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2 years ago

Please help 50 points please help hast to be right

Mathematics

1 answer:

artcher [175]2 years ago

7 0

Answer:

D, B, C; see attached

Step-by-step explanation:

You want to identify the transformations from Figure A to each of the other figures.

<h3>a. Translation</h3>

A translated figure has the same orientation (left-right, up-down) as the original figure. Figure D is a translation of Figure A. The arrow of translation joins corresponding points.

<h3>b. Reflection</h3>

A figure reflected across a vertical line has left and right interchanged. Up and down remain unchanged. Figure B is a reflection of Figure A. The line of reflection is the perpendicular bisector of the segment joining corresponding points.

<h3>c. Rotation</h3>

A rotated figure keeps the same clockwise/counterclockwise orientation, but has the angle of any line changed by the same amount relative to the axes. Figure C is a 180° rotation of Figure A. The center of rotation is the midpoint of the segment joining corresponding points. Unless the figures overlap, the center of rotation is always outside the figure.

<em>Additional comment</em>

The center of rotation is the coincident point of the perpendicular bisectors of the segments joining corresponding points on the figure. It will be an invariant point, so will only be on or in the figure of the figures touch or overlap. In the attachment, the center of rotation is shown as a purple dot.

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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

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

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

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

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

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topjm [15]

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Box #1
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Dafna1 [17]

6.11

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makvit [3.9K]

Answer:

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Step-by-step explanation:

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dexar [7]

Answer:

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