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bija089 [108]
3 years ago
8

Jason bought 10 of the 30 raffle tickets for a drawing. What is the probability that Jason will win all 3 of the prizes if once

a raffle ticket wins a prize it is thrown away?
Mathematics
2 answers:
lyudmila [28]3 years ago
6 0
10/30) x (9/29) x (8/28)  =  720 / 24,360

                                                             =  6 / 203  =  2.96 percent (rounded)   
Yuliya22 [10]3 years ago
6 0

Answer:  The required probability that Jason wins all the 3 prizes is 2.96%.

Step-by-step explanation:  Given that Jason bought 10 of the 30 raffle tickets for a drawing.

We are to find the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away.

Let S denote the sample space for the experiment of drawing 3 tickets from 30 raffle tickets and A denote the event that Jason wins all the 3 prizes.

Since a raffle ticket is thrown away once it wins a prize, so

n(S)=^{30}P_3=\dfrac{30!}{(30-3)}=\dfrac{30!}{27!}=\dfrac{30\times29\times28\times27!}{27!}=24360,\\\\\\n(A)=^{10}P_3=\dfrac{10!}{(10-3)!}=\dfrac{10!}{7!}=\dfrac{10\times9\times8\times7!}{7!}=720.

Therefore, the probability of event A is given by

P(A)=\dfrac{n(A)}{n(S)}=\dfrac{720}{24360}=0.029955=2.96\%.

Thus, the required probability that Jason wins all the 3 prizes is 2.96%.

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Kryger [21]

Answer:

1)

Given the triangle RST with Coordinates  R(2,1), S(2, -2) and T(-1 , -2).

A dilation is a transformation which produces an image that is the same shape as original one, but is different size.  

Since, the scale factor \frac{5}{3} is greater than 1, the image is enlargement or a stretch.  

Now, draw the dilation image of the triangle RST with center (2,-2) and scale factor \frac{5}{3}

Since, the center of dilation at S(2,-2) is not at the origin, so the point S and its image S{}' are same.

Now, the distances from the center of the dilation at point S to the other points R and T.  

The dilation image will be\frac{5}{3} of each of these distances,

SR=3, so S{}'R{}'=5 ;


ST=3, so S{}'T{}'=5  

Now, draw the image of RST i.e R'S'T'

Since, RT=3\sqrt{2} [By using hypotenuse of right angle triangle] and R{}'T{}'=5\sqrt{2}.


2)

(a)

Disagree with the given statement.

Side Angle Side postulate (SAS) states that:

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then these two triangles are congruent.

Given: B is the midpoint of \overline{AC} i.e \overline{AB}\cong \overline{BC}

In the triangle ABD and triangle CBD, we have

\overline{AB}\cong \overline{BC}   (SIDE)            [Given]

\overline{BD}\cong \overline{BD}   (SIDE)            [Reflexive post]

Since, there is no included angle in these triangles.

∴ \Delta ABD is not congruent to \Delta CBD .

Therefore, these triangles does not follow the SAS congruence postulates.

(b)

SSS(SIDE-SIDE-SIDE) states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Since it is also given that  \overline{AD}\cong \overline{CD}.

therefore, in the triangle ABD and triangle CBD, we have

\overline{AB}\cong \overline{BC}   (SIDE)            [Given]

\overline{AD}\cong \overline{CD}   (SIDE)           [Given]

\overline{BD}\cong \overline{BD}   (SIDE)            [Reflexive post]

therefore by, SSS postulates \Delta ABD\cong \Delta CBD.

3)

Given that:  \angle1=\angle 3 are vertical angles, as they are formed by intersecting lines.

Therefore

, by the definition of linear pairs

\angle 1 and \angle 2 and \angle 3  and \angle 2 are linear pair.

By linear pair theorem, \angle 1 and \angle 2   are supplementary, \angle 2 and \angle 3  are supplementary.

m\angle1+m\angle 2=180^{\circ}

m\angle2+m\angle 3=180^{\circ}

Equate the above expressions:

m\angle 1+m\angle 2=m\angle 2+m\angle 3

Subtract the angle 2 from both sides in the above expressions

∴m\angle 1=m\angle 3

By Congruent Supplement theorem: If two angles are supplements of the same angle, then the two angles are congruent.


therefore, \angle 1\cong \angle 3.















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