of black and white balls, for the sake of readability. You can switch the variable names at any time and the ideas won't change a bit!

<h2>(a)</h2>

Case 1: both balls are white.

At the beginning we have b+w balls. We want to pick a white one, so we have a probability of \frac{w}{b+w} of picking a white one.

If this happens, we're left with w-1 white balls and still b black balls, for a total of b+w-1 balls. So, now, the probability of picking a white ball is

\dfrac{w-1}{b+w-1}

The probability of the two events happening one after the other is the product of the probabilities, so you pick two whites with probability

\dfrac{w}{b+w}\cdot \dfrac{w-1}{b+w-1}=\dfrac{w(w-1)}{(b+w)(b+w-1)}

Case 2: both balls are black

The exact same logic leads to a probability of

\dfrac{b}{b+w}\cdot \dfrac{b-1}{b+w-1}=\dfrac{b(b-1)}{(b+w)(b+w-1)}

These two events are mutually exclusive (we either pick two whites or two blacks!), so the total probability of picking two balls of the same colour is

\dfrac{w(w-1)}{(b+w)(b+w-1)}+\dfrac{b(b-1)}{(b+w)(b+w-1)}=\dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

<h2>(b)</h2>

Case 1: both balls are white.

In this case, nothing changes between the two picks. So, you have a probability of \frac{w}{b+w} of picking a white ball with the first pick, and the same probability of picking a white ball with the second pick. Similarly, you have a probability \frac{b}{b+w} of picking a black ball with both picks.

This leads to an overall probability of

\left(\dfrac{w}{b+w}\right)^2+\left(\dfrac{b}{b+w}\right)^2 = \dfrac{w^2+b^2}{(b+w)^2}

Of picking two balls of the same colour.

<h2>(c)</h2>

We want to prove that

\dfrac{w^2+b^2}{(b+w)^2}\geq \dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

Expading all squares and products, this translates to

\dfrac{w^2+b^2}{b^2+2bw+w^2}\geq \dfrac{w^2+b^2-b-w}{b^2+2bw+w^2-b-w}

As you can see, this inequality comes in the form

\dfrac{x}{y}\geq \dfrac{x-k}{y-k}

With x and y greater than k. This inequality is true whenever the numerator is smaller than the denominator:

\dfrac{x}{y}\geq \dfrac{x-k}{y-k} \iff xy-kx \geq xy-ky \iff -kx\geq -ky \iff x\leq y

And this is our case, because in our case we have

  1. x=b^2+w^2
  2. y=b^2+w^2+2bw so, y has an extra piece and it is larger
  3. k=b+w which ensures that k<x (and thus k<y), because b and w are integers, and so b<b^2 and w<w^2

4 0
3 years ago
The amount $180.00 is what percent greater than $135.00? 
sergiy2304 [10]

Answer:

Its Option C

Step-by-step explanation:

The difference is 180 - 135 = $45

So  it is 45 * 100 / 135  

= 33.33% greater

4 0
3 years ago
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