Answer:
The chance of rolling a number greater than 4 (a 5 and 6) is 2/6 = 1/3 after simplification. The probability it WON'T happen is 1 - 1/3 = 2/3.
The ratio of against to for is 2/3:1/3
You can further simplify this ratio by multiplying each side by 3 and yielding
2:1.
The chance of it not happening is twice as likely as it is to roll a number greater than 4
The function after the transformation has an equation of y = ∛(x - 7) + 5
<h3>How to determine the equation of the transformation?</h3>
The transformation statement is given as
"The cubic function shifts 7 units right and 5 units up."
A cubic function is represented as
y = ∛x
So, the transformations are:
- Shifts 7 units right
- Shift 5 units up
Mathematically, this can be represented as
(x, y) = (x - 7, y + 5)
So, we have the following equation
y = ∛(x - 7) + 5
Hence, the equation of the transformation is y = ∛(x - 7) + 5
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Answer:
Step-by-step explanation:
This is an geometric series.
Common ratio = second number÷ first number
To get the next number, 256 should be divide by (-4)
The three numbers are : -64 , 16 , -4
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:
Q' (-3,4)
Step-by-step explanation:
A reflection across the x-axis would mean that only the x value of the point would change. This means that the y value would still be 4. To find the x value, just flip it to a negative. The negative of 3 is -3
