Answer:
26
Step-by-step explanation:
Given
4x - a ← substitute a = - 2, x = 6 into the expression
= 4(6) - (- 2) [ note - (- ) is equivalent to + ]
= 24 + 2
= 26
<h3>
Answer:</h3>
![\large\boxed{C).\,13.5\%}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BC%29.%5C%2C13.5%5C%25%7D)
<h3>
Step-by-step explanation:</h3>
In this question, we're trying to find the probability of it being cloudy and raining.
In this case, we know that:
- Probability of it being cloudy is 30%
- Probability of it raining is 25% (this is necessarily not needed)
- If it's cloud, the probability of it raining is 45%
With the information above, we can find the probability.
We know that from a 100% scale, the chance of it being cloudy is 30%.
We know that if it's cloudy, the chances of raining is 45%
To find the probability of it being cloudy and raining, we would multiply 0.3 (30%) by 0.45 (45%)
Solve:
![0.3*0.45=0.135\\\\\text{Move the decimal place two times to the right}\\\text{to turn it into a percent}\\\\\boxed{13.5\%}](https://tex.z-dn.net/?f=0.3%2A0.45%3D0.135%5C%5C%5C%5C%5Ctext%7BMove%20the%20decimal%20place%20two%20times%20to%20the%20right%7D%5C%5C%5Ctext%7Bto%20turn%20it%20into%20a%20percent%7D%5C%5C%5C%5C%5Cboxed%7B13.5%5C%25%7D)
Your answer would be C). 13.5%
<h3>
I hope this helped you out.</h3><h3>
Good luck on your academics.</h3><h3>
Have a fantastic day!</h3>
Answer:
x=1
y=s
z=1
Step-by-step explanation:
(x, y, z)=(1, 0, 1)
Substitute 0 for y
![y = e^{-2t} *sin 4t\\0 = e^{-2t} *sin 4t\\\\0 = e^{-2t} *(\frac{e^{4t}-e^{-4t}}{2j} )\\0 = e^{-2t} *(e^{4t}-e^{-4t} )\\0 = e^{-2t} *e^{4t}*(1-e^{-8t} )\\\\0 = e^{2t}*(1-e^{-8t} )\\\\\\Either \\0 = e^{2t}\\t = -inf\\or\\0 = (1-e^{-8t} )\\(e^{-8t} ) = 1\\ -8t = ln(1) =0\\t=0\\\\](https://tex.z-dn.net/?f=y%20%3D%20e%5E%7B-2t%7D%20%2Asin%204t%5C%5C0%20%3D%20e%5E%7B-2t%7D%20%2Asin%204t%5C%5C%5C%5C0%20%3D%20e%5E%7B-2t%7D%20%2A%28%5Cfrac%7Be%5E%7B4t%7D-e%5E%7B-4t%7D%7D%7B2j%7D%20%29%5C%5C0%20%3D%20e%5E%7B-2t%7D%20%2A%28e%5E%7B4t%7D-e%5E%7B-4t%7D%20%29%5C%5C0%20%3D%20e%5E%7B-2t%7D%20%2Ae%5E%7B4t%7D%2A%281-e%5E%7B-8t%7D%20%29%5C%5C%5C%5C0%20%3D%20e%5E%7B2t%7D%2A%281-e%5E%7B-8t%7D%20%29%5C%5C%5C%5C%5C%5CEither%20%20%20%5C%5C0%20%3D%20e%5E%7B2t%7D%5C%5Ct%20%3D%20-inf%5C%5Cor%5C%5C0%20%3D%20%281-e%5E%7B-8t%7D%20%29%5C%5C%28e%5E%7B-8t%7D%20%29%20%3D%201%5C%5C%20-8t%20%3D%20ln%281%29%20%3D0%5C%5Ct%3D0%5C%5C%5C%5C)
Confirming if t=0 satisfy the other equation
x = e^−2t cos 4t = e^−2(0)cos(4*0)
= e^(0)cos(0) = 1
z = e^−2t = e^−2(0) = 0
Therefore t=0 satisfies the other equation
Finding the tangent vector at t=0
![\frac{dx}{dt}=-2te^{-2t} cos4t + e^{-2t}(-4sin4t)=-2(0)e^{-2(0)} cos4(0) + e^{-2(0)}(-4sin4(0))=0\\\\ \frac{dy}{dt} =-2te^{-2t} sin4t + e^{-2t}(4cos4t)=-2(0)e^{-2(0)} sin4(0)+ e^{-2(0)(4cos4(0)) }= 1\\\\\frac{dz}{dt} = -2te^{-2t} = -2(0)e^{-2(0)} = 0](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D-2te%5E%7B-2t%7D%20cos4t%20%2B%20e%5E%7B-2t%7D%28-4sin4t%29%3D-2%280%29e%5E%7B-2%280%29%7D%20cos4%280%29%20%2B%20e%5E%7B-2%280%29%7D%28-4sin4%280%29%29%3D0%5C%5C%5C%5C%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D-2te%5E%7B-2t%7D%20sin4t%20%2B%20e%5E%7B-2t%7D%284cos4t%29%3D-2%280%29e%5E%7B-2%280%29%7D%20sin4%280%29%2B%20e%5E%7B-2%280%29%284cos4%280%29%29%20%7D%3D%201%5C%5C%5C%5C%5Cfrac%7Bdz%7D%7Bdt%7D%20%20%3D%20-2te%5E%7B-2t%7D%20%20%3D%20-2%280%29e%5E%7B-2%280%29%7D%20%20%3D%200)
The vector equation of the tangent line is
(1, 0, 1) +s(0,1,0)= (1, s, 1)
The parametric equations are:
x=1
y=s
z=1
Answer:
$1200
Step-by-step explanation:
180 divided by 9 is 20, so they earned $20 per car washed. They want to wash 60 cars, and if they wash 60 cars they would earn $1200. (60 x 20)
Answer:
3a. 7.2
3b. 0.9
4a. 7.2
4b. 2.4
5a. 104
5b. 260
hope this helps, everything in bold is the correct answer,
have an awesome day, -TJ