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Anestetic [448]
3 years ago
10

if in a triangle, measure of angle A is 71 degrees, measure of angle B is 42 degrees, and BC= 8, find AC to the nearest hundredt

h.
Mathematics
1 answer:
olasank [31]3 years ago
7 0
Length BC is opposite of angle A and AC is opposite of angle B. 

<span>Since we know one set of opposite angles and lengths and looking for the length where we know the opposite angle, we can use law of sines: </span>

<span>a / sin(A) = b / sin(B) </span>
<span>8 / sin(71) = b / sin(42) </span>
<span>b sin(71) = 8 sin(42) </span>
<span>b = 8 sin(42) / sin(71) </span>
<span>b ≈ 5.66 units (rounded to 2DP)</span>
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ohaa [14]

Answer:

Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48

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n = 6

Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484

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Part B

Confidence interval is written as sample mean ± margin of error

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Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5

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Margin of error = 3.365 × 0.16/√6 = 0.22

Confidence interval is 2.48 ± 0.22

Part C

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 2.3

For the alternative hypothesis,

H1: µ > 2.3

This is a right tailed test

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 6

Degrees of freedom, df = n - 1 = 6 - 1 = 5

t = (x - µ)/(s/√n)

Where

x = sample mean = 2.48

µ = population mean = 2.3

s = samples standard deviation = 0.16

t = (2.48 - 2.3)/(0.16/√6) = 2.76

We would determine the p value using the t test calculator. It becomes

p = 0.02

Assuming significance level, alpha = 0.05.

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Step-by-step explanation:

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3 years ago
4+8+12=3x8 the next equation is
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Answer:

True 24=24

Step-by-step explanation:

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