All categories

1 year ago

The lion population in a certain reserve drops by 5\%5%5, percent every year. Currently, the population's size is 200200200.

Mathematics

1 answer:

EastWind [94]1 year ago

8 0

Answer:

$P(t) = 200\cdot 0.95^t$

Step-by-step explanation:

The lion population in a certain reserve drops by 5\%5%5, percent every year. Currently, the population's size is 200200200.

Write a function that gives the lion population size,

Each year, the population drops to 95% of its previous value. (100 - 5)%

That is, the population is multiplied by 0.95 each year.

Repeated multiplication is signified by an exponent.

Here, that exponent is the number of years from today (t).

<h3>There fore, The population function can be written as ...</h3><h3 /><h3> P(t) = 200·0.95^t</h3><h3> $P(t) = 200\cdot 0.95^t$ </h3>

You might be interested in

Ten turns of a wire are helically wrapped around a cylindrical tube with outside circumference 4 inches and length 9 inches. The

kari74 [83]

Answer:

b) 36 inches

Step-by-step explanation:

Length of the wire = Outside circumference of the cylindrical tube * length of the cylinder

= 4 * 9

= 36 inches

Length of the wire will be same to the surface area of the cylinder

Surface area of cylinder = circumference * length

8 0

1 year ago

A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the pr

Igoryamba

Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Random voting:

So 50% of voting yes, 50% no, so $p = 0.5$

15 members:

This means that $n = 15$

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

$p = P(X = 0) + P(X = 15)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003$

$P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003$

$p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006$

0.006% probability that the final vote count is unanimous.

7 0

1 year ago

The number of gallons of gas that were in the tank minus 9 leaves 3 gallons

erastovalidia [21]

<em><u>To solve the missing number of the original amount of gallons that were in the tank is simply by adding the two numbers we have: </u></em>

9+3= 12 gallons

<u><em>To make sure 12 was the original number, subtract 12 from 9. </em></u>

<u><em /></u>

<u><em>12-9= 3 gallons </em></u>

So your answer to your question is 12 gallons!

Hope this helped! °ω°

7 0

2 years ago

Read 2 more answers

An archway is modeled by the equation y = -2x^2 + 8x. A rod is to be placed across the archway at an angle defined by the equati

DIA [1.3K]

To solve this problem you must apply the proccedure shown below:

1. You have that the the <span>archway is modeled by the equation y=-2x^2+8x and the angle mentioned in the problem is defined by the equation x−2.23y+10.34=0.
</span>
2. Therefore, you must susbtitute y=-2x^2+8x into x−2.23y+10.34=0, as below:

x−2.23(-2x^2+8x)+10.34=0

3. When you apply the distributive property, you obtain:

x−2.23(-2x^2+8x)+10.34=0
x+4.46x^2-17.84x+10.34=0
4.46x^2-16.84x+10.34=0

4. When you solve the quadratic equation, you obtain:

x=3 units

Therefore, the answer is the option D: D. 3 units.

3 0

2 years ago

Read 2 more answers

This table shows the numbers of trucks and spare tires sold by an automobile company. The ratio of the number of trucks sold to

Pavlova-9 [17]

Answer:

y=-4+100

Step-by-step explanation:

4 0

1 year ago