Y>2 is the 1st one. x>-4 is the 3rd one. Write the inequality. 1. 3, 2. 3
Answer:
Step-by-step explanation:
Given function is,
f(x) = ![\sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D)
If the given function is vertically stretched by a scale factor of
Or 1.5,
Transformed function will be,
h(x) = ![\frac{3}{2}[f(x)]](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%5Bf%28x%29%5D)
h(x) = ![\frac{3}{2}(\sqrt{x})](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%28%5Csqrt%7Bx%7D%29)
Further function 'h' is shifted 1 units upwards,
g(x) = h(x) + 1
g(x) = ![\frac{3}{2}(\sqrt{x} )+1](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%28%5Csqrt%7Bx%7D%20%29%2B1)
Domain of the function → x ≥ 0 Or [0, ∞)
Range of the function → y ≥ 1 Or [1, ∞)
Transformations done → Parent function f(x) is vertically stretched by a scale factor of
then shifted 1 unit upward.
Answer:
![\frac{10}{53 \times 46 \times 26}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B53%20%5Ctimes%2046%20%5Ctimes%2026%7D%20)
Step-by-step explanation:
The probability of matching the number drawn on the gold ball is
![\frac{1}{46}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B46%7D%20)
The number of possible pairs of numbers from 1 to 53 is
![\binom{53}{2} = \frac{53 \times 52}{2} = 53 \times 26](https://tex.z-dn.net/?f=%20%5Cbinom%7B53%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B53%20%5Ctimes%2052%7D%7B2%7D%20%20%3D%2053%20%5Ctimes%2026)
Choosing 5 numbers, you are choosing 10 different pairs:
![\binom{5}{2} = \frac{5 \times 4}{2} = 10](https://tex.z-dn.net/?f=%20%5Cbinom%7B5%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B5%20%5Ctimes%204%7D%7B2%7D%20%20%3D%2010)
Therefore the probability of correctly matching the drawn pair is
![\frac{10}{53 \times 26}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B53%20%5Ctimes%2026%7D%20)
Thus, the probability of winning (matching the pair AND the gold ball) is
![\frac{10}{53 \times 46 \times 26}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B53%20%5Ctimes%2046%20%5Ctimes%2026%7D%20)