Answer:
4
Step-by-step explanation:
Based on the given budget, <span> the income would need to be at least $1125.
Add the following budgeted expenses:
</span><span> $400
</span><span> $150
</span><span> $175
</span><span> $125
</span><span> $75
</span><span><u> +$200 </u>
</span> $1,125
Answer: 0.02x
Step-by-step explanation:
The value of the cars the salesman makes is x in this instance.
The salesman makes a 2% commission on every sale so this can be represented by multiplying 2% by the value of the cars which in this case is x.
= 2% * x
= 0.02 * x
= 0.02x
If for instance he sells $40,000 worth of cars, his commission would be:
= 0.02 * x
= 0.02 * 40,000
= $800
Answer:
0.33411
The probability that a particular criminal trial lasted atleast 24 days is 0.33411
Step-by-step explanation:
The random variable X is normally distributed with a mean of 21 and standard deviation of 7
;
X ~ N(μ = 21 ; σ = 7)
X ~ N(21, 7)
Probability that a trial lasted atleast 24 days :
P(X ≥ 24) :
The standardized score :
Z = (x - μ) / σ ; (24 - 21) / 7 ; 3 / 7 = 0.4286
Hence,
P(Z ≥ 0.4286) = 0.33411
The probability that a particular criminal trial lasted atleast 24 days is 0.33411
Answer:
![-\dfrac{463}{7}](https://tex.z-dn.net/?f=-%5Cdfrac%7B463%7D%7B7%7D)
Explanation:
Given equation: 2x² - 6x - 7 = 0
In quadratic equation: ax² + bx + c
![Sum \ of \ roots : \alpha + \beta = \dfrac{-b}{a}](https://tex.z-dn.net/?f=Sum%20%5C%20of%20%5C%20roots%20%3A%20%5Calpha%20%20%2B%20%5Cbeta%20%20%3D%20%5Cdfrac%7B-b%7D%7Ba%7D)
![product \ of \ roots : \alpha \beta = \dfrac{c}{a}](https://tex.z-dn.net/?f=product%20%5C%20of%20%5C%20roots%20%3A%20%5Calpha%20%5Cbeta%20%20%3D%20%5Cdfrac%7Bc%7D%7Ba%7D)
So, here given:
![Sum : \alpha + \beta = \dfrac{-(-6)}{2} = 3](https://tex.z-dn.net/?f=Sum%20%3A%20%5Calpha%20%20%2B%20%5Cbeta%20%20%3D%20%5Cdfrac%7B-%28-6%29%7D%7B2%7D%20%20%3D%203)
![Product : \alpha \beta = \dfrac{-7}{2} = - 3.5](https://tex.z-dn.net/?f=Product%20%3A%20%5Calpha%20%5Cbeta%20%20%3D%20%5Cdfrac%7B-7%7D%7B2%7D%20%20%3D%20-%203.5)
For finding value:
![\dfrac{\alpha^3}{\beta } + \dfrac{\beta^3 }{\alpha }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Calpha%5E3%7D%7B%5Cbeta%20%7D%20%20%2B%20%5Cdfrac%7B%5Cbeta%5E3%20%7D%7B%5Calpha%20%7D)
join fractions
![\dfrac{\alpha^4+ \beta^4}{\alpha \beta }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Calpha%5E4%2B%20%5Cbeta%5E4%7D%7B%5Calpha%20%5Cbeta%20%7D)
factor out
![\dfrac{(\alpha^2 + \beta ^2)^2 -2\alpha ^2 \beta ^2 }{\alpha \beta }](https://tex.z-dn.net/?f=%5Cdfrac%7B%28%5Calpha%5E2%20%2B%20%5Cbeta%20%5E2%29%5E2%20-2%5Calpha%20%5E2%20%5Cbeta%20%20%5E2%20%20%7D%7B%5Calpha%20%5Cbeta%20%7D)
when factored more
![\dfrac{((\alpha + \beta)^2 -2\alpha \beta )^2 -2(\alpha \beta)^2 }{\alpha \beta }](https://tex.z-dn.net/?f=%5Cdfrac%7B%28%28%5Calpha%20%2B%20%5Cbeta%29%5E2%20-2%5Calpha%20%5Cbeta%20%29%5E2%20-2%28%5Calpha%20%5Cbeta%29%5E2%20%7D%7B%5Calpha%20%5Cbeta%20%7D)
insert values inside
![\dfrac{((3)^2 -2(-3.5) )^2 -2(-3.5)^2 }{-3.5 }](https://tex.z-dn.net/?f=%5Cdfrac%7B%28%283%29%5E2%20-2%28-3.5%29%20%29%5E2%20-2%28-3.5%29%5E2%20%7D%7B-3.5%20%7D)
calculate for value
![-\dfrac{463}{7}](https://tex.z-dn.net/?f=-%5Cdfrac%7B463%7D%7B7%7D)