The answer is not applicable. theres not enough information. -fvmousskaylaa
Answer:
n + 6 = 7n
Step-by-step explanation:
"The sum of a number and six" would mean the number plus 6: n+6 and "is seven times the number" indicates that it would be equal to the product of 7 for n: 7n. According to this, the answer is that the translation of the sentence into an equation is: n+6=7n.
n − 6 = 7n is not right because the statement says the sum of a number and six.
7(n + 6) = n is not right because the statement indicates that seven multiplies n on the right side as it says seven times the number.
n = 7n + 6 is not right because the statement says the sum of a number and six which would be on the left side and that this would be equal to seven for n.
Answer:
Mean = 35
Variance = 291.7
Step-by-step explanation:
Data provided in the question:
X : 1, 2, 3, 4, 5, 6
All the data are independent
Thus,
The mean for this case will be given as:
Mean, E[X] = ![\frac{\textup{Sum of all the observations}}{\textup{Total number of observations}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7BSum%20of%20all%20the%20observations%7D%7D%7B%5Ctextup%7BTotal%20number%20of%20observations%7D%7D)
or
E[X] = ![\frac{\textup{1+2+3+4+5+6}}{\textup{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7B1%2B2%2B3%2B4%2B5%2B6%7D%7D%7B%5Ctextup%7B6%7D%7D)
or
E[X] = 3.5
For 10 days, Mean = 3.5 × 10 = 35
And,
variance = E[X²] - ( E[X] )²
Now, for this case of independent value,
E[X²] = ![\frac{1^2+2^2+3^2+4^2+5^2+6^2}{\textup{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%5E2%2B2%5E2%2B3%5E2%2B4%5E2%2B5%5E2%2B6%5E2%7D%7B%5Ctextup%7B6%7D%7D)
or
E[X²] = ![\frac{1+4+9+16+25+36}{\textup{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B4%2B9%2B16%2B25%2B36%7D%7B%5Ctextup%7B6%7D%7D)
or
E[X²] = ![\frac{91}{\textup{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B91%7D%7B%5Ctextup%7B6%7D%7D)
or
E[X²] = 15.167
Therefore,
variance = E[X²] - ( E[X] )²
or
variance = 15.167 - 3.5²
or
Variance = 2.917
For 10 days = Variance × Days²
= 2.917 × 10²
= 291.7
The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.
Data;
- Mean rate = 0.3
- x = 50
- standard deviation = ?
<h3>Poission Rule</h3>
Using poission formula,
![P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute](https://tex.z-dn.net/?f=P%28x%3Dx%29%20%3D%20%5Cfrac%7Be%5E-%5E%5Clambda%20-%20%5Clambda%5Ex%7D%7Bx%21%7D%5C%5C%5Clambda%20%3D%200.3%20per%20minute)
Let's substitute the values into the formula.
For 50 calls in 150 hours
For 150 hours = x = 0.3 * 150 = 45
![p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431](https://tex.z-dn.net/?f=p%28x%3D50%29%20%3D%20%5Cfrac%7Be%5E-%5E4%5E5%20%2A%2045%5E5%5E0%7D%7B50%21%7D%20%3D%200.0431)
b)
The probability the next call arrives after 2 hours.
![\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488](https://tex.z-dn.net/?f=%5Clambda%20%3D%200.3%20%2A%202%20%3D%200.6%5C%5Cp%28x%3D0%29%20%3D%20%5Cfrac%7Be%5E-%5E0%5E.%5E6%20%2A%200.6%5E0%7D%7B0%21%7D%20%3D%200.5488)
c)
The number of calls recieved each day is recorded for 50 consecutive days.
for 50 days;
![\lambda = 0.3 * 50 * 24 = 360](https://tex.z-dn.net/?f=%5Clambda%20%3D%200.3%20%2A%2050%20%2A%2024%20%3D%20360)
The mean = 360
The standard deviation is given as
![S.D = \sigma =\sqrt{360} = 18.974\\](https://tex.z-dn.net/?f=S.D%20%3D%20%5Csigma%20%3D%5Csqrt%7B360%7D%20%3D%2018.974%5C%5C)
The probability the sum of these 50 number is less than 356 is
![p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165](https://tex.z-dn.net/?f=p%20%3D%20%28x%20%3C%20356%29%20%3D%20z%20%3D%20%5Cfrac%7B356%20-%20360%7D%7B18.974%7D%20%3D%20-0.2108%5C%5Cp%28z%20%3C%20-0.2108%29%20%3D%200.4165)
Learn more on poission formula here;
brainly.com/question/7879375