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3 years ago

Given that A=84, B=66 and a=13 solve triangle ABC. Round to the nearest hundredth.

1 answer:

5 0

In this item, we are asked to determine the sides and the angles of the given triangle ABC. We use the cosine law for the first one,

A/cos A = B/cos B

Substituting,
84 / cos 13° = 66/ cos b
The value of b is equal to 40°.

The sum of the measures of the angle in the triangle is equal to 180°
a + b + c = 180°

13 + 40 + c = 180°

c = 127°

Use again Sine Law,
B/ sinb= C / sin c

Substituting,
66/sin 13 = C/sin .
The value of c from the equation is 127.32.

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4 years ago

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never [62]

Answer:

Step-by-step explanation:

$y(t>1) = x(t) + y(t-1)\\x(t>1) = 1.2x(t-1)\\y(1) = x(1) = 100\\\\y(t>1) = 1.2x(t-1) + y(t-1)\\y(2) = 1.2x(1) + y(1) = 120+100 = 220\\y(3) = 1.2x(2) + y(2) = 144+220 = 364\\y(4) = 1.2x(3) = y(3) = 172.8+364=536.8\\$

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3 years ago

Periodically a bottling company gets complaints that their bottles are not holding enough liquid. To test this claim the bottlin

kompoz [17]

Answer:

The null hypothesis was not rejected at 1% and 5% level of significance, but was rejected at 10% level of significance.

Step-by-step explanation:

The complaints made by the customers of a bottling company is that their bottles are not holding enough liquid.

The company wants to test the claim.

Let the mean amount of liquid that the bottles are said to hold be, μ₀.

The hypothesis for this test can be defined as follows:

H₀: The mean amount of liquid that the bottles can hold is μ₀, i.e. μ = μ₀.

Hₐ: The mean amount of liquid that the bottles can hold is less than μ₀, i.e. μ < μ₀.

The p-value of the test is, p = 0.054.

Decision rule:

The null hypothesis will be rejected if the p-value of the test is less than the significance level. And vice-versa.

Assume that the significance level of the test is, α = 0.01.

The p-value = 0.054 > α = 0.01.

The null hypothesis was failed to be rejected at 1% level of

significance. Concluding that the mean amount of liquid that the

bottles can hold is μ₀.

Assume that the significance level of the test is, α = 0.05.

The p-value = 0.054 > α = 0.05.

The null hypothesis was failed to be rejected at 5% level of

significance. Concluding that the mean amount of liquid that the

bottles can hold is μ₀.

Assume that the significance level of the test is, α = 0.10.

The p-value = 0.054 < α = 0.10.

The null hypothesis will be rejected at 10% level of

significance. Concluding that the mean amount of liquid that the

bottles can hold is less than μ₀.

5 0

3 years ago

4. You draw a single card from a standard deck of cards. What is the probability

zhenek [66]

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3 0

3 years ago

You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is sign

Furkat [3]

Answer:

1. Yes, the sample data provides convincing evidence to support the claim that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37

2. The correct hypotheses are;

The null hypothesis is H₀: p ≥ p₀

The alternative hypothesis is Hₐ: p < p₀

Step-by-step explanation:

given

The null hypothesis is H₀: p ≥ p₀ where p₀ = 0.37

The alternative hypothesis is Hₐ: p < p₀

The formula for the z test is presented as follows;

$z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0 (1 - p_0)}{n}}}$

Where:

$\hat p$ = Sample proportion = 206/780 = 0.264

p₀ = Population proportion = 0.37

n = Sample size = 780

α = Significance level = 10% = 0.01

Plugging in the values, we have;

$z=\dfrac{0.264-0.37}{\sqrt{\dfrac{0.37 (1 - 0.37)}{780}}} = -6.13$

From the the z relation/computation, we have the p value = 0.000000000451

Since the p value which is 0.000000000451 is less than α, which is 0.01 we reject the null hypothesis and we fail to reject the alternative hypothesis, that is there is sufficient statistical evidence to suggest that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37.

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3 years ago