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3 years ago

11

In a chess match, a win counts as 1 point, a draw counts as ½ point, and a loss counts as 0 points. After 15 games, the winner w

as 4 points ahead of the loser. How many points did the loser have?

1 answer:

Tanzania [10]3 years ago

8 0

Answer:

The loser had 5.5 points

The he winner had 9.5 points

Step-by-step explanation:

9.5 - 5.5 = 4

5.5 + 9.5 = 15

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A company is interviewing potential employees. Suppose that each candidate is either qualified, or unqualified with given probab

stira [4]

Answer:

$P(C=1|T=1)=q(\sum_{i=15}^{20}\binom{20}{i} p^i(1-p)^{20-i})( \sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i])^{-1}$

Step-by-step explanation:

Hi!

Lets define:

C = 1 if candidate is qualified

C = 0 if candidate is not qualified

A = 1 correct answer

A = 0 wrong answer

T = 1 test passed

T = 0 test failed

We know that:

$P(C=1)=q\\P(A=1 | C=1) = p\\P(A=0 | C=0) = p$

The test consist of 20 questions. The answers are indpendent, then the number of correct answers X has a binomial distribution (conditional on the candidate qualification):

$P(X=x | C=1)=f_1(x)=\binom{20}{x}p^x(1-p)^{20-x}\\P(X=x | C=0)=f_0(x)=\binom{20}{x}(1-p)^xp^{20-x}$

The probability of at least 15 (P(T=1))correct answers is:

$P(X\geq 15|C=1)=\sum_{i=15}^{20}f_1(i)\\P(X\geq 15|C=0)=\sum_{i=15}^{20}f_0(i)\\$

We need to calculate the conditional probabiliy P(C=1 |T=1). We use Bayes theorem:

$P(C=1|T=1)=\frac{P(T=1|C=1)P(C=1)}{P(T=1)}\\P(T=1) = qP(T=1|C=1) + (1-q)P(T=1|C=0)$

$P(T=1)=q\sum_{i=15}^{20}f_1(i) + (1-q)\sum_{i=15}^{20}f_0(i)\\P(T=1)=\sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i)]$

$P(C=1|T=1)=q(\sum_{i=15}^{20}\binom{20}{i} p^i(1-p)^{20-i})( \sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i])^{-1}$

5 0

3 years ago

In 1995, Orlando, Florida, was about 175,000. At the time, the population was growing at a rate of about 2000 per year. Write an

gladu [14]

Answer:

y= 2000 * x + 175000

Step-by-step explanation:

Given is Population is 175,000

Increase in rate = 2000/year

Let x be the population in 1995 which is C= 175,000

y= Population after per year

We know the formula for slope intercept form is

y= mx + C ............... (i)

Now from the suppose values and given

m= 2000

Now putting values in equation (i) gives

y= 2000 * x + 175000

Here x is the No of years

6 0

3 years ago

Please help me out....

Agata [3.3K]

Answer:

x = 6

Step-by-step explanation:

Given that the line segment is an angle bisector then the following ratios are equal

$\frac{42}{78}$ = $\frac{6x-1}{10x+5}$ , that is

$\frac{7}{13}$ = $\frac{6x-1}{10x+5}$ ( cross- multiply )

13(6x - 1) = 7(10x +5) ← distribute parenthesis on both sides

78x - 13 = 70x + 35 ( subtract 70x from both sides )

8x - 13 = 35 ( add 13 to both sides )

8x = 48 ( divide both sides by 8 )

x = 6

7 0

3 years ago

Miriam has a bamboo plant that is 20 centimeters tall. The plant grows at a rate of 2 centimeters a week. Which recursive formul

adoni [48]

Plz help explain i think you have info missing

6 0

3 years ago

The formula for converting the temperature in Fahrenheit to degrees Celsius is given by the formula C=5/9(F-32), where c is the

nikitadnepr [17]

Answer:

(C * 9/5) + 32

Step-by-step explanation:

Basically, going from fahrenheit to celcius, you have to Deduct 32, then multiply by 5/9. So just reverse it, instead, you multiple it by the reciprocal, which is "9/5" then you add 32. Simple. :)

7 0

3 years ago