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3 years ago

Find the measure of an exterior angle of a regular polygon with 19 sides.

Mathematics

2 answers:

Contact [7]3 years ago

5 0

Answer: $18.94\°$

Step-by-step explanation:

The exterior angle of a regular polygon of $n$ sides is given by:

$\frac{360\°}{n}$

In the case of a 19-side polygon $n=19$

Hence:

$\frac{360\°}{19}=18.94\°$

Elza [17]3 years ago

4 0

Answer:

The measure of the exterior angle is 18. 95 Degrees.

Step-by-step explanation:

Step 1:

Given data:

Let us assume ‘I’ as interior angle of Regular polygon and ‘E’ as Exterior angle of Regular Polygon.

Exterior angle for Regular polygon is 19 sides.

By the formula:

$I=\frac{180(n-2)}{n}$ degrees. ------1.n(s) is the side of polygon.

Step 2:

Substitute the value of n in the given formula. Where n=19 from the given data

$I=\frac{180(n-2)}{n}$ degrees

Step 3:

$\begin{array}{l}{I=\frac{180(19-2)}{19} \text { degrees }} \\ {I=\frac{180(17)}{19} \text { degrees }}\end{array}$

I = 3060/19

I = 161.05 degrees.

Step 4:

Measure of the exterior angles of a regular polygon is given by the formula:

E= 360 / n degrees. ----- n(s) side of polygon.

From the given data n are 19.

E = 360 / 19

E= 18. 95 Degrees.

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Police records in the town of Saratoga show that 17 percent of the drivers stopped for speeding have invalid licenses. If 24 dri

Ymorist [56]

Answer:

Step-by-step explanation:

Given

17 % of the drivers stopped have invalid licenses

n=24 drivers are stopped

using Binomial distribution

$^nC_r(p)^r(q)^{n-r}$

here p=0.17

q=1-0.17=0.83

(a)none will have valid license i.e. r=0

$P(r=0)^{24}C_0(0.17)^0(0.83)^{24}=(0.83)^{24}=0.0114$

(b)Exactly one have invalid license i.e. r=1

$P(r=1)=^{24}C_1(0.17)^1(0.83)^{23}=24\times 0.17\times (0.83)^{23}$

$=0.0561$

(c)At least 2 will have invalid license i.e. $r\geq 2$

$P(r\geq 2)=1-P(r=0)-P(r=1)$

$P(r\geq 2)=1-0.0114-0.0561$

$P(r\geq 2)=0.932$

3 0

3 years ago

I need to know the lengths of MN, NP, and PM

andrezito [222]

Answer:

MN = 12 units

NP = 16 units

PM = 20 units

Step-by-step explanation:

You can find MN and NP by counting on the graph. To find PM you will need to use the formula a^2 + b^2 = c^2 ( ^ stands for exponent)

MN and NP will be a and b.

Example: 12^2 + 16^2 = c^2

Simplify.

Example:

144 + 256 = c^2

144 + 256 = 400

Then find the square root of 400 which is 20.

To check your work put all of the sides into the formula and it should be true.

8 0

2 years ago

Read 2 more answers

Allen�s hummingbird (Selasphorus sasin ) has been studied by zoologist Bill Alther A small group of 15 Allen� s hummingbirds has

Bogdan [553]

Answer:

1) 80% CI: [3.04; 3.26]gr

d= 0.11

2) n= 28 hummingbirds

Step-by-step explanation:

Hello!

The study variable of this experiment is:

X: the weight of a hummingbird. (gr)

And it has a normal distribution, symbolically: X~N(μ;σ²)

And (I hope I got it correctly) its population standard deviation is σ= 0.33

There was a sample of n= 15 hummingbirds taken, its sample mean X[bar]= 3.15 gr

1) You need to construct an 80% Confidence Interval for the population mean of the hummingbird's weight.

Since the study variable has a normal distribution, you can use either the standard normal distribution or the Student's t distribution. Both are useful to estimate the population mean. Since the population standard variance is known, the best choice is the Standard normal.

Z= X[bar] - μ ~ N(0;1)

σ/√n

The formula for the interval is:

X[bar] ± $Z_{1- \alpha /2}$ * (σ/√n)

$Z_{1- \alpha /2}= Z_{0.90} = 1.28$

3.15 ± 1.28 * (0.33/√15)

[3.04; 3.26]gr

The margin of error (d) of a confidence interval is hal its amplitude (a)

a= Upper bond - Lower bond

d= (Upper bond - Lower bond)/2

d= $\frac{(3.26-3.04)}{2}$ = 0.11

2) You need to calculate a sample size for a 80% Confidence interval for the average weight of the hummingbirds with a margin of error of d= 0.08

As I said before, the margin of error is half the amplitude of the interval, the formula you use to estimate the population mean has the following structure:

"point estamator" ± "margin of error"

Then the margin of error is:

d= $Z_{1- \alpha /2}$ * (σ/√n)

Now what you have to do is rewrite the formula based on the sample size

d= $Z_{1- \alpha /2}$ * (σ/√n)

$\frac{d}{Z_{1- \alpha /2}}$ = σ/√n

√n * $\frac{d}{Z_{1- \alpha /2}}$ = σ

√n = σ * $\frac{Z_1- \alpha /2}{d}$

n = (σ * $\frac{Z_1- \alpha /2}{d}$ )²

n= (0.33 * $\frac{1.28}{0.08}$ )²

n= 27.8784 ≅ 28 hummingbirds.

I hope it helps!

4 0

3 years ago

I also need help on this one smh

AysviL [449]

Answer:

C. 176.6 Square feet (I think)

Step-by-step explanation:

I tried many different ways and got three of the answers above but I think this is the right one.

The equation to find area of a circular cone base: $A= \pi r^2$

We are given the diameter (15 Feet) but we need to find the radius. So we use the diameter to radius formula: $r = \frac{d}{2}$
Plug in numbers: $r=\frac{15}{2}$ ≈ $7.5$
Use the Area formula now that you have radius: $A=\pi 7.5^2$
Solve and get = $a = 176.71458676$
Looking at the options the closest one to our answer (off by one-tenth) is C.

Sorry if you get this wrong. I tried lol.

7 0

2 years ago

The angle of elevation of the top of a tower from a point 42 metres away from it's base on level ground is 26 degrees. find the

Hatshy [7]

Answer:

20.485 Meters

Step-by-step explanation:

So first you wanna draw a diagram. Start with the tower, then on the ground to the left (or right) draw a point. The point will be labeled as 42 m away from the tower. Now draw a line from that point to the top of the tower. This makes your triangle, and that angle you just drew that touches the point is 26 degrees.

Now, since you have a right triangle you can use trig. You know an angle and a side. Specifically, relative to the 26 degree angle you know the adjacent angle and want the opposite, which is the tower. So opposite and adjacent is tangent. So you set up tan(26) = o/42 where o is the opposite side.

So solving you get o = 20.485 meters

3 0

3 years ago