Answer:
John can use no more than 2 GB of additional data
Step-by-step explanation:
Monthly fee = $40
Additional fee = $15 for each 1 GB of data (rounded up) over his 8 GB.
Let x be the number of additional data in GB over his 8 GB of data that comes with his plan.
Total monthly charge is
![C(x)=40+15x](https://tex.z-dn.net/?f=C%28x%29%3D40%2B15x)
It is given that monthly charge before taxes to be at most $70.
![C(x)\leq 70](https://tex.z-dn.net/?f=C%28x%29%5Cleq%2070)
![40+15x\leq 70](https://tex.z-dn.net/?f=40%2B15x%5Cleq%2070)
![15x\leq 70-40](https://tex.z-dn.net/?f=15x%5Cleq%2070-40)
![15x\leq 30](https://tex.z-dn.net/?f=15x%5Cleq%2030)
Divide both sides by 2.
![x\leq 2](https://tex.z-dn.net/?f=x%5Cleq%202)
Therefore, John can use no more than 2 GB of additional data.
<span>B. {x|–5 < x < 6} and</span>C. (–5, 6)
Answer:
A) 3/110
B) 3/110
C) 3/110
D) The order doesn’t matter as long as you are drawing out the same three colors. The probability doesn’t change.
Step-by-step explanation:
A) 3/12x3/11x4/10=36/1320= 9/330 = 3/110
B) 3/12x4/11x3/10=36/1320= 9/330 = 3/110
C) 4/12x3/11x3/10=36/1320 = 9/330 = 3/110
D) The order doesn’t matter as long as you are drawing out the same three colors. The probability doesn’t change.
I hope this helps! Have a good day (PLZ GIVE BRAINLIEST)
Answer:
![f(x)= \sin(6x)+3](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Csin%286x%29%2B3)
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
![f(x) = \sf A \sin (B(x + C)) + D](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csf%20A%20%5Csin%20%28B%28x%20%2B%20C%29%29%20%2B%20D)
- A = amplitude (height from the mid-line to the peak)
- 2π/B = period (horizontal distance between consecutive peaks)
- C = phase shift (horizontal shift - positive is to the left)
- D = vertical shift
The parent function y = sin(x) has the following:
- Amplitude (A) = 1
- Period = 2π
- Phase shift (C) = 0
- Vertical shift (D) = 0
- Mid-line: y = 0
From inspection of the given graph:
- Amplitude (A) = 1
![\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}](https://tex.z-dn.net/?f=%5Csf%20Period%3D%5Cdfrac%7B%5Cpi%7D%7B12%7D-%5Cdfrac%7B-%5Cpi%7D%7B4%7D%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D)
- Phase shift (C) = 0
- Vertical shift (D) = +3 (as mid-line is y = 3)
![\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6](https://tex.z-dn.net/?f=%5Csf%20If%5C%3APeriod%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D%20%5Cimplies%20%5Cdfrac%7B2%20%5Cpi%7D%7BB%7D%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D%5Cimplies%20B%3D6)
Substituting the values into the standard form:
![\implies f(x) =1 \sin (6(x + 0)) + 3](https://tex.z-dn.net/?f=%5Cimplies%20f%28x%29%20%3D1%20%5Csin%20%286%28x%20%2B%200%29%29%20%2B%203)
![\implies f(x) = \sin (6x) + 3](https://tex.z-dn.net/?f=%5Cimplies%20f%28x%29%20%3D%20%5Csin%20%286x%29%20%2B%203)
Therefore, the equation of the given trigonometric graph is:
![f(x)= \sin(6x)+3](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Csin%286x%29%2B3)
Answer: £245
Step-by-step explanation:
24.5 hours from wednesday to saturday
24.5 X 10 = 245