Remember ‘difference’ refers to subtraction, so they are looking for the ‘difference’ of a a number, which is unknown, so we can use the variable ‘x.’ X-7
The term ‘at least’ refers to our greater than, less than, equal to signs
Difference of a number and 7 = x-7
Four times = (4) or •4
At least = <
-52 = Answer negative 52
Plug them all in,
x-7(4)<-52
Answer:
UNLIKELY
Step-by-step explanation:
Given that:
Probability of rolling a six with a six sided nuner cube = 1/6
Required outcome / Total possible outcomes
Number of 6 / total sides of number cube = 1/6
The probability value obtained shows that there is a chance of getting a six ; however it is possible at about once in every 6 rolls of the dice.
Hence getting a six isn't impossible but the chance is small. A probability of 1/6 is the smallest that can be obtained for any of each number on the dice. Hence, it could be said that the likelihood is 'UNLIKELY'
The answer in itself is 1/128 and here is the procedure to prove it:
cos(A)*cos(60+A)*cos(60-A) = cos(A)*(cos²60 - sin²A)
<span>= cos(A)*{(1/4) - 1 + cos²A} = cos(A)*(cos²A - 3/4) </span>
<span>= (1/4){4cos^3(A) - 3cos(A)} = (1/4)*cos(3A) </span>
Now we group applying what we see above
<span>cos(12)*cos(48)*cos(72) = </span>
<span>=cos(12)*cos(60-12)*cos(60+12) = (1/4)cos(36) </span>
<span>Similarly, cos(24)*cos(36)*cos(84) = (1/4)cos(72) </span>
<span>Now the given expression is: </span>
<span>= (1/4)cos(36)*(1/4)*cos(72)*cos(60) = </span>
<span>= (1/16)*(1/2)*{(√5 + 1)/4}*{(√5 - 1)/4} [cos(60) = 1/2; </span>
<span>cos(36) = (√5 + 1)/4 and cos(72) = cos(90-18) = </span>
<span>= sin(18) = (√5 - 1)/4] </span>
<span>And we seimplify it and it goes: (1/512)*(5-1) = 1/128</span>