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3 years ago

Why is it important to study the environment as a system?

Mathematics

1 answer:

V125BC [204]3 years ago

4 0

Answer:

Step-by-step explanation:

Our environment is very important to us because it is where we live and share resources with other species. ... Environmental science enlightens us on how to conserve our environment in the face of increasing human population growth and anthropogenic activities that degrade natural resources and ecosystems. hope it help

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The two angles shown in the figure are supplementary. What is the value of x?

Ipatiy [6.2K]

48+6(x+1)=180°, because they are supplementary. you would then simply solve the equation for x

48+6(x+1)=180
6(x+1)=132
x+1=22
x=21

5 0

4 years ago

Read 2 more answers

Amber earned $14.50 babysitting on Saturday. On Sunday, she spent $6.95 when she purchased a movie ticket. She needed to borrow

Usimov [2.4K]

Answer:

I think the answer is B. $12.55

Step-by-step explanation:

14.50 - 6.95 = 7.55

7.55 + 5 = 12.55

8 0

3 years ago

Read 2 more answers

The n candidates for a job have been ranked 1, 2, 3,..., n. Let X 5 the rank of a randomly selected candidate, so that X has pmf

jeka57 [31]

Question:

The n candidates for a job have been ranked 1, 2, 3,..., n. Let x = rank of a randomly selected candidate, so that x has pmf:

$p(x) = \left \{ {{\frac{1}{n}\ \ x=1,2,3...,n} \atop {0\ \ \ Otherwise}} \right.$

(this is called the discrete uniform distribution).

Compute E(X) and V(X) using the shortcut formula.

[Hint: The sum of the first n positive integers is $\frac{n(n +1)}{2}$ , whereas the sum of their squares is $\frac{n(n +1)(2n+1)}{6}$

Answer:

$E(x) = \frac{n+1}{2}$

$Var(x) = \frac{n^2 -1}{12}$ or $Var(x) = \frac{(n+1)(n-1)}{12}$

Step-by-step explanation:

Given

PMF

$p(x) = \left \{ {{\frac{1}{n}\ \ x=1,2,3...,n} \atop {0\ \ \ Otherwise}} \right.$

Required

Determine the E(x) and Var(x)

E(x) is calculated as:

$E(x) = \sum \limits^{n}_{i} \ x * p(x)$

This gives:

$E(x) = \sum \limits^{n}_{x=1} \ x * \frac{1}{n}$

$E(x) = \sum \limits^{n}_{x=1} \frac{x}{n}$

$E(x) = \frac{1}{n}\sum \limits^{n}_{x=1} x$

From the hint given:

$\sum \limits^{n}_{x=1} x =\frac{n(n +1)}{2}$

So:

$E(x) = \frac{1}{n} * \frac{n(n+1)}{2}$

$E(x) = \frac{n+1}{2}$

Var(x) is calculated as:

$Var(x) = E(x^2) - (E(x))^2$

Calculating: $E(x^2)$

$E(x^2) = \sum \limits^{n}_{x=1} \ x^2 * \frac{1}{n}$

$E(x^2) = \frac{1}{n}\sum \limits^{n}_{x=1} \ x^2$

Using the hint given:

$\sum \limits^{n}_{x=1} \ x^2 = \frac{n(n +1)(2n+1)}{6}$

So:

$E(x^2) = \frac{1}{n} * \frac{n(n +1)(2n+1)}{6}$

$E(x^2) = \frac{(n +1)(2n+1)}{6}$

So:

$Var(x) = E(x^2) - (E(x))^2$

$Var(x) = \frac{(n+1)(2n+1)}{6} - (\frac{n+1}{2})^2$

$Var(x) = \frac{(n+1)(2n+1)}{6} - \frac{n^2+2n+1}{4}$

$Var(x) = \frac{2n^2 +n+2n+1}{6} - \frac{n^2+2n+1}{4}$

$Var(x) = \frac{2n^2 +3n+1}{6} - \frac{n^2+2n+1}{4}$

Take LCM

$Var(x) = \frac{4n^2 +6n+2 - 3n^2 - 6n - 3}{12}$

$Var(x) = \frac{4n^2 - 3n^2+6n- 6n +2 - 3}{12}$

$Var(x) = \frac{n^2 -1}{12}$

Apply difference of two squares

$Var(x) = \frac{(n+1)(n-1)}{12}$

3 0

3 years ago

Вычисли длину стороны ромба, если его периметр равен 14,8 dm

sergey [27]

Answer:

I dont knoww

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dnskdjskskrmrkdksskskskkssosoososs

3 0

3 years ago

4 2/3÷(-1 1/4)<br><br> A. 2.57<br> B. 7 20/21<br> C. 1/36

Anna35 [415]

2/3 divided by (-1 and 1/4)
= 2/3 divided by -3/4
= 2/3 * 4/-3
= 8/-9.
= -8/9

5 0

3 years ago