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3 years ago

34 th question Plz ans fast urgent

Mathematics

1 answer:

nevsk [136]3 years ago

4 0

Answer:

(i) x = 1/2

(ii) x^-2 = (2/3)^12

Step-by-step explanation:

Part 1

Preceding from given question:

As bases are same so powers will be added as follows:

(2/3)^2x+1 + x = (3/2)^-2-x

(2/3)^3x+1 = (3/2)^-(2+x)

By inverting right fraction

(2/3)^3x+1 = (2/3)^2+x

Now both bases are same so cancel out them

3x + 1 = 2 + x

3x - x = 2 - 1

2x = 1

x = 1/2

-------------------------------------------------------------------------

Part 2

Preceding from given question:

The fraction on right will be inverted and sign will be changed

x = (3/2)^2 * (3/2)^4

Bases are same so powers will be added

x = (3/2)^6 = 729/ 64 ---------- eq1

We have to find x^-2 so

x^-2 = (729/64)^-2

by inverting to change negative sign

x^-2 = (64/729)^2

Using eq1:

x^-2 = (2/3)^12

i hope it will help you!

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Suppose the weights of tight ends in a football league are normally distributed such that σ2=400. A sample of 11 tight ends was

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Answer:

$217.636-1.96\frac{20}{\sqrt{11}}=205.817$

$217.636+1.96\frac{20}{\sqrt{11}}=229.455$

So on this case the 95% confidence interval would be given by (205.82;229.46)

Step-by-step explanation:

Assuming the following data: Weight 150 169 170 196 200 218 219 262 269 270 271

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)

$\sigma= \sqrt{400}= 20$ represent the population standard deviation

n=11 represent the sample size

Solution to the problem

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

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

In order to calculate the mean we can use the following formula:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

The mean calculated for this case is $\bar X=217.636$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$217.636-1.96\frac{20}{\sqrt{11}}=205.817$

$217.636+1.96\frac{20}{\sqrt{11}}=229.455$

So on this case the 95% confidence interval would be given by (205.82;229.46)

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