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svetlana [45]
3 years ago
10

The Board of Directors of a small company consists of five people. Two of those directors are considered "strong leaders". If th

ey like an idea, the entire board will agree. The three remaining directors have no influence. Three sales people are scheduled, one after another, to make a sales presentation to a single board member of the salesperson's choice. The sales people are all convincing but do not know who the "strong leaders" are. However, they will know who the previous sales person spoke to. The first sales person to find a strong leader will win the sale. Do the three sales people all have the same chance of winning the account? If not, what are the three respective probabilities for winning the account?
Mathematics
1 answer:
Pavel [41]3 years ago
7 0
1: 40%
2: 30%
3: 20%

If we know one of the succeeded, then 
1: 44.44%
2: 33.33%
3: 22.22%

If under the circumstance that they all fail to meet a strong leader, the board picks one of them at random,
1: 43.33%
2: 33.33%
3: 23.33%

The first person has a 2 in 5 chance of randomly getting a strong leader. If the first person doesn't find a strong leader, the second person has a 2/4 chance of getting a strong leader. If neither the first nor second person gets a strong leader, the third sales person has a 2/3 chance of getting a strong leader.

1: 2/5=40% Chance
2: (3/5)*(2/4)=30% Chance You have to take the probability the first rep failed to get a strong leader, then multiply by the probability the second rep gets a strong leader.
3: (3/5)*(2/4)*(2/3)=20% You have to take the probability both the other people failed, then multiply by the probability they succeeded.
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Can you help me find the volume base area latera area and total area please to this problem
krek1111 [17]

Answer:

BA = 25π,

LA = 25√2π,

TA = 25π + 25√2π,

V = 41 and 2 / 3π

Step-by-step explanation:

We need to determine the height here, as it is not given, and is quite important to us. The height is a perpendicular line segment to the radius, hence forming a 45 - 45 - 90 degree triangle as you can see. Therefore, by " Converse to Base Angles Theorem " the height should be equal in length to the radius,

( Height = 5 inches = Radius

______

Now knowing the height, let's begin by calculating the base area. By it's name, we have to find the area of the base. As it is a circle, let us apply the formula " πr^2 "

\pi r^2\\= \pi ( 5 )^2\\= 25\pi - Base Area = 25π

______

The lateral area is simply the surface area excluding the base area, the surface area having a formula of " πr^2 + πrl. " Thus, the lateral area can be calculated through the formula " πrl, " but as we are not given the slant height ( l ) we have to use another formula, l= \sqrt{r^2+h^2} -

\pi r( \sqrt{r^2+h^2} )\\= \pi( 5 )( \sqrt{5^2 + 5^2} )\\= 25\sqrt{2} \pi- Lateral Area = 25√2π

______

And the surface area is the base area + lateral area -

25\pi + 25\sqrt{2} \pi - Surface Area

______

The volume of a cone is 1 / 3rd that of a cylinder, with a simple formula of Base * height. Therefore, we can conclude the following -

1 / 3( 25\pi )( 5 )\\= 25 / 3( 5 )( \pi )\\= 41 \frac{2}{3}\pi- Volume = 41 and 2 / 3π

8 0
3 years ago
In four years, 40% of a radioactive element decays. Find its half-life. Round to one decimal place.
White raven [17]

To find the answer, use k = \frac{2.303 }{ 4} (log\frac {100 }{ 40}) , and then use the equation t=\frac{.693}{k} To find it's half life.

5 0
3 years ago
Read 2 more answers
The fox population in a certain region has a continuous growth rate of 5% per year. It is estimated that the population in the y
kvasek [131]

Answer:

P(t) = A * (1 + r)^t ;

14,922 ;

Year 2013

Step-by-step explanation:

Given the following :

Continuous growth rate(r) = 5% = 0.05

Population in year 2000 = Initial population (A) = 10,100

Time(t) = period (years since year 2000)

A)

Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).

P(t) = A * (1 + r)^t

Trying out our function for t = year 2000, t =0

P(0) = 10,100 * (1 + 0.05)^0

P(0) = 10,100 * 1.05^0 = 10,100

B.)

Use your function from part (a) to estimate the fox population in the year 2008.

Year 2008, t = 8

P(8) = 10,100 * (1 + 0.05)^8

P(8) = 10,100 * 1. 05^8

P(8) = 10,100 * 1.4774554437890625

= 14922.29

= 14,922

c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.

P(t) = A * (1 + r)^t

18400 = 10,100 * (1.05)^t

18400/10100 = 1.05^t

1.8217821 = 1.05^t

1.05^t = 1.8217821

In(1.05^t) = ln(1.8217821)

0.0487901 * t = 0.5998151

t = 0.5998151 / 0.0487901

t = 12.293787

Therefore eit will take 13 years

2000 + 13 = 2013

4 0
3 years ago
Serenity invested $2,400 in an account paying an interest rate of 3.4% compounded
Alisiya [41]

Answer:

It would take 5.9 years to the nearest tenth of a year

Step-by-step explanation:

The formula of the compound continuously interest is A = Pe^{rt} , where

  • A is the value of the account in t years
  • P is the principal initially invested
  • e is the base of a natural logarithm
  • r is the rate of interest in decimal

∵ Serenity invested $2,400 in an account

∴ P = 2400

∵ The account paying an interest rate of 3.4%, compounded continuously

∴ r = 3.4% ⇒ divide it by 100 to change it to decimal

∴ r = 3.4 ÷ 100 = 0.034

∵ The value of the account reached to $2,930

∴ A = 2930

→ Substitute these values in the formula above to find t

∵ 2930 = 2400e^{0.034t}

→ Divide both sides by 2400

∴ \frac{293}{240} = e^{0.034t}

→ Insert ㏑ in both sides

∴ ㏑(\frac{293}{240}) = ㏑(e^{0.034t})

→ Remember ㏑(e^{n}) = n

∴ ㏑(\frac{293}{240}) = 0.034t

→ Divide both sides by 0.034 to find t

∴ 5.868637814 = t

→ Round it to the nearest tenth of a year

∴ t = 5.9 years

∴ It would take 5.9 years to the nearest tenth of a year

8 0
2 years ago
The 7th grade students at Palm Coast Middle School made some apple pies for a bake sale. The school cafeteria also donated 9 pie
ratelena [41]

Answer:

19 i think

Step-by-step explanation:


5 0
3 years ago
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