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Zanzabum
3 years ago
13

Three fair dice are rolled at once. Let X denote the number of dice that land with the same number of dots on top as at least on

e other die. The probability distribution for X is x 0 u 3 P ( x ) p 15 36 1 36 Find the missing value u of X. Find the missing probability p. Compute the mean of X. Compute the standard deviation of X.
Mathematics
1 answer:
adell [148]3 years ago
6 0

X can be any of 0, 2, or 3, which is to say the value of the dice are all different, 2 of them match, or all 3 are the same. So u=2.

For any probability density, the probabilities of all possible outcomes must sum to 1. This means

p+\dfrac{15}{36}+\dfrac1{36}=1\implies p=\dfrac59

The mean/expectation of X is

E[X]=\displaystyle\sum_xx\,P(X=x)=0\cdot p+2\cdot\frac{15}{36}+3\cdot\frac1{36}=\frac{11}{12}

The variance of X is

V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2

where the second moment is

E[X^2]=\displaystyle\sum_xx^2\,P(X=x)=0^2\cdot p+2^2\cdot\frac{15}{36}+3^2\cdot\frac1{36}=\frac{23}{12}

\implies V[X]=\dfrac{23}{12}-\left(\dfrac{11}{12}\right)^2=\dfrac{155}{144}

Then the standard deviation is the square root of the variance:

\sqrt{V[X]}=\dfrac{\sqrt{155}}{12}\approx1.037

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Answer:

(x,y) --> (-1, -3)

Step-by-step explanation:

Solve by elimination...

2x - 3y = 7

4x + y = -7 (times 3; so -3y and 3y cancel out)

2x - 3y = 7

12x + 3y = -21

2x = 7

12x = -21

add together...

14x = -14

x = -1

plug x into one of the original equations and solve for y...

-2 - 3y =7

-3y = 9

y = -3

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3 years ago
How do I solve for the quadratic function?
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Nat2105 [25]

Answer:

I'm sorry I don't know the equation, but she walks 3 mph.

Step-by-step explanation:

We know that the answer is asking for speed, which needs both distance and time, so we also need both. Which is where the 9 mph is used. 9 mph means its a difference. b means biking mph, w means walking mph, sooo ----->>> b=w+9, and the difference in the 1st equation is 36, which means the first equation is 4 times larger than the b=w+9, so she walked 48 miles, as well as walked 12 miles in 4 hours. Divide then distances by 4, and you get 12 miles and 3 miles in one hour. Or 12 mph & 3 mph, which fits into 12=3+9. So she walks 3 miles per hour.

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QRINC offered new employees a starting salary of $34,862 in 2013. What would a comparable starting salary have been in 2003?
Vlad1618 [11]

Complete Question

Table of Annual CPI values

2003-184.00            

2004-188.90

2005-195.3

2006-201.6

2007-207.342

2008-215.303

2009-214.537

2010-218.056

2011-224.939

2012-229.594

2013-232.957

2014-236.736

QRINC offered new employees a starting salary of $34,862 in 2013. What would a comparable starting salary have been in 2003?

Answer:

C=27535.5881128

Step-by-step explanation:

From the question we are told that

CPI for 2003(index)=2003-184.00  

CPI for 2013(index)=2013-232.957  

Starting salary in 2013 at $34,862

Generally  comparable starting salary C is given as

   C=\frac{starting salary}{CPI for 2013(index} *CPI for 2003(index)

   C=\frac{34,862}{232.957} *184

Therefore C the comparable starting salary is givrn to be

   C=27535.5881128

   C=27536 appro

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3 years ago
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Answer:

See below

Step-by-step explanation:

I assume you mean f(x) = 3(x-1)^2-4

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The minimum value is the smallest value in the range of the function. In the case of a parabola, the y-coordinate of the vertex is the minimum value. Therefore, the minimum value is y=-4.

The interval where the function is decreasing is (-\infty,1)

The interval where the function is increasing is (1,\infty)

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