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r-ruslan [8.4K]

3 years ago

13

Eli ran the width of a field, a distance of 39 meters. Then he ran the length of the field, a distance of 80 meters. Finally he

ran diagonally across it to get back to his starting point. How far did eli run? - Pythagorean theorem

1 answer:

stepladder [879]3 years ago

7 0

Answer:

I think it's 158 meters

Step-by-step explanation:

I could be wrong I'm not sure

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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

What equivalent expression for 3a + 13

andrezito [222]

Answer:

3

Step-by-step explanation:

6 0

3 years ago

[Calculus] particle at rest question. Show steps, please!

Vinvika [58]

Answer:

E

Step-by-step explanation:

We are given that a particle's position along the x-axis at time <em>t </em>is modeled by:

$x(t)=2t^3-21t^2+72t-53$

And we want to determine at which time(s) <em>t</em> is the particle at rest.

If the particle is at rest, this suggests that its velocity at that time is 0.

Since are we given the position function, we can differentiate it to find the velocity function.

So, by differentiating both sides with respect to <em>t</em>, we acquire:

$\displaystyle x^\prime(t)=v(t)=\frac{d}{dt}\big[2t^3-21t^2+72t-53\big]$

Differentiate. So, our velocity function is:

$v(t)=6t^2-42t+72$

So, we will set the velocity to 0 and solve for <em>t</em>. Hence:

$0=6t^2-42t+72$

We can divide both sides by 6:

$0=t^2-7t+12$

Factoring yields:

$(t-3)(t-4)=0$

By the Zero Product Property:

$t-3\text{ and } t-4=0$

Hence:

$t=3\text{ and } t=4$

Therefore, at the 3rd and 4th seconds, the velocity of the particle is 0, impling that the particle is at rest.

Our answer is E.

6 0

3 years ago

I think you have to use the pythagorean theorem, would like you to explain how you did it as well, thanks!

Olegator [25]

Answer:

16

Step-by-step explanation:

Pythagoras theorem states that:

In a right-angled triangle,the hypotenuse , altitude and base are related as:

$(Hypotenuse)^2=(Base)^2+(Altitude)^2$

In this question:

Hypotenuse = 20 units

Base = 12 units

Altitude = w = ?

By Pythagoras theorem:

$20^{2}=12^{2}+w^2\\w=\sqrt{400-144}=\sqrt{256}\\w=16\ units$

Hence w = 16 units.

5 0

4 years ago

Read 2 more answers

A student draws a triangle with a perimeter of 36cm. The student says the longest length is 18cm. How do you know the student is

Crazy boy [7]

The length of the first two sides of a triangle must be greater than the length of the last side. If the longest length were 18, the first two sides would be too short. 36-18=18, 18 is equal not greater than 18 which means the sum of the first two sides are too short.

6 0

4 years ago