Let a =107° and b=42°;
So cos 107° cos 42° + sin 107° sin 42° = cosa.cos42 + sina.sinb = cos(a-b)
and cos 107° cos 42° + sin 107° sin 42° = cos(107-42) = cos(65°)
Answer:
Step-by-step explanation:
From the given information,
Considering both cases when p = 0.5 and when p ≠ 0.5
the probability that the gambler will quit an overall winner is:
where ;
N.k = n and k = m
Hence, the probability changes to:
is p ≠ 0.5 and k/N =
is P = 0.5
Answer:
D
Step-by-step explanation:
Answer:
40%
Step-by-step explanation:
Degree representing students who prefer burgers = 144°
Percentage of students who like burger = 


Percentage of students who offered burger = 40%
The answer is: " 2 :5 " ; or, write as: " 2/5 " .
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The ratio of 'girls' to 'all students' is: "2: 5 " ; or, write as: " 2/5 ".
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Explanation:
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Given: The ratio of boys to girls is: " 3:2 " .
Problem: Find the ratio of "girls" to "all students:
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Note: This ratio of "boys to girls", which is " 3 : 2 " ;
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→ can be expressed as " 3x: 2x" ;
in which the total number of students is: " 3x + 2x " = 5x " .
→ The total number of students is represented as: " 5x " .
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→ The ratio of "girls to boys" is: "2x : 3x" .
→ {that is; the "inverse" of the ratio of "boys to girls"} ;
→ {that is; the "inverse" of " 3x: 2x" } ; → which is: " 2x : 3x " .
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The ratio of "girls" to "all students" is: "2x : 5x " ; or " 2x/5x " ;
→ Both "x" values cancel ; {since: " x/x = 1 "} ;
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→ and we have the answer: " 2 :5 " ; or, write as: " 2/5 " .
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The ratio of 'girls' to 'all students' is: " 2 :5 " ; or, write as: " 2/5 ".
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