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Nitella [24]
3 years ago
5

Abdul rolls a fair six-sided die and a fair four-sided die simultaneously. The sample space of all possible

Mathematics
1 answer:
gregori [183]3 years ago
4 0

Answer: 7/24

Step-by-step explanation:

Probability is the branch of mathematics that is concerned with the numerical descriptions of how likely an event will occur or how likely a proposition is true

The probability that the six-sided die is three or Abdul rolls doubles is 7/24. The calculation is attached.

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In the adjoining equilateral triangle PQR , X , Y and Z are the middle points of the sides PQ , QR and RP respectively. Prove th
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Answer:

See Below

Step-by-step explanation:

<u>Statements:</u>                                                        <u>Reasons:</u>

<u />1)\text{ } \Delta PQR\text{ is equilateral}                                        Given

2)\text{ }PQ=QR=RP                                               Definition of Equilateral

3)\text{ } X, Y, Z\text{ are the midpoints of } PQ, QR, RP       Given

4)\text{ } PX=XQ                                                        Definition of Midpoint

5)PQ=PX+XQ                                               Segment Addition

6)\text{ } PQ=2XQ                                                      Substitution

7)\text{ } QY=YR                                                        Definition of Midpoint

8)\text{ }QR=QY+YR                                               Segment Addition

9)\text{ } QR=2QY                                                       Substitution

10)\text{ } 2XQ=2QY                                                  Substitution

11)\text{ } XQ=QY                                                      Division Property of Equality

12)\text{ }  XQ=PX=QY=YR                                Transitive Property

13)\text{ } RZ=ZP                                                       Definition of Midpoint

14)\text{ } RP=RZ+ZP                                             Segment Addition

15)\text{ } RP=2RZ                                                     Substitution

16)\text{ } 2XQ=2RZ                                                   Substitution

17)\text{ } XQ=RZ                                                       Substitution

18)\text{ } XQ=PX=QY=YR=RZ=ZP            Transitive Property

19)\text{ } \angle Q\cong \angle R\cong \angle P                                             Definition of Equilateral

20)\text{ } \Delta XQY\cong \Delta YRQ \cong \Delta ZPX                          SAS Congruence

21)\text{ } XY\cong YZ\cong ZX                                           CPCTC

22)\text{ } \Delta XYZ\text{ is equilateral}                                     Equilateral Triangle Theorem

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Step-by-step explanation:

Alternate exterior angles formed when two parallel lines are cut across by the same transversal line, are said to be congruent.

Therefore, a pair of alternate exterior angles cannot have different angle measures of 130° and 50°. Rather, both alternate exterior angles should be of equal measure of degree.

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