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Lunna [17]
1 year ago
7

There is a safety fence around a circular pool with a gate. The gate is 150 cm wide. What is the length of the fence not includi

ng the gate? m Use π = 3.14
Mathematics
1 answer:
Zolol [24]1 year ago
4 0

Answer:

The length of the fence is 6.28x-150 cm.

Step-by-step explanation:

Let the circular pool has the radius (r ) = x cm.

Since the pool is in a circular shape so the circumference will be the length of the fence. Moreover, there is a 150cm wide so we have to subtract the 150 cm from the value of circumference in order to get the actual length of the fence.

Length of fence  = Circumference of the pool – width of the gate.

Length of fence = 2 π r – 150

Length of fence = 2 × 3.14 × x – 150

Length of fence = 6.28x – 150 cm.

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For a polygon to be convex means that all of its interior angles are less than 180 degrees. Prove that for all integers n ≥ 3, t
Alexeev081 [22]

Answer: check explanation

Step-by-step explanation:

Let K(n) be the sum of the interior angles in any n-sided convex polygon which is exactly 180(n −2)

degrees.

CASE: n = 3. A 3-sided polygon is a triangle, whose interior angles were shown always to sum to be 180 degree

INDUCTION HYPOTHESIS: Suppose that K(b) holds for some b ≥ 3. Which means that the interior angles in any b-sided convex

polygon is exactly 180(n −2) degrees.

INDUCTION STEP: We need to show that K(n is greater than or equals to 3) . That is, the interior angles of any b+1-sided convex polygon

is exactly 180(b−2) = 180(b −1) degrees,

Let X be any (b+1)-vertex convex polygon, say with successive vertices x1, x2,..., xb+

Now Y is also a convex polygon , so by the induction hypothesis K(b), the sum of the interior

angles of Y is 180(k −2).

Now let T be the triangle with vertices xk , xb+1, x1. The sum of the interior angles in X is the sum of those

in Y plus the sum of those in T .

So the sum of the interior angles in X is

180(b −2)+180 = 180((b +1)−2) = 180(b −1).

Since X was arbitrary, we conclude that the sum of the interior angles of any (b +1)-sided convex polygon

is 180((b−2)+1) = 180(b−1). That is, P(b +1) holds.

And which means that n is greater or equals to 3

8 0
1 year ago
A store gets a bucket of eggs for $16.20 and sells a dozen eggs for $3.50. If there are 450 eggs in the bucket, by what percent
Jet001 [13]
Price of a bucket of eggs $16.20
price for a dozen of eggs $3.50
number of dozens in 450 eggs:
450/12
=37.5
price of 37.5 will be:
37.5×3.50=$131.25
The percentage the store has increased the price will be:
(131.25-16.20)/16.20×100
=710%

6 0
2 years ago
Read 2 more answers
The highest recorded temperature during the month of July for a given year in Death Valley, California has an approximately norm
S_A_V [24]

Answer:

P(X

And we can find this probability using excel or the normal standard tabe and we got:

P(z

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:

X \sim N(123.8,3.1)  

Where \mu=123.8 and \sigma=3.1

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using excel or the normal standard tabe and we got:

P(z

6 0
2 years ago
The ratio of boys to girls in a certain classroom was 2 : 3. If boys represented five more than one third of the class, how many
Tju [1.3M]
Let the no. Of boys=x and that of girls=y.
The total no. Of students = x+y .
As given by statement the no. Of boys=x={(x+y)/3} + 5
This implies that
X=(x+y+15)/3
Also we know that x/y = 2/3 therefore
From this equation we get x=2y/3 and y=3x/2
By method of substitution we get
X=(x+3x/2+15)/3
•x=(15x+90)/2
•2x=15x+90
•-13x=90
X= -90/13
Now. Y= 3x/2=-270/26
Therefore total
no. Of students= -270/26+(-90/13)
•no. Of students= -450/26
According to me this is an imaginary question i mean how can their be a negative person
6 0
2 years ago
Today, John ran 15 miles in 2 hours and 30 minutes. He wants to represent the relationship between the distance he ran, in miles
jeyben [28]

Answer:

d = 6t

Step-by-step explanation:

Firstly, lets change the 2 hours and 30 minutes to 2.5 hours, you could devide the time in minutes by 60 to get that number 2[hours]+(\frac{30}{60})[minutes to hours] = 2.5Hours.

Anyway, John ran 15 miles in 2.5 hours which means he ran (15÷2.5) in one hour which is equal to 6miles per hour. That means if you multiply the hours he ran by 6 you will get the miles he ran.

So the answer would be:

d = 6t

3 0
1 year ago
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