Principle: Law of Exponents - Combination of product to a power & power to a power. The first is when raising a product of two integers to a power, the power is distributed to each factor. In equation it is,
(xy)^a = (x^a)(y^a)
The latter is when raising the base with a power to a power, the base will remain the same and the powers will be multiplied. In equation it is,
(x^a)(x^b) = x^ab
Check:
f(x) = 5*(16)^.33x = 5*(8*2)^0.33x = 5*(8^0.33x)(2^0.33x) = 5*(2^x)*(2^0.33x) = 5*(2^1.33x)
f(x) = 2.3*(8^0.5x) = 2.3*(4*2)^0.5x = 2.3*(2^x)(2^0.5x) = 2.3*(2^1.5x)
f(x) = 81^0.25x = 3^x
f(x) = 0.75*(9*3)^0.5x = 0.75*(3^x)*(3^0.5x) = 0.75*3^1.5x
f(x) = 24^0.33x = (8*3)^0.33x = (2^x)*(3^0.33x)
Therefore, the answer is third equation.
<em>ANSWER: f(x) = 81^0.25x = 3^x</em>
Answer:
Step-by-step explanation:
<R=<P=70degrees
<Q=180-70=110 degrees
Answer:
B
Step-by-step explanation:
Recall that if two functions, <em>f</em> and <em>g</em>, are inverses, then by definition:
Hence, the graph of f(g(x)) should be simply <em>y</em> = <em>x</em>.
Therefore, our answer is B, as both coordinates are equivalent for all three points.
Answer:
70 oz
Step-by-step explanation:
You know that one kitten weighs 2 lbs 4 oz. and the other ways 2 lbs 2 oz all you need to do is add that together to get 4 lbs 6 oz then convert that into lbs (1 lbs = 16 oz)
In total the 4 lbs gets you 64 oz, then you just need to add the 6 remaining oz to get 70 lbs!
Answer:
Step-by-step explanation:
We will use the binomial distribution. Let X be the random variable representing the no. of boxes Hannah buys before betting a prize.
Our success is winning the prize, p =40/100 = 0.4
Then failure q = 1-0.4 = 0.6
Hannah keeps buying cereal boxes until she gets a prize. Then n be no. times she buys the boxes.
P(X ≤ 3) = P(X=0) +P(X=1)+P(X=2)+P(X=3)
= 
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= 
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= ![(0.6)^{n}+n(0.4)(0.6)^{n-1}+[tex]\frac{n(n-1)(0.4)^{2}0.6^{n-2}}{2} +\frac{n(n-1)(n-2)0.4^{3}0.6^{n-3}}{6}](https://tex.z-dn.net/?f=%280.6%29%5E%7Bn%7D%2Bn%280.4%29%280.6%29%5E%7Bn-1%7D%2B%5Btex%5D%5Cfrac%7Bn%28n-1%29%280.4%29%5E%7B2%7D0.6%5E%7Bn-2%7D%7D%7B2%7D%20%2B%5Cfrac%7Bn%28n-1%29%28n-2%290.4%5E%7B3%7D0.6%5E%7Bn-3%7D%7D%7B6%7D)
