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Nezavi [6.7K]
3 years ago
15

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they

charged a total of $775
. What was the rate charged per hour by each mechanic if the sum of the two rates was $100 per hour?
Mathematics
1 answer:
almond37 [142]3 years ago
5 0

Answer:

102 an hour

Step-by-step explanation:

all you do is add all of them together

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Find the mean, variance &a standard deviation of the binomial distribution with the given values of n and p.
MrMuchimi
A random variable following a binomial distribution over n trials with success probability p has PMF

f_X(x)=\dbinom nxp^x(1-p)^{n-x}

Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.

\displaystyle\sum_xf_X(x)=\sum_{x=0}^n\binom nxp^x(1-p)^{n-x}=1

The mean is given by the expected value of the distribution,

\mathbb E(X)=\displaystyle\sum_xf_X(x)=\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle\sum_{x=1}^nx\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle\sum_{x=1}^n\frac{n!}{(x-1)!(n-x)!}p^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}
\mathbb E(X)=\displaystyle np\sum_{x=0}^n\frac{(n-1)!}{x!((n-1)-x)!}p^x(1-p)^{(n-1)-x}
\mathbb E(X)=\displaystyle np\sum_{x=0}^n\binom{n-1}xp^x(1-p)^{(n-1)-x}
\mathbb E(X)=\displaystyle np\sum_{x=0}^{n-1}\binom{n-1}xp^x(1-p)^{(n-1)-x}

The remaining sum has a summand which is the PMF of yet another binomial distribution with n-1 trials and the same success probability, so the sum is 1 and you're left with

\mathbb E(x)=np=126\times0.27=34.02

You can similarly derive the variance by computing \mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2, but I'll leave that as an exercise for you. You would find that \mathbb V(X)=np(1-p), so the variance here would be

\mathbb V(X)=125\times0.27\times0.73=24.8346

The standard deviation is just the square root of the variance, which is

\sqrt{\mathbb V(X)}=\sqrt{24.3846}\approx4.9834
7 0
3 years ago
Which phrases can be used to represent the inequality 12-3x≥9? Check all that apply. (multi choice)
balandron [24]

Answer:

Which phrases can be used to represent the inequality 12-3x≥9? Check all that apply. (multi choice)

<u> A Twelve less than three times a number is greater than or equal to nine. </u>

B Twelve less than three times a number is at least nine.

C Twelve less three times a number is at least nine.

D Twelve minus the product of three and a number is no more than nine.

E Twelve less three times a number is at most nine.

F Twelve minus the product of three and a number is no smaller than nine.

G Twelve minus the product of three and a number is larger than nine.

Step-by-step explanation:

12 - 3x>=9

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Take 38,000 minus 6,840 and then you got your answer 
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Step-by-step explanation:

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Please help!!! It's a quiz
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Answer: 3,2.50)

Step-by-step explanation:

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