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1 year ago

two angles form a linear pair. If one angle is 7/2 larger than the other, what is the measurement of each angle.

Mathematics

1 answer:

masha68 [24]1 year ago

5 0

The angles are 40 degrees and 140 degrees.

• In plane geometry, a figure which is created by two rays or two lines or line segments that share a common end point is known as angle.

• The two rays which are share a common point are called as sides of the angle an the common end point is called as the vertex.

• Some types of angles are acute angle, right angle, obtuse angle, straight angle and many more.

Let one angle be x

Other angle = 7/2 x

Since it is a linear pair, it’s sum will be 180 degrees.

So, x + 7/2 x = 180

9/2 x = 180

9 x = 360

X = 40

7/ 2 x = 7/2 × 40 = 140

Therefore, the angles are 40 degrees and 140 degrees.

Learn more about angles here:

brainly.com/question/25770607

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What is the area of this irregular figure knowing that the formula for the area of a rectangle is l x w.

Lubov Fominskaja [6]

9514 1404 393

Answer:

42 cm²

Step-by-step explanation:

The attachment shows a couple of ways the figure can be considered.

a) Left and Right rectangles that are 5 cm high and 3 cm wide, together with a central rectangle that is 3 cm high and 4 cm wide. Then the total area is ...

5×3 + 3×4 + 5×3 = 15 + 12 + 15 = 42 . . . . cm²

b) An enclosing rectangle that is 5 cm high and 10 cm wide with a cut-out that is 2 cm high and 4 cm wide. Then the total area is ...

5×10 -2×4 = 50 -8 = 42 . . . . cm²

The area of the irregular figure is 42 cm².

3 0

3 years ago

Again ... Commute times in the U.S. are heavily skewed to the right. We select a random sample of 500 people from the 2000 U.S.

VladimirAG [237]

Answer:

We conclude that the mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

We are given that a random sample of 500 people from the 2000 U.S. Census is selected who reported a non-zero commute time.

In this sample the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes.

Let $\mu$ = mean commute time in the U.S..

So, Null Hypothesis, $H_0$ : $\mu \geq$ 30 minutes {means that the mean commute time in the U.S. is more than or equal to half an hour}

Alternate Hypothesis, $H_A$ : $\mu$ < 30 minutes {means that the mean commute time in the U.S. is less than half an hour}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean commute time = 27.6 minutes

s = sample standard deviation = 19.6 minutes

n = sample of people from the 2000 U.S. Census = 500

So, the test statistics = $\frac{27.6 -30}{\frac{19.6}{\sqrt{500} } }$ ~ $t_4_9_9$

= -2.738

The value of t test statistic is -2.738.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical values of -1.645 at 499 degree of freedom for left-tailed test.

Since our test statistic is less than the critical value of t as -2.378 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean commute time in the U.S. is less than half an hour.

4 0

4 years ago

strojnjashka [21]

For this case we have the variable $x = -3$ :