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3 years ago

Express in exponential form. x = logby

Mathematics

2 answers:

Lunna [17]3 years ago

6 0

X = log (base b) y
The base of the log becomes the base of the exponent.
The x and y switch.
b^x = y

shutvik [7]3 years ago

3 0

Answer:

In exponential form given equation is expressed as $b^x=y$

Step-by-step explanation:

Given equation is $x=log_b\,y$

We use the following logarithmic result,

$a^{log_a\,x}=x$

Consider,

$x=log_b\,y$

Take both to the power of b.

$b^{x}=b^{log_b\,y}$

$b^x=y$

Therefore, In exponential form given equation is expressed as $b^x=y$

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A journal article reports that a sample of size 5 was used as a basis for calculating a 95% CI for the true average natural freq

oksano4ka [1.4K]

Answer:

$Lower = 231.134- 3.098=228.036$

$Upper = 231.134+ 3.098=234.232$

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=5 represent the sample size

Solution to the problem

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case we know that the 95% confidence interval is given by:

$\bar X=\frac{233.002 +229.266}{2}= 231.134$

And the margin of error is given by:

$ME = \frac{233.002 -229.266}{2}= 1.868$

And the margin of error is given by:

$ME= t_{\alpha/2} \frac{s}{\sqrt{n}}$

The degrees of freedom are given by:

$df = n-1 = 5-1=4$

And the critical value for 95% of confidence is $t_{\alpha/2}= 2.776$

So then we can find the deviation like this:

$s = \frac{ME \sqrt{n}}{t_{\alpha/2}}$

$s = \frac{1.868* \sqrt{5}}{2.776}= 1.506$

And for the 99% confidence the critical value is: $t_{\alpha/2}= 4.604$

And the margin of error would be:

$ME = 4.604 *\frac{1.506}{\sqrt{5}}= 3.098$

And the interval is given by:

$Lower = 231.134- 3.098=228.036$

$Upper = 231.134+ 3.098=234.232$

6 0

3 years ago

28. Find the perimeter of the polygon.<br> 9 mm<br> a. 55 mm<br> b. 54 mm<br> c. 52 mm

UNO [17]

Answer:

I don't see a polygon anywhere...

6 0

3 years ago

Cquation

I am Lyosha [343]

One solution because it only has one answer that can come out if those properties. If you add the -3 to -6 it will make it 6=12 -3x. Subtract the 12 it will be -6=-3x divide by -3 and x=2

6 0

3 years ago

Find j(3x^4y^7) if j(n)=n^3

qaws [65]

Answer:

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3*x-(4*y-7)=0

STEP

Equation of a Straight Line

1.1 Solve 3x-4y+7 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x-4y+7 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/4 so this line "cuts" the y axis at y= 1.75000

y-intercept = 7/4 = 1.75000

Calculate the X-Intercept :

When y = 0 the value of x is -7/3 Our line therefore "cuts" the x axis at x=-2.33333

x-intercept = -7/3 = -2.33333

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.750 and for x=2.000, the value of y is 3.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.250 - 1.750 = 1.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 1.500/2.000 = 0.750

Geometric figure: Straight Line

Slope = 1.500/2.000 = 0.750

x-intercept = -7/3 = -2.33333

y-intercept = 7/4 = 1.75000

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3 years ago

Cal added 2 3/8 cups of raisins. Write this number as a fraction greater than 1 in simplest form.

xxTIMURxx [149]

$2\frac{3}{8}=2(\frac{8}{8}) +\frac{3}{8} = \frac{16}{8} +\frac{3}{8} = \frac{19}{8}$

8 0

3 years ago