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3 years ago

Find the circumference and area of the circle

Mathematics

2 answers:

Dimas [21]3 years ago

5 0

Answer:

Step-by-step explanation:

The formula for determining the circumference of a circle is expressed as

Circumference = 2πr

Where

r represents the radius of the circle

π is a constant whose value is 3.14

From the diagram,

Diameter = 16 inches

Radius = diameter/2 = 16/2 = 8 inches

Circumference = 2 × 3.14 × 8 = 50.24 inches

The formula for determining the circumference of a circle is expressed as

Area = πr²

Area = 3.14 × 8² = 200.96 inches²

jekas [21]3 years ago

4 0

Answer:

The area of a circle is
$\pi \: r {}^{2}$
while the circumference is
$\pi \: d$

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According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

blagie [28]

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5.1% of burglaries are cleared with arrests.

This means that $p = 0.051$

A new detective is assigned to six different burglaries.

This means that $n = 6$

What is the probability that at least one of them is cleared with an arrest?

Either none are cleared, or at least one is. The sum of the probabilities of these events is 100% = 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.051)^{0}.(0.949)^{6} = 0.7305$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7305 = 0.2695$

26.95% probability that at least one of them is cleared with an arrest

8 0

3 years ago

Using an ordered alphabet of 26 letters, how many ways are there to choose a set of six letters such that no two letters in the

mestny [16]

To find our solution, we can start off by creating a string of 27 boxes, all followed by the letters of the alphabet. Underneath the boxes, we can place 6 pairs of boxes and 15 empty boxes.The stars represent the six letters we pick. The empty boxes to the left of the stars provide the "padding" needed to ensure that no two adjacent letters are chosen. We can create this -
$\binom {21} {6}= \frac{21*20*19*18*17*16}{6*5*4*3*2*1} =21*19*17*8=54264$
Thus, the answer is that there are $\boxed{54264}$ ways to choose a set of six letters such that no two letters in the set are adjacent in the alphabet. Hope this helped and have a phenomenal New Year! <em>2018</em>

5 0

3 years ago

What’s the product of r and 9

Nina [5.8K]

Answer:

Step-by-step explanation:

Multiply 9 and r together.

3 0

3 years ago

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Fertilizer for your lawn has to be mixed with water. Every 5 ounces of mix needs 1 gallon of water. How many cups of mix do you

Mkey [24]

Answer:

5 cups

Step-by-step explanation:

There are 8 ounces in a cup, so the ratio given is ...

5/8 cup : 1 gallon

Multiplying this by 8, we have ...

5 cups : 8 gallons

If you are using 8 gallons of water, you need 5 cups of mix.

6 0

3 years ago

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Solve the simultaneous equations y=3x+2 and y=x+6

kogti [31]

Answer:

x=2

Step-by-step explanation:

y=3x+2

y=x+6

Since you're stating that, they both equal because equation is equated to equation 2 because of the Y.

Therefore, substitute into both equations as shown:

3x+2=x+6

3x-x=6-2 (bring 2 to the other side by subtracting 2 as well as x)

2x=4

2x/2=4/2 (dividing 2 on both sides to get rid off 2 in 2x)

x=2.

5 0

3 years ago

Find the circumference and area of the circle​

Find the circumference and area of the circle