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2 years ago

Can a triangle have sides with the given lengths? Explain. a = 6 yd, b = 9 yd, c = 11 yd

Mathematics

1 answer:

RideAnS [48]2 years ago

3 0

Answer:

Step-by-step explanation:

Use the cosine rule and see if the numbers hold true. a^2 = b^2 + c^2 - (2bc (cos x))

By substituting in our values I get that cos x = 0.838... which is possible. If cos x would equal 1.5, the there is no solution and the triangle would not be possible.

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Step-by-step explanation:

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2 years ago

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3 years ago

Is the collection of US museums well-defined and therefore is not a set

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3 years ago

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2 years ago

When 258 college students are randomly selected and surveyed, it is found that 106 own a car. Find a 99% confidence interval for

juin [17]

Answer: 0.332 < p < 0.490

Step-by-step explanation:

We know that the confidence interval for population proportion is given by :-

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where n= sample size

$\hat{p}$ = sample proportion

z* = critical z-value.

As per given , we have

n= 258

Sample proportion of college students who own a car = $\hat{p}=\dfrac{106}{258}\approx0.411$

Critical z-value for 99% confidence interval is 2.576. (By z-table)

Therefore , the 99% confidence interval for the true proportion(p) of all college students who own a car will be : $0.411\pm (2.576)\sqrt{\dfrac{0.411(1-0.411)}{258}}\\\\=0.411\pm (2.576)\sqrt{0.00093829}\\\\= 0.411\pm (2.576)(0.0306315197142)\\\\=0.411\pm 0.0789=(0.411-0.0789,\ 0.411+0.0789)\\\\=(0.3321,\ 0.4899)\approx(0.332,\ 0.490)$

Hence, a 99% confidence interval for the true proportion of all college students who own a car : 0.332 < p < 0.490

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2 years ago