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3 years ago

F (x) = 5x + 3 What is the value of x when f(x) = 6?

Mathematics

1 answer:

lapo4ka [179]3 years ago

6 0

Answer:

The value of x when f(x) equals 6 is 3/5.

Step-by-step explanation:

In order to solve this problem, we shall start by inputting what we know.

Since the problem provides you with the value of f(x), we will input the value in the given equation.

Original Equation: f(x) = 5x + 3

New Equation: 6 = 5x + 3

Now that all known values of variables have been added to the equation, we will begin to solve.

Start by subtracting both sides of the equation by 3. This step is necessary to isolate x in order to find it's value.

6 = 5x + 3

6 - 3 = 5x + 3 - 3

3 = 5x

Next, we shall divide both side of the equation by 5. This step will allow us to isolate x and finally solve its value.

3 = 5x

3/5 = 5x/5

3/5 = x

Thus, the value of x in f(x) = 5x + 3 is 3/5.

---

To be sure your answer is correct, insert the values of both f(x) and x into the equation provided and solve like so...

f(x) = 5x + 3

6 = 5(3/5) + 3

6 = 3 + 3

6 = 6 ✅

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3 years ago

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size

julsineya [31]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

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