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VMariaS [17]
3 years ago
6

A landscaper makes a $2,000 profit in a week when he services 25 lawns. He makes a $600 profit in a week when he services 11 law

ns. If his profit for the week is a linear function of the number of lawns serviced, how much profit would he recieve in a week that he services 36 lawns?
Mathematics
1 answer:
SOVA2 [1]3 years ago
8 0
2000 - 600 = 1400
-------------- 
25 - 11 = 14

100 dollars per 1 lawn. 

36 * 100 = 3,600 

He will earn $3,600.
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A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average
marysya [2.9K]

Answer:

a) player’s expected payoff is $ 240

b) probability the player loses $1000 or more is 0.1788

c)  probability the player wins is 0.3557

d) probability of going broke is 0.0594

Step-by-step explanation:

Given:

Since there are 60 hands per hour and the player plays for four hours then the sample size is:

n = 60 * 4 = 240

The player’s strategy provides a probability of .49 of winning on any one hand so the probability of success is:

p = 0.49

a)

Solution:

Expected payoff is basically the expected mean

Since the bet is $50 so $50 is gained when the player wins a hand and $50 is lost when the player loses a hand. So

Expected loss =  μ

                        = ∑ x P(x)

                        = 50 * P(win) - 50 * P(lose)

                        = 50 * P(win) + (-50) * (1 - P(win))

                         = 50 * 0.49 - 50 * (1 - 0.49)

                        = 24.5 - 50 ( 0.51 )

                        = 24.5 - 25.5

                        = -1

Since n=240 and expected loss is $1 per hand then the expected loss in four hours is:

240 * 1 = $ 240

b)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 110.5 - 117.6 / √117.6(1-0.49)

  = −7.1/√117.6(0.51)

  = −7.1/√59.976

  = −7.1/7.744417

  =−0.916789

Here the player loses 1000 or more when he loses at least 130 of 240 hands so the wins is 240-130 = 110

Using normal probability table:

P(X≤110) = P(X<110.5)

             = P(Z<-0.916)

             = 0.1788

c)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 120.5 - 117.6 / √117.6(1-0.49)

  = 2.9/√117.6(0.51)

  = 2.9/√59.976

  = 2.9/7.744417

  =0.374463

Here the player wins when he wins at least 120 of 240 hands

Using normal probability table:

P(X>120) = P(X>120.5)

              = P(Z>0.3744)  

             =  1 - P(Z<0.3744)

             = 1 - 0.6443

             = 0.3557

d)

Player goes broke when he loses $1500

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 105.5 - 117.6 / √117.6(1-0.49)

  = -12.1/√117.6(0.51)

  = -12.1/√59.976

  = -12.1/7.744417

  =−1.562416

Here the player loses 1500 or more when he loses at least 135 of 240 hands so the wins is 240-135 = 105

Using normal probability table:

P(X≤105) = P(X<105.5)

             = P(Z<-1.562)

             = 0.0594

7 0
3 years ago
1-cos^2 A / sec^2 A - tan^2 A
tiny-mole [99]
I hope this helps you



✔cos^2A+sin^2A=1


✔1-cos^2A=sin^2A

✔cos2A=cos^2A-sin^2A

✔sin2A=2.sinA.cosA


secA=1/cosA


tgA=sinA/cosA


sin^2A/1/cos^2A-sin^2A/cos^2A


sin^2A.cos^2A/cos2A

2.sin^2A.cos^2A/cos2A


sin2A.2.sin2A/cos2A


tg2A.2.sin2A


6 0
2 years ago
A man invest 5,200,part at 4% and the balance at 3%. If his total income for the two investments is $194,how much money did he i
Fed [463]

Let the amount invested at 4% be = x

Let the amount invested at 3% be = y

Given is:

x+y=5200 or x=5200-y  .... (1)

As, total income for the two investments is $194, so equation is:

0.04x+0.03y=194   ....(2)

Putting value of x from (1) in (2)

0.04(5200-y)+0.03y=194

208-0.04y+0.03y=194

0.01y=14

y=1400

And x=5200-y

x=5200-1400=3800

Hence, money invested at 4% is $3800 and money invested at 3% is $1400

6 0
2 years ago
the cost of plastering a wall of a room having length 8m and heights 4m at 4s 15 per m² is rs 1560 . find the cost of carpeting
Virty [35]

Answer:

Here,

length = 8m

height = 4m

4s = 15 per m^2

Now,

300 per meter = 300 * 15 per m^2

= 4500 per m^2

4 0
3 years ago
intrun depozit sunt 240 t de cereale in prima zi se scoate a cincea parte din cantitateiar a doua zi se scoate o sesime din rest
Alex73 [517]
Cat is out on the first day: 
<span>240: 5 = 48 t </span>

<span>What remains after you take it out on day 48 t </span>

<span>240-48 = 192 t </span>

<span>Cat is out in the next </span>
<span>192 6 = 32t </span>

<span>What remains after you take it out 32 t of the day? </span>
<span>192-32 = </span>160t<span>
</span>
7 0
3 years ago
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