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Aleksandr [31]
3 years ago
7

One of the roots of the equation 3x^2+7x−q=0 is −5. Find the other root and q.

Mathematics
1 answer:
statuscvo [17]3 years ago
3 0

Answer: The answer is \textup{The other root is }\dfrac{8}{3}~\textup{and}q=40.Step-by-step explanation:  The given quadratic equation is[tex]3x^2+7x-q=0\\\\\Rightarrow x^2-\dfrac{7}{3}x-\dfrac{q}{3}=0.

Also given that -5 is one of the roots, we are to find the other root and the value of 'q'.

Let the other root of the equation be 'p'. So, we have

p-5=-\dfrac{7}{3}\\\\\\\Rightarrow p=5-\dfrac{7}{3}\\\\\\\Rightarrow p=\dfrac{8}{3},

and

p\times(-5)=-\dfrac{q}{3}\\\\\\\Rightarrow \dfrac{8}{3}\times 5=\dfrac{q}{3}\\\\\\\Rightarrow q=40.

Thus, the other root is \dfrac{8}{3} and the value of 'q' is 40.

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A consumer survey indicates that the average household spendsμ= $185on groceries each week. The distribution of spending amounts
Vitek1552 [10]

Answer:

P(X>200)=P(\frac{X-\mu}{\sigma}>\frac{200-\mu}{\sigma})=P(Z>\frac{200-185}{25})=P(Z>0.6)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>0.6)=1-P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the average household spent of a population, and for this case we know the distribution for X is given by:

X \sim N(185,25)  

Where \mu=185 and \sigma=25

We are interested on this probability

P(X>200)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(X>200)=P(\frac{X-\mu}{\sigma}>\frac{200-\mu}{\sigma})=P(Z>\frac{200-185}{25})=P(Z>0.6)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>0.6)=1-P(z

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3 years ago
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