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2 years ago

A habitat of prairie dogs can support mmm dogs at most.

Mathematics

1 answer:

Sloan [31]2 years ago

3 0

Answer:

The correct answer is p = K × x × (m - p) , where K is the constant of proportionality and x is the current population of the habitat.

Step-by-step explanation:

A habitat of prairie dogs can support m dogs at most.

Let us consider the current population of the habitat be x.

Given the condition that the habitat's population, p, grows proportionally to the product of the current population (x) and the difference between m and p.

Thus the proportional equation would look like:

p ∝ x × (m - p)

⇒ p = K × x × (m - p) , where K is the constant of proportionality.

Thus the equation describing the above mentioned relationship is given by the above equation.

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A real estate agent has 14 properties that she shows. She feels that there is a 50% chance of selling any one property during a

Ratling [72]

Answer:

91.02% probability of selling more than 4 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either it is sold, or it is not. The chance of selling any one property is independent of selling another property. 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.

In this problem we have that:

$n = 14, p = 0.5$

Compute the probability of selling more than 4 properties in one week.

Either you sell 4 or less properties in one week, or you sell more. The sum of the probabilities of these events is decimal 1. So

$P(X \leq 4) + P(X > 4) = 1$

We want to find $P(X > 4)$ . So

$P(X > 4) = 1 - P(X \leq 4)$

In which

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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

$P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.000061$

$P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.000854$

$P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056$

$P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222$

$P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611$

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.000061 + 0.000854 + 0.0056 + 0.0222 + 0.0611 = 0.0898$

Finally

$P(X > 4) = 1 - P(X \leq 4) = 1 - 0.0898 = 0.9102$

91.02% probability of selling more than 4 properties in one week.

8 0

2 years ago

Consider the polynomial function p given by p(x)=7x^3-2x^2+3x+10. Evaluate the function for p(-3). Show your work.

Norma-Jean [14]

Answer:

$p(-3)=-206$

Step-by-step explanation:

$p(-3)=7x^3-2x^2+3x+10$

$p(-3)=7(-3)^3-2(-3)^2+3(-3)+10$

$p(-3)= 7(-27)-2(9)-9+10$

$p(-3)= -189-18-9+10$

$p(-3)= -206$

In the function p(x), the leading coefficient is 7, the constant is 10, and the degree is 3.

Hope this helps!

3 0

2 years ago

Read 2 more answers

Solve each equation for the indicated variable. Please use a separate sheet of paper to show your work.

Novay_Z [31]

Go to ask rose.org they help with science and math you’ll just have to say your from Indiana for it to work they help and it’s awesome

8 0

2 years ago

Solve 8a – 15 – 6a + 3a = 85

Dafna11 [192]

Answer:

a = 20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

8a - 15 - 6a + 3a = 85

Step 2: Solve for a

Combine like terms: 5a - 15 = 85
Isolate a term: 5a = 100
Isolate a: a = 20

7 0

3 years ago

How to solve <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%28a%20-%205%29%7D%7B6%7D%20%20-%201%20%3D%200" id="TexFormula1

Anna71 [15]

Answer:

a = -1 and 6

Step-by-step explanation:

$\frac{a(a - 5)}{6} = 1$

$a(a - 5) = 6$

${a}^{2} - 5a = 6$

${a}^{2} - 5a - 6 = 0$

$(a + 1)( a- 6)$

a = -1 and a = 6

8 0

2 years ago