Answer:
y = 0
Step-by-step explanation:
It is always a good idea to look at the question and make some observations about it. Here, you might observe ...
- all of the bases are powers of 3: 243 = 3^5; 9 = 3^2
- y is a factor of every exponent
The latter observation is important, because it means that when y=0, every exponential expression has a value of 1. Hence y = 0 is a solution.
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To solve the equation, you can write it in terms of powers of 3.
(3^5)^(-y) = (3^-5)^(3y)·(3^2)^(-2y)
3^(-5y) = 3^(-15y)·3^(-4y)
3^(-5y) = 3^(-19y)
-5y = -19y . . . . . . . . equating exponents; equivalent to taking log base 3
14y = 0 . . . . . . . . . . add 19y
y = 0 . . . . . . . . . . . one solution
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The rules of exponents we used are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
1/a^b = a^-b
Answer: 21/44
Step-by-step explanation:
Given that:
Bag contains :
6 red apples
6 yellow apples
Number of samples drawn = 3
Probability that sample contains more red than yellow :
Then from the three samples, red = 2 and yellow = 1 or red for all 3
Prob of RRR = (6/12)(5/11)(4/10)= 120 / 1320
Prob RRY = (6/12)(5/11)(6/10)= 150/1320
Prob RYR is (6/12)(6/11)(5/10)= 180/1320
Prob YRR is (6/12)(6/11)(5/10)=180/1320
120/1320 + 150/1320 + 180/1320 +. 180/1320 = 630/1320 =126/264 = 42/88 = 21/44
Answer:
3 ≤ w ≤ 4
Step-by-step explanation:
the statements are 3 ≤ w and 4 ≥ w ( or w ≤ 4 )
These can be combined into the single inequality
3 ≤ w ≤ 4
