What is the smallest angle of rotational symmetry that maps a regular nonagon onto itself?

Max points!! help please!!! tyyyyy

krek1111 [17]

Answer:

b. 70

Step-by-step explanation:

The Binomial Coefficient can be used to calculate the number of ways objects can be arranged.

<u>Binomial Coefficient</u>

$\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}$

The exclamation mark "!" placed after a number means factorial and indicates to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

The Binomial Coefficient gives us the number of ways of picking "r" unordered outcomes from "n" possibilities.

As there are 8 friends ⇒ n = 8.

As each car takes 4 friends ⇒ r = 4.

Substitute these values into the formula:

$\begin{aligned} \implies \displaystyle \rm \binom{8}{4} \: = \:^{8}C_{4} & = \rm \frac{8!}{4!(8-4)!}\\\\ & = \rm \dfrac{8 \times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1\times 4\times 3\times 2\times 1}\\\\ & = \rm \dfrac{8 \times 7\times 6\times 5}{4\times 3\times 2\times 1}\\\\ & = \rm \dfrac{1680}{24}\\\\ & = \rm 70\end{aligned}$

Learn more about the binomial coefficient here:

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6 0

1 year ago

Read 2 more answers

Find the value of x in the triangle shown below. x = 56° 99°

anyanavicka [17]

Answer:

x = 25 degrees

Step-by-step explanation:

All angles in a triangle should add up to 180 degrees. So to solve for x, set up an equation where all three angles added up equals 180.

180 = 99 + 56 + x

180 = 155 + x

25 = x

The unknown angle is equal to 25 degrees.

4 0

3 years ago

A box of Georgia peaches has 3 bad and 12 good peaches. (a) If you make a peach cobbler of 12 peaches randomly selected from the

Eddi Din [679]

Answer:

a) 0.21% probability that there are no bad peaches in the peach cobbler.

b) 99.79% probability of having at least 1 bad peach in the peach cobbler

c) 7.91% probability of having exactly 2 bad peaches in the peach cobbler.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the peaches are chosen is not important. So the combinations formula is used to solve this question.

Combinations formula:

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

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

(a) If you make a peach cobbler of 12 peaches randomly selected from the box, what is the probability that there are no bad peaches in the peach cobbler?

Desired outcomes:

12 good peaches, from a set of 12. So

$D = C_{12,12} = \frac{12!}{12!(12 - 12)!} = 1$

Total outcomes:

12 peaches, from a set of 15. So

$T = C_{15,12} = \frac{15!}{12!(15 - 12)!} = 455$

Probability:

$p = \frac{D}{T} = \frac{1}{455} = 0.0021$

0.21% probability that there are no bad peaches in the peach cobbler.

(b) What is the probability of having at least 1 bad peach in the peach cobbler?

Either there are no bad peaches, or these is at least 1. The sum of the probabilities of these events is 100%. So

p + 0.21 = 100

p = 99.79

99.79% probability of having at least 1 bad peach in the peach cobbler

(c) What is the probability of having exactly 2 bad peaches in the peach cob- bler?

Desired outcomes:

2 bad peaches, from a set of 3.

One good peach, from a set of 12.

$D = C_{3,2}*C_{12,1} = \frac{3!}{2!(3-2)!}*\frac{12!}{1!(12 - 1)!} = 36$

Total outcomes:

12 peaches, from a set of 15. So

$T = C_{15,12} = \frac{15!}{12!(15 - 12)!} = 455$

Probability:

$p = \frac{D}{T} = \frac{36}{455} = 0.0791$

7.91% probability of having exactly 2 bad peaches in the peach cobbler.

3 0

3 years ago

A sedan will drive ten miles north, 15 miles east, 13 miles south, 15 miles west, and 22 miles

pishuonlain [190]

The total distance is 75 miles

4 0

2 years ago

How to do this question plz

Artyom0805 [142]

Answer:

90(8) + 2(38) = 270 + 76 = 346p

Step-by-step explanation:

5 0

3 years ago