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3 years ago

Use the distance formula to find the distance between the points (−10,−9) and (−3,8).

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

7 0

Step-by-step explanation:

the distance can be seen as Hypotenuse of a right-angled triangle with its legs being the x and y coordinate differences.

so, we use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90 degree angle).

distance² = (-10 - -3)² + (-9 - 8)² = (-7)² + (-17)² = 49+289 =

= 338

distance = sqrt(338) = sqrt(2×169) = 13×sqrt(2) =

= 18.38477631...

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2 years ago

A random sample of 4000 college students yielded 2250 who are in favor of banning Hawaiian shirts. Estimate the true proportion

Andreas93 [3]

Answer: (0.5496, 0.5754)

Step-by-step explanation:

The confidence interval for population proportion (p) is given by :-

$\hat{p}\pm z*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$ , where $\hat{p}$ = Sample proportion , n= sample size , z*= Critical z-value.

Let p be the proportion of all college students who are in favor of banning Hawaiian shirt.

Given, A random sample of 4000 college students yielded 2250 who are in favor of banning Hawaiian shirts.

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z-value for 90% confidence level is 1.645

Now , 90% confidence interval for p would be :

$0.5625\pm (1.645)(\sqrt{\dfrac{0.5625(1-0.5625)}{4000}})$

$=0.5625\pm (1.645)(\sqrt{0.0000615234375})\\\\=0.5625\pm (1.645)(0.00784368774876)\\\\\approx0.5625\pm0.0129\\\\=(0.5625-0.0129, \ 0.5625+0.0129)\\\\=(0.5496,\ 0.5754)$

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4 years ago

Convert (4,000°) to rectangular form.

Dafna1 [17]

Answer:

x=4, y =0

Step-by-step explanation:

To convert to rectangular from, we use the formulas

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y = rsin theta

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Step-by-step explanation:

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