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2 years ago

In the given figure AB||CD, then find the measurements of the angles 1 and 2.

Mathematics

2 answers:

svetlana [45]2 years ago

4 0

Answer:

1 = 112°

2 = 106°

Step-by-step explanation:

Because a straight line's angle equals up to 180°, all we have to do is subtract 180° by the two parallel angle given in CD. Because both lines are congruent, we can use those numbers to find out the value of angle 1 and 2.

leonid [27]2 years ago

3 0

$\bf \underline{★Solution-} \\$

First, we should find the angles marked as x and y.

We know that the corresponding angles measure the same. So,

$\sf \leadsto x = {75}^{\circ}$

$\sf \leadsto y = {68}^{\circ}$

Now, we can find the values of the first and second angles.

Measurement of first angle :

$\sf \leadsto Straight \: line \: angle = {180}^{\circ}$

$\sf \leadsto y + \angle{1} = {180}^{\circ}$

$\sf \leadsto {68}^{\circ} + \angle{1} = {180}^{\circ}$

$\sf \leadsto \angle{1} = 180 - 68$

$\sf \leadsto \angle{1} = {112}^{\circ}$

Measurement of second angle :

$\sf \leadsto x + \angle{2} = {180}^{\circ}$

$\sf \leadsto {75}^{\circ} + \angle{2} = {180}^{\circ}$

$\sf \leadsto \angle{2} = 180 - 75$

$\sf \leadsto \angle{2} = {105}^{\circ}$

Hence, the values of first and second angle is 112° and 105° respectively.

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3 years ago

What is the probability that you get two even numbers if you roll two dice?

RoseWind [281]

Answer:

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Step-by-step explanation:

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3 years ago

A journal article reports that a sample of size 5 was used as a basis for calculating a 95% CI for the true average natural freq

oksano4ka [1.4K]

Answer:

$Lower = 231.134- 3.098=228.036$

$Upper = 231.134+ 3.098=234.232$

Step-by-step explanation:

Previous concepts

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=5 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case we know that the 95% confidence interval is given by:

$\bar X=\frac{233.002 +229.266}{2}= 231.134$

And the margin of error is given by:

$ME = \frac{233.002 -229.266}{2}= 1.868$

And the margin of error is given by:

$ME= t_{\alpha/2} \frac{s}{\sqrt{n}}$

The degrees of freedom are given by:

$df = n-1 = 5-1=4$

And the critical value for 95% of confidence is $t_{\alpha/2}= 2.776$

So then we can find the deviation like this:

$s = \frac{ME \sqrt{n}}{t_{\alpha/2}}$

$s = \frac{1.868* \sqrt{5}}{2.776}= 1.506$

And for the 99% confidence the critical value is: $t_{\alpha/2}= 4.604$

And the margin of error would be:

$ME = 4.604 *\frac{1.506}{\sqrt{5}}= 3.098$

And the interval is given by:

$Lower = 231.134- 3.098=228.036$

$Upper = 231.134+ 3.098=234.232$

6 0

3 years ago

What is the surface area of this rectangular pyramid?

Alexxx [7]

Answer:

304m^2

Step-by-step explanation:

First find the surface area of the base by multiplying the length by the width.

(12m) (8m)= 96m^2

Second, find the surface area of the front and back triangles using the formula <em>1/2 (base) (height)</em>. Use the length for the base.

1/2 (12m) (10m)= 60m^2

Next, find the surface area of the side triangles using the formula <em>1/2 (base) (height). </em>Use the width as the base.

1/2 (8m) (11m)= 44m^2

Last, add the surface area of each section. Make sure you add the area of each face.(we only solved for 1 of the front/ back triangles and 1 of the side triangles) To make it easier to understand I wrote out an equation to show how I added the surface areas.

base=a, front/ back triangles= b, side triangles=c

SA= a + 2b +2c or SA= a +b +b +c +c

Using one of the equations above solve for the total surface area.

SA= (96m^2) + (60m^2) +(60m^2) +(44m^2) +(44m^2)

SA= (96m^2) + 2(60m^2) +2(44m^2)

SA= (96m^2) +(120m^2) +(88m^2)

SA= 304m^2

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3 years ago

The radius of a circle is 9 yards. What is the circle's area?

max2010maxim [7]

Answer:

area of the circle is 254.47yd^2

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3 years ago

In the given figure AB||CD, then find the measurements of the angles 1 and 2.​

In the given figure AB||CD, then find the measurements of the angles 1 and 2.