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3 years ago

Explain how to estimate 360+231 two different ways

1 answer:

4 0

One way to estimate is by rounding to the nearest hundreds. (400 + 200), The other way is by rounding to the nearest tens (360 + 230). I hope this helped you out and answered your question! Good luck!

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the intensity, I, of light varies inversely as the square of the distance, D2 , from the light source. If I is 150 units when D

podryga [215]

$\bf \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{I} varies inversely with }\underline{D^2}}{I = \cfrac{k}{D^2}} \qquad \qquad \textit{we also know that } \begin{cases} I=150\\ D=6 \end{cases}$

$\bf 150=\cfrac{k}{6^2}\implies 150=\cfrac{k}{36}\implies 5400=k~\hfill \boxed{I=\cfrac{5400}{D^2}} \\\\\\ \textit{when I = 24, what is \underline{D}?}\qquad \qquad 24=\cfrac{5400}{D^2}\implies D^2=\cfrac{5400}{24} \\\\\\ D^2=225\implies D=\sqrt{225}\implies D=15$

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4 years ago

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galben [10]

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4 years ago

What is the solution of x2+49 = x+5?

nikklg [1K]

Answer:

x = 12/5

Step-by-step explanation:

take the square of both sides

(x^2+49) = (x+5)^2

x^2 + 49 = (x+5) (x+5)

x^2+49= x^2 + 10x + 25

10x + 25 = 49

10x = 24

x = 12/5

4 0

3 years ago

Your teacher will report the mean and standard deviation of the sampling distribution created by the class.

sukhopar [10]

Answer:

$\hat p = \frac{\sum_{i=1}^{40} \hat p_i}{40}$

$\hat p = 0.493$

And the deviation is given by this formula:

$s_{\hat p}= \frac{\sum_{i=1}^{40} (\hat p_i - \hat p)^2}{n-1}= 0.085$

And as we can see the population proportion expected for the number of heads 0.5 is very close to the mean of the sampling distribution, the error is :

$\% Error = \frac{0.5-0.493}{0.5}* 100 = 1.4\%$

Step-by-step explanation:

Assuming the data on the figure attached. We ar assuming that this is a sampling distribution of sample proportions of heads in 40 flips of a coin.

As we can see we have the following values:

0.25, 0.35, 0.375,0.375, 0.40,0.40,0.40, 0.425,0.425,0.425, 0.45,0.45,0.45,0.45, 0.475,0.475,0.475, 0.475,0.475, 0.50,0.50,0.50, 0.525,0.525,0.525,0.525, 0.55,0.55,0.55,0.55,0.55, 0.575,0.575,0.575 0.575, 0.575, 0.60,0.60, 0.65,0.65

And we can calculate the sample proportion with the following formula:

$\hat p = \frac{\sum_{i=1}^{40} \hat p_i}{40}$

$\hat p = 0.493$

And the deviation is given by this formula:

$s_{\hat p}= \frac{\sum_{i=1}^{40} (\hat p_i - \hat p)^2}{n-1}= 0.085$

And as we can see the population proportion expected for the number of heads 0.5 is very close to the mean of the sampling distribution, the error is :

$\% Error = \frac{0.5-0.493}{0.5}* 100 = 1.4\%$

4 0

3 years ago

Estimate the sum to the nearest hundreds 166+427

quester [9]

The answer to your question is 600

5 0

4 years ago

Read 2 more answers