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4 years ago

Solve the triangle: b=200, c=250, A=75 degrees.

Mathematics

1 answer:

ValentinkaMS [17]4 years ago

6 0

Answer:

see below

Step-by-step explanation:

You can use the law of sines to choose the correct answer:

b/c = sin(B)/sin(C) ≈ 0.8

For the first answer choice,

sin(44.3)/sin(60.7) ≈ 0.8009 . . . . . . as close as you expect to get

____

The second answer choice has the wrong ratio of sines.

The third answer choice has B > C, which it cannot be since b < c.

_____

The law of cosines can be used to find "a":

a^2 = b^2 + c^2 -2bc·cos(A) = 102500-100000cos(75°) ≈ 76,618

a ≈ √76618 ≈ 276.8 . . . . . . matches the first answer choice

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Teen Court is a juvenile diversion program designed to circumvent the formal processing of first-time juvenile offenders within

valentinak56 [21]

Answer:

Z-statistic = 1.4017 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

The data suggest that the true proportion of Teen Court individuals who recidivate during the specified follow-up period differs from the proportion of Department of Juvenile Services individuals

Step-by-step explanation:

Step(i):-

Given first sample size (n₁ ) = 57

Of the 57 Teen Court individuals, 18 subsequently recidivated during the 18-month follow-up period

First sample proportion

$p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{18}{57} =0.3157$

Second sample proportion

$p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{11}{54} =0.2037$

Null Hypothesis : p₁⁻ = p₂⁻

Alternative Hypothesis : p₁⁻ ≠ p₂⁻

Step(ii):-

Test statistic

$Z = \frac{p_{1} ^{-} -p^{-} _{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }$

where

$P = \frac{n_{1}p^{-} _{1} +n_{2} p^{-} _{2} }{n_{1} +n_{2} }$

$P = \frac{57 X0.3157+0.2037X54}{54+57} = 0.2612$

Q = 1 - P = 1 - 0.2612 = 0.7387

$Z = \frac{0.3157-0.2037}{\sqrt{0.2612 X0.7387 (\frac{1}{57} +\frac{1}{54} )} }$

Z = 1.4017

Level of significance ∝ =0.05

The tabulated value Z₀.₀₅ = 1.96

Z-statistic = 1.4017 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

The data suggest that the true proportion of Teen Court individuals who recidivate during the specified follow-up period differs from the proportion of Department of Juvenile Services individuals

7 0

3 years ago

21. A linear function g(x) passes through the points (3, -1) and (-6, -4). What is the y-intercept of the function? Write the so

choli [55]

Answer:

the y-intercept is -2 or (0, -2)