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2 years ago

Label the vertices and all the elements needed. find x

Mathematics

1 answer:

Mandarinka [93]2 years ago

4 0

The value of x would be 30 degrees.

<h3>What is the angle sum property?</h3>

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Let's consider an angle CAD be t.

In a triangle ABD

x + 90 + t = 180

t = 180 -x - 90

t = 90 - x ( by angle sum property)

Now, we know that the sum of the corresponding angle on a transversal is 180

So,

Angle A + angle D = 180

2x + t + x + x = 180

substitute the t value

2x + 90 - x + 2x = 180

3x + 90 = 180

3x = 90

x = 30 degree

Hence, the value of x would be 30 degrees.

Learn more about the triangles;

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You might be interested in

(-3/2)x - 9 = - 27 solve for x

aleksklad [387]

Answer:

x = 12

Step-by-step explanation:

Solve for x:

(-3 x)/2 - 9 = -27

Put each term in (-3 x)/2 - 9 over the common denominator 2: (-3 x)/2 - 9 = (-18)/2 - (3 x)/2:

(-18)/2 - (3 x)/2 = -27

(-18)/2 - (3 x)/2 = (-3 x - 18)/2:

(-3 x - 18)/2 = -27

Multiply both sides of (-3 x - 18)/2 = -27 by 2:

(2 (-3 x - 18))/2 = -27×2

(2 (-3 x - 18))/2 = 2/2×(-3 x - 18) = -3 x - 18:

-3 x - 18 = -27×2

2 (-27) = -54:

-3 x - 18 = -54

Add 18 to both sides:

(18 - 18) - 3 x = 18 - 54

18 - 18 = 0:

-3 x = 18 - 54

18 - 54 = -36:

-3 x = -36

Divide both sides of -3 x = -36 by -3:

(-3 x)/(-3) = (-36)/(-3)

(-3)/(-3) = 1:

x = (-36)/(-3)

The gcd of -36 and -3 is -3, so (-36)/(-3) = (-3×12)/(-3×1) = (-3)/(-3)×12 = 12:

Answer: x = 12

3 0

3 years ago

A survey is to be conducted in which a random sample of residents in a certain city will be asked whether they favor or oppose t

marshall27 [118]

Answer:

n=269 residents should be sample required to be sure that a 90% confidence interval for the proportion who favor the construction will have a margin of error no greater than 0.05

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimates proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.64})^2}=268.96$