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4 years ago

"Find the tangent ratio of angle Θ. "

Mathematics

2 answers:

PSYCHO15rus [73]4 years ago

8 0

Tangent Θ = opposite / adjacent

AB = short leg = opposite = 12
AC = long leg = adjacent = 5
BC = hypotenuse = 13

tangent Θ = 12/5 ⇒⇒⇒ this is in ratio form
tanΘ = 2.4 ⇒⇒⇒ this is in decimal form

Vadim26 [7]4 years ago

6 0

Answer:

Tangent Ratio would be 12/5

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3 years ago

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Answer:

The decision rule is

Reject the null hypothesis

The test statistics is $t = -2.699$

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 15$

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The standard deviation is $s_1 = \$ 40000$

The second sample size is $n_2 = 25$

The mean at second deployment is $\= x_2 = \$ 180000$

The standard deviation is $s_2 = \$ 30 000$

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis is $H_a : \mu_1 \ne \mu_2$

The level of significance is $\alpha = 0.05$

Generally the degree of freedom is mathematically represented as

$df =n_1 + n_2 -2$

=> $df =40 -2$

=> $df =38$

Generally the pooled variance is mathematically represented as

$s_p^2 = \frac{x(n_1 -1) s_1^2 + (n_2 - 1)s_2^2}{df}$

=> $s_p^2 = \frac{(15 -1) 40000^2 + (25 - 1)30000^2}{38}$

=> $s_p^2 = 1.1579 * 10^{9}$

Generally the test statistics is mathematically represented as

$t = \frac{ \= x_1 - \= x_2 }{\sqrt{s_p [\frac{1}{n_1} + \frac{1}{n_2} ]} }$

=> $t = \frac{ 150000 - 180000 }{\sqrt{1.11579 *10^{9} [\frac{1}{15} + \frac{1}{25} ]} }$

=> $t = -2.699$

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$t_{-2.699 , 38} = 0.00516046$

Generally the p -value is mathematically represented as

$p-value = 2* t_{-2.699, 38}$

=> $p-value = 2* 0.00516046$

=> $p-value = 0.01032$

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The decision rule is

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Answer:

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3 0

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