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3 years ago

I need steps to find the equation of the inverse of the function f(x) = log2 (9x).

Mathematics

1 answer:

Step2247 [10]3 years ago

8 0

Answer:

f⁻¹(x) = 2ˣ / 9

Step-by-step explanation:

f(x) = log₂ (9x)

y = log₂ (9x)

swap y and x: x = log₂ (9y)

solve y: 9y = 2ˣ y = 2ˣ / 9

f⁻¹(x) = 2ˣ / 9

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In a clinical trial of 268 subjects treated with a drug, 11% of the subjects reported dizziness. The margin of error is plus o

Mariulka [41]

Answer:

$\hat p =0.11$ represent the proportion estimated of subjects reported with dizziness

n = 268 represent the random sample selected

$\hat q = 1-\hat p = 1-0.11= 0.89$ represent the proportion of subjects No reported with dizziness

E= 0.04 = 4% represent the margin of error for the confidence interval

$\alpha= 1-0.90 =0.1$ and this value represent the significance level of the test or the probability of error type I

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

The confidence interval for the mean is given by the following formula:

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

The margin of error is given by:

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

$Lower= 0.11-0.04 = 0.07$

$Upper= 0.11+0.04 = 0.15$

And for this case we have the following info:

$\hat p =0.11$ represent the proportion estimated of subjects reported with dizziness

n = 268 represent the random sample selected

$\hat q = 1-\hat p = 1-0.11= 0.89$ represent the proportion of subjects No reported with dizziness

E= 0.04 = 4% represent the margin of error for the confidence interval

$\alpha= 1-0.90 =0.1$ and this value represent the significance level of the test or the probability of error type I

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John has a rectangular-shaped field whose length is 62.5 yards and width is 45.3 yards. The area of the field is ________ square

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Area = 2831.25 square yards

Perimeter =215.6 yards

EXPLANATION

The area and perimeter of a rectangular field are found using the formula for finding the area and perimeter of a rectangle respectively.

That means, area of the rectangular field is given by the formula,

$A= l\times w$

We just have to substitute
$l=62.5$ and $w= 45.3$ into the given formula and evaluate.

This implies that;

$A= 62.5\times 45.3$

This gives the area of the rectangular-shaped field to be;

$A= 2831.25$ square yards.

Now for the perimeter, we use the formula

$P=2w +2l$

Or

$P=2(w +l)$

Substituting the values for the length and width gives,

$P=2(62.5+45.3)$

$\Rightarrow P=2(107.8)$

$\Rightarrow P=215.6$

Hence the perimeter of the rectangular shaped field is 215.6 yards.

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