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3 years ago

What is the first step In solving a question with variables on both sides

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

8 0

Answer:

Identify the variable term on one side and subtract it from both sides.

Step-by-step explanation:

We assume the question relates to terms containing the variable you want to solve for.

In general, you want to rearrange the equation so there is only one term containing the variable of interest. This can be accomplished by identifying the variable term(s) on one side of the equation and subtracting that from both sides of the equation.

For example, consider ...

ax + b = cx + d

First step

Terms ax and cx are on opposite sides of the equal sign. If we're solving for x, we need to remove one of those terms. We can do that by subtracting cx from both sides of the equation:

ax -cx +b = cx -cx +d . . . . . showing the subtraction

x(a -c) +b = d . . . . . . . . . . . . .the simplified result of the subtraction

_____

Additional comment

Please note that the coefficient of the variable is now (a-c). This will be positive if the term we subtracted (cx) had the smaller of the two coefficients (c < a). While not essential, this is a convenient choice to make when choosing which term to subtract.

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If the number of professors in a college is P and the number of students is S, and there are 19 times as many students as profes

morpeh [17]

Answer:

$S =19P\\S-19P = 0$

Step-by-step explanation:

We are given the following in the question:

Let P be the number of professor and S be the student in a college.

According to the question:

There are 19 times as many students as professors.

We have to write an equation to show the given relationship between professors and students.

$S =19P\\S-19P = 0$

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Answer:

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Step-by-step explanation:

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3 years ago

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wariber [46]

Answer:

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Step-by-step explanation:

We need to use Permutation method,

$nPr= \frac{n!}{(n-r)!}$

Where n is the sample of size and r the combination considered, so

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3 years ago

The average salary of all residents of a city is thought to be about $39,000. A research team surveys a random sample of 200 res

Rina8888 [55]

Answer:

$z=\frac{40000-39000}{\frac{12000}{\sqrt{200}}}=1.179$

$p_v =2*P(z>1.179)=2*[1-P(Z$

Step-by-step explanation:

Data given and notation

$\bar X=4000$ represent the average score for the sample

$s=12000$ represent the sample standard deviation

$n=200$ sample size

$\mu_o =39000$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to apply a two tailed test.

What are H0 and Ha for this study?

Null hypothesis: $\mu = 39000$

Alternative hypothesis : $\mu \neq 39000$

Compute the test statistic

The sample size is large enough to assume the distribution for the statisitc normal. The statistic for this case is given by:

$z=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{40000-39000}{\frac{12000}{\sqrt{200}}}=1.179$

Give the appropriate conclusion for the test

Since is a two tailed test the p value would be:

$p_v =2*P(z>1.179)=2*[1-P(Z$

Conclusion

If we compare the p value and a significance level given for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, then the true population mean for the salary not differs significantly from the value of 39000.

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worty [1.4K]

it's B

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