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2 years ago

In TUV the measure of V=90 TU=88 and UV=43 feet. Find the measure of T to the nearest tenth of a degree

Mathematics

2 answers:

Nimfa-mama [501]2 years ago

6 0

Answer:

29.3

Step-by-step explanation:

T=29.251\approx 29.3^{\circ}

T=29.251≈29.3

ps. i just did it

LekaFEV [45]2 years ago

5 0

Answer:

m∠T = 27.9°

Step-by-step explanation:

Use the law of cosines

$UV^{2} = TU^{2} + UV^{2} - 2(TU)(UV)cos T\\43^{2} = 88^{2} + 90^{2} - 2(88)(90) cos T\\1849 = 7744 + 8100 - 15840 cos T\\1849 = 15844 - 15840 cos T\\-13995 = - 15840 cos T\\cos T = \frac{-13995}{-15840} = .883522...\\T = arccos .883522... = 27.9$

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<em>The question is incomplete:</em>

<em>The significance level is 0.05.</em>

<em>Brand X: 91, 100, 88, 89</em>

<em>Brand Y: 99, 96, 94, 99</em>

<em>Brand Z: 83, 88, 89, 76</em>

We have to check if there is a significant difference between the absorbency rating of each brand.

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$H_0:\mu_x=\mu_y=\mu_z$

Alternative hypothesis: the means are not equal

$H_a: \mu_x\neq\mu_y\neq\mu_z$

We have to apply a one-way ANOVA

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$s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33$

Then, we calculate the mean standard error (MSE):

$MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78$

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

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The MSB is then:

$s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172$

Now we calculate the F statistic as:

$F=MSB/MSE=172/23.78=7.23$

The degrees of freedom of the numerator are:

$dfn=a-1=3-1=2$

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$dfd=N-a=3*4-3=12-3=9$

The P-value of F=7.23, dfn=2 and dfd=9 is:

$P-value=P(F>7.23)=0.01342$

As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

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In TUV the measure of V=90 TU=88 and UV=43 feet. Find the measure of T to the nearest tenth of a degree​

In TUV the measure of V=90 TU=88 and UV=43 feet. Find the measure of T to the nearest tenth of a degree