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3 years ago

Which equations are equivalent to log 4x=3

1 answer:

6 0

I'm not sure that this is what you wanted, but the solution is x = 2500
$log(4x) = 3 \\ rule > \: log_{a}(b) = x < = > \: b = {a}^{x} \\ 4x = {10}^{3} \\ 4x = 10 \: 000 \\ x = \frac{10 \: 000}{4} \\ x = 2500$
Note: when we have no number as the logarithmic base, it is 10 by default.

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A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time student

Butoxors [25]

Answer: $(21.541,\ 23.059)$

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : $n=240$ , which is a large sample , so we apply z-test .

Sample mean : $\overline{x}=22.3$

Standard deviation : $\sigma= 6$

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.960$

Now, a confidence interval at the 95% level of confidence will be :-

$22.3\pm(1.960)\dfrac{6}{\sqrt{240}}\\\\\approx22.3\pm0.759\\\\=(22.3-0.759,\ 22.3+0.759)\\\\=(21.541,\ 23.059)$

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3 years ago

Engineering An overpass intersects two

JulijaS [17]

Answer:

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Step-by-step explanation:

4 0

3 years ago

After 5 years, a $2,450 investment is worth $3,123.75.

kondaur [170]

Answer:

5.5%

Step-by-step explanation:

To solve this problem we can use a modified version of the simple interest formula which is shown below:

$r=\frac{I}{Pt}$

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P = principal amount

t = time (years)

The first step is to find the interest gained from the investment.

$3,123.75-2,450=673.75$

Next, plug in the values into the equation:

$r=\frac{673.75}{(2,450)(5)}$ Multiply the bottom values

$r=\frac{673.75}{12,550}$ Divide the values

$r=.055$

The last step is to convert 0.055 into a percent:

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The interest rate is 5.5%

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3 years ago

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max2010maxim [7]

Kilograms would be the most appropriate way

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3 years ago

What is the zero in the quadratic function f(x)= 9x^2-54x-19?

Alex17521 [72]

Answer:

6.33... and 0.333...

Step-by-step explanation:

The quadratic formula is

$x=\frac{-b+\sqrt{b^2-4ac} }{2a}$ .

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-54)+/-\sqrt{(-54)^2-4(9)(-19)} }{2(9)}\\x=\frac{54+/-\sqrt{2916+684} }{18}$

We will now solve for the plus and the minus.

The plus,,,

$x=\frac{54+\sqrt{3600}}{18}\\x=\frac{54+60}{18}\\x=\frac{114}{18}\\x=6.3$

and the minus...

$x=\frac{54-\sqrt{3600}}{18}\\x=\frac{54-60}{18}\\x=\frac{-6}{18}\\x=-0.333...$

8 0

4 years ago