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2 years ago

Change 1.34 repeating into a fraction

1 answer:

3 0

$x=1.\overline{34}\\\\x=1.343434...\qquad|\cdot100\\\\100x=134.343434...\\\\100x-x=134.343434...-1.343434...\\\\99x=133\qquad|:99\\\\x=\dfrac{133}{99}$

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Farmer Emmet used to own 2,300 acres of farmland. However, he recently sold 28% of his farm to a residential developer.

kap26 [50]

9514 1404 393

Answer:

1656 acres left
644 acres sold
$32,200,000

Step-by-step explanation:

1. The number of acres sold is ...

28% × 2300 = 0.28 × 2300 = 644

Then the number of acres Emmet has left will be ...

2300 -644 = 1656 . . . acres left

2. Emmet sold 644 acres.

3. At $50,000 per acre, the value of the land sold was ...

$50,000 × 644 = $32,200,000 . . . . paid by the developer

5 0

2 years ago

You estimated the average rental cost of a 2 bedroom apartment in Denton. A random sample of 16 apartments was taken. The sample

Zigmanuir [339]

Answer:

The new sample size required in order to have the same confidence 95% and reduce the margin of erro to $60 is:

n=28

Step-by-step explanation:

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".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=160)$

And the distribution for $\bar X$ is:

$\bar X \sim N(\mu, \frac{160}{\sqrt{n}})$

We know that the margin of error for a confidence interval is given by:

$Me=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The next step would be find the value of $\z_{\alpha/2}$ , $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$

Using the normal standard table, excel or a calculator we see that:

$z_{\alpha/2}=\pm 1.96$

If we solve for n from formula (1) we got:

$\sqrt{n}=\frac{z_{\alpha/2} \sigma}{Me}$

$n=(\frac{z_{\alpha/2} \sigma}{Me})^2$

And we have everything to replace into the formula:

$n=(\frac{1.96(160)}{78.4})^2 =16$

And this value agrees with the sample size given.

For the case of the problem we ar einterested on Me= $60, and we need to find the new sample size required to mantain the confidence level at 95%. We know that n is given by this formula:

$n=(\frac{z_{\alpha/2} \sigma}{Me})^2$

And now we can replace the new value of Me and see what we got, like this:

$n=(\frac{1.96*160}{60})^2 =27.32$

And if we round up the answer we see that the value of n to ensure the margin of error required $Me=\pm 60$ $ is n=28.

5 0

2 years ago

A cliff diver jumps from a ledge 96 feet above the ocean with an initial upward velocity of 16 feet per second. How long will it

Nimfa-mama [501]

In my opinion it would be about 36 seconds

5 0

3 years ago

Read 2 more answers

At a local clothing store you can purchase 3 t shirts for 18.00$ at that rate how much would it cost to purchase 7 t shirts

Ksju [112]

3t shirts cost $18

1 shirt will cost 18/3t = 6/t

7t shirts will then cost = (6/t)*7t = 42

7t shirts will cost $42.00

3 0

3 years ago

If the average grade of an English class rose from 70 to 85, what is the approximate percent increase?

FrozenT [24]

Answer:

The correct answer is actually around 21%. Are you sure the question wasn't asking what the approximate percent decrease from 85 to 70 was? Because in that case it would be around 17%.

Step-by-step explanation:

6 0

2 years ago