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Molodets [167]
3 years ago
9

¿Cuántas soluciones tiene la ecuación 2 + 6 (x - 4) = 3x - 18 + 3x?

Mathematics
1 answer:
Elena-2011 [213]3 years ago
3 0

Answer:

x is undefined

Step-by-step explanation:

2 + 6(x - 4) = 3x - 18 + 3x

Open the bracket

2 + 6x - 24 = 3x - 18 + 3x

collect the like terms

6x -3x - 3x = -18 +24 - 2

0x = 4

x = 4/0

x is undefined

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The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a st
Zepler [3.9K]

Answer:

At least 75% of these commuting times are between 30 and 110 minutes

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by 100(1 - \frac{1}{k^{2}}).

In this question:

Mean of 70 minutes, standard deviation of 20 minutes.

Since nothing is known about the distribution, we use Chebyshev's Theorem.

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110 = 70 + 2*20

THis means that 30 and 110 minutes is within 2 standard deviations of the mean, which means that at least 75% of these commuting times are between 30 and 110 minutes

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The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounc
Ludmilka [50]

Answer:

\mu = 12.1\\\sigma = 0.3

a) Find the probability that the drink is less than 11.9 fluid ounces

We are supposed to find P(x<11.9)

x= 11.9

We will use z score formula :

z=\frac{x-\mu}{\sigma}

z=\frac{11.9-12.1}{0.3}

z=-0.67

Refer the z table

So, P(z<-0.67) = 0.2514

Hence the probability that the drink is less than 11.9 fluid ounces is 0.2514

b)Find the probability that the drink is between 11.6 and 11.9 fluid ounces

x= 11.6

We will use z score formula :

z=\frac{x-\mu}{\sigma}

z=\frac{11.6-12.1}{0.3}

z=-1.67

x= 11.9

We will use z score formula :

z=\frac{x-\mu}{\sigma}

z=\frac{11.9-12.1}{0.3}

z=-0.67

We are supposed to find P(11.6<x<11.9)

So, P(11.6<x<11.9)= P(x<11.9)-P(x<11.6)

P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)

Refer the z table

P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)

P(-1.67<z<-0.67)= 0.2514-0.0475

P(-1.67<z<-0.67)= 0.2039

So, the probability that the drink is between 11.6 and 11.9 fluid ounces is 0.2039.

c)Find the probability that the drink is more than 12.6 fluid ounces

We are supposed to find P(x>12.6)

x= 12.6

We will use z score formula :

z=\frac{x-\mu}{\sigma}

z=\frac{12.6-12.1}{0.3}

z=1.67

Refer the z table

P(x>12.6)=1-P(x<12.6)

P(z>1.67)=1-P(z<1.67)

P(z>1.67)=1-0.9525

P(z>1.67)=0.0475

Hence  the probability that the drink is more than 12.6 fluid ounces is 0.0475

d) Is the drink containing more than 12.6 fluid ounces an unusual event?

Since p value is less than  alpha (0.05)

Answer = No, because the probability that a drink containing more than 12.6 fluid ounces is less than 0.05, this event is not unusual.

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