All categories

2 years ago

Five of the interior angles of a hexagon are 90°, 100°, 110°, 120° and 130°.

Mathematics

1 answer:

qwelly [4]2 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6 ( sides of a hexagon ) , then

sum = 180° × 4 = 720°

(a)

let x be the sixth interior angle , then

90° + 100° + 110° + 120° + 130° + x = 720 , that is

550° + x = 720° ( subtract 550° from both sides )

x = 170°

(b)

the sum of the exterior angles of a polygon is 360°

exterior angle + interior angle = 180°

exterior angle = 180° - interior angle

Then

180° - 90° = 90°

180° - 100° = 80°

180° - 110° = 70°

180° - 120° = 60°

180° - 130° = 50°

180° - 170° = 10°

sum = 90° + 80° + 70° + 60° + 50° + 10° = 360° ← correct total

You might be interested in

Pleease help me with this math work

OleMash [197]

The first one because the left bound is included [ and the right one is not )

6 0

4 years ago

What is the result of 36 divided by 9? Use the number line to find the answer. A number line going from 0 to 39. The numbers 0,

Vladimir79 [104]

Answer:

Step-by-step explanation:

36/9=4

7 0

4 years ago

Read 2 more answers

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the are

Nastasia [14]

Answer:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

$z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{100}}}=-1.017$

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

$\hat p=0.36$ estimated proportion with the survey

$p_o=0.41$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.41.:

Null hypothesis: $p\geq 0.41$

Alternative hypothesis: $p < 0.41$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{100}}}=-1.017$

8 0

3 years ago

Read 2 more answers

The solution of |x-2|>5

zzz [600]

Answer:

Step-by-step explanation:

|x-2|>5

x-2<-5

x<-3

or x-2>5

x>7

5 0

4 years ago

Read 2 more answers

A man invest 5,200,part at 4% and the balance at 3%. If his total income for the two investments is $194,how much money did he i

Fed [463]

Let the amount invested at 4% be = x

Let the amount invested at 3% be = y

Given is:

$x+y=5200$ or $x=5200-y$ .... (1)

As, total income for the two investments is $194, so equation is:

$0.04x+0.03y=194$ ....(2)

Putting value of x from (1) in (2)

$0.04(5200-y)+0.03y=194$

$208-0.04y+0.03y=194$

$0.01y=14$

$y=1400$

And x=5200-y

$x=5200-1400=3800$

Hence, money invested at 4% is $3800 and money invested at 3% is $1400

6 0

3 years ago