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tankabanditka [31]
3 years ago
7

A circular plate has circumference 32.7 inches. What is the area of this​ plate? Use 3.14 for pie.

Mathematics
1 answer:
sveta [45]3 years ago
6 0

Answer: 85.13

Step-by-step explanation:

We know:

Circumference = 2*3.14r

Area of a circle = 3.14r²

We need to find the radius given the circumference before solving for the area:

32.7 = 2*3.14r

32.7/6.28 = 6.28r/6.28

r = 5.20700637

Now that we know the radius, we can plug it in to find the area:

A = 3.14(5.20700637)²

A = 3.14(27.1129153)

A = 85.134554

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Three consecutive odd integers have a sum of 27. Find the integers.
jek_recluse [69]

\sf \bf {\boxed {\mathbb {GIVEN:}}}

Sum of three consecutive odd integers = 27

\sf \bf {\boxed {\mathbb {TO\:FIND:}}}

The values of the three integers.

\sf \bf {\boxed {\mathbb {SOLUTION:}}}

\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}

\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}

Let us assume the three consecutive odd integers to be x, (x+2) and (x+4).

As per the condition, we have

Sum \:  \:  of \:  \:  the  \:  \: three \:  \:  consecutive \:  \:  odd \:  \:  integers  = 27

➺ \: x + (x + 2) + (x + 4) = 27

➺ \: x + x + 2 + x + 4 = 27

Now, collect the like terms.

➺ \: (x + x + x) + (2 + 4) = 27

➺ \: 3x + 6 = 27

➺ \: 3x = 27 - 6

➺ \: 3x = 21

➺ \: x =  \frac{21}{3} \\

➺ \: x = 7

Therefore, the three consecutive odd integers whose sum is 27 are \boxed{  7  }, \boxed{ 9   } and \boxed{ 11   } respectively.

\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}

⇢ 7 + 9 + 11 = 27

⇢ 27 = 27

⇢ L. H. S. = R. H. S.

\sf\blue{Hence\:verified.}

\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}

4 0
3 years ago
A coin is to be spun 25 times. Let x be the number of spins that result in heads (H). Consider the following rule for deciding w
larisa [96]

Answer:

0.0433

Step-by-step explanation:

Since we have a fixed number of trials (N = 25) and the probability of getting heads is always p = 0.05, we are going to treat this as a binomial distribution.

Using a binomial probability calculator, we find that the probability of obtaining heads from 8 to 17 times is 0.9567 given that the con is fair. The probability of obtaining any other value given that the coin is fair is going to be:

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Since we are going to conclude that the coin is baised if either x<8 or x>17, the probability of judging the coin to be baised when it is actually fair is 4.33%

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