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Studentka2010 [4]
3 years ago
7

Problem 3 in your textbook presents three different sample spaces for a horse race with five horses running. Let the horses be d

esignated by the letters A, B, C, D, and E. A more complete characterization of an outcome of the horse race would be to designate which horse finishes in first through fifth places
(a) Consider the sample space for the set of outcomes characterized in this way. How many such outcomes are in the sample space?
b) How many outcomes are in the event that horse A finishes first?
(c) If G is the event that horse A finishes first and H is the event that horse B does not finish second, describe in words the event GnH. How many outcomes are in this event?
Mathematics
1 answer:
KiRa [710]3 years ago
5 0

Answer:

a) 120

b) 24

c) 18

Step-by-step explanation:

part a

The sample space is defined by the rank of the horses.

Hence, 5 ranks would permute to = 5! = 120 outcomes

part b

Fixing the first position for horse A we are left with four horses and 4 positions, the position are permutated to 4! = 24 outcomes

part c

Fixing the first position for horse A we are left with four horses and 4 positions, and horse B can not finish second hence:

A _ B _ _  the rest can permute hence, 3! = 6 outcomes

A _ _ B _ the rest can permute hence, 3! = 6 outcomes

A _ _ _ B the rest can permute hence, 3! = 6 outcomes

Total outcomes is sum of 3 cases above = 18 outcomes

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Answer:

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Step-by-step explanation:

49-42= 7

7/49 can be simplified by dividing by 7

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Please help this for my pre calculus finals
dsp73

Answer:

a) It will take 17.71 years

b) It will take 17.58 years

c) I will earn $6.60 more in compound continuously

Step-by-step explanation:

a) Lets talk about the compound interest

- The formula for compound interest is A = P (1 + r/n)^(nt)

, Where:

- A = the future value of the investment, including interest

- P = the principal investment amount (the initial deposit)

- r = the annual interest rate (decimal)

- n = the number of times that interest is compounded per unit t

- t = the time the money is invested

* Lets solve the problem

∵ The money deposit is $2000

∵ The rate is 6.25%

∵ The interest is compound quarterly

∵ The future value is $6000

∴ P = 2000

∴ A = 6000

∴ r = 6.25/100 = 0.0625

∴ n = 4

∴ t = ?

∵ A = P (1 + r/n)^(nt)

∴ 6000 = 2000 (1 + 0.0625/4)^4t ⇒ divide both sides by 2000

∴ 3 = (1.015625)^4t ⇒ insert ㏑ for both sides

∴ ㏑(3) = ㏑(1.015625)^4t

∵ ㏑(a)^b = b ㏑(a)

∴ ㏑(3) = 4t ㏑(1.015625) ⇒ divide both sides by ㏑(1.015625)

∴ 4t = ㏑(3)/㏑(1.015625) ⇒ divide both sides by 4

∴ t = [㏑(3)/㏑(1.015625)] ÷ 4 = 17.71

* It will take 17.71 years

b) Lets talk about the compound continuous interest  

- Compound continuous interest can be calculated using the formula:

  A = P e^rt  

- A = the future value of the investment, including interest

- P = the principal investment amount (the initial amount)

- r = the interest rate  

- t = the time the money is invested

* Lets solve the problem

∵ The money deposit is $2000

∵ The rate is 6.25%

∵ The interest is compound continuously

∵ The future value is $6000

∴ P = 2000

∴ A = 6000

∴ r = 6.25/100 = 0.0625

∴ t = ?

∵ A = P e^rt  

∴ 6000 = 2000 e^(0.0625 t) ⇒ divide both sides by 2000

∴ 3 = e^(0.0625 t) ⇒ insert ㏑ to both sides

∴ ㏑(3) = ㏑[e^0.0625 t]

∵ ㏑(e^a) = a ㏑(e) ⇒ ㏑(e) = 1 , then ㏑(e^a) = a

∴ ㏑(3) = 0.0625 t ⇒ divide both sides by 0.0625

∴ t = ㏑(3)/0.0625 = 17.5778

* It will take 17.58 years

c) If t = 5 years

# The compound quarterly:

∵ A = P (1 + r/n)^(nt)

∴ A = 2000 (1 + 0.0625/4)^(4×5)

∴ A = 2000 (1.015625)^20 = $2727.08

# Compound continuously

∵ A = P e^(rt)

∴ A = 2000 e^(0.0625×5) = $2733.68

∴ I will earn = 2733.68 - 2727.08 = $6.60

* I will earn $6.60 more in compound continuously

5 0
3 years ago
CE
Ainat [17]

Answer:

1. Transcrie din text enunturile potrivite următoarelor afirmaţii.

a Tocănel vorbeşte şi-l înţelege pe stăpân.

b. In imaginația copilului, cocoşii de lemn au viață.

c In închipuirea lui Bănică, greierul respectă indicaţiile lui.

c is the answer

Step-by-step explanation:

4 0
2 years ago
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