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3 years ago

What is the value of x in the rhombus below?

Mathematics

2 answers:

GuDViN [60]3 years ago

7 0

Answer:

Option C

$21\°$

Step-by-step explanation:

we know that

The two diagonals of a rhombus are perpendicular

Let

O------> the center of the rhombus

m∠AOB= $90\°$

Remember that

The sum of the internal angles of a triangle is equal to $180\°$

therefore

in the triangle AOB

m∠AOB+m∠OAB+m∠OBA= $180\°$

substitute the values

$90\°+(2x+1)\°+(2x+5)\°=180\°$

solve for x

$(4x+6)\°=90\°$

$4x=90\°-6\°$

$x=21\°$

Maurinko [17]3 years ago

5 0

Look into my attachment

in rhombus ABCD, ∠AOB = 90°

Look at ΔAOB
the sum of inner angles = 180°
∠BAO + ∠AOB + ∠ABO = 180°
2x + 1 + 90 + 2x + 5 = 180°
4x + 96 = 180
4x = 84
x = 21

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kirza4 [7]

Answer:

a) H0: $\sigma = 1.34$

H1: $\sigma \neq 1.34$

b) $df = n-1= 10-1=9$

And the critical values with $\alpha/2=0.005$ on each tail are:

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d) For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

Step-by-step explanation:

Information provided

n = 10 sample size

s= 1.186 the sample deviation

$\sigma_o =1.34$ the value that we want to test

$p_v$ represent the p value for the test

t represent the statistic (chi square test)

$\alpha=0.01$ significance level

Part a

On this case we want to test if the true deviation is 1,34 or no, so the system of hypothesis are:

H0: $\sigma = 1.34$

H1: $\sigma \neq 1.34$

The statistic is given by:

$t=(n-1) [\frac{s}{\sigma_o}]^2$

Part b

The degrees of freedom are given by:

$df = n-1= 10-1=9$

And the critical values with $\alpha/2=0.005$ on each tail are:

$\chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589$

Part c

Replacing the info we got:

$t=(10-1) [\frac{1.186}{1.34}]^2 =7.05$

Part d

For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

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