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2 years ago

The frequency distribution of two data sets are shown in the dot plots below

Mathematics

1 answer:

crimeas [40]2 years ago

4 0

Answer:

1,4,6

Step-by-step explanation:

not sure it’s common sense

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Prove that u(n) is a group under the operation of multiplication modulo n.

katrin2010 [14]

Answer:

The answer is the proof so it is long.

The question doesn't define u(n), but it's not hard to guess.

Group G with operation ∘

For all a and b and c in G:

1) identity: e ∈ G, e∘a = a∘e = a,

2) inverse: a' ∈ G, a∘a' = a'∘a = e,

3) closed: a∘b ∈ G,

4) associative: (a∘b)∘c = a∘(b∘c),

5) (optional) commutative: a∘b = b∘a.

Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.

If n isn't prime, we exclude from the group all integers which share factors with n.

Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).

Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).

Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.

Associative and Commutative:

(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)

a∘b = b∘a because ab = ba.

5 0

2 years ago

Read 2 more answers

Please help me! I don't understand this its confusing to me :(

Alex787 [66]

Answer:

Perdón

Step-by-step explanation:

Lo siento pero tengo que hacer una pregunta urgente.

6 0

2 years ago

Read 2 more answers

Which relationships have the same constant of proportionality between yyy and xxx as the equation 3y=27x3y=27x3, y, equals, 27,

Tanya [424]

Answer:

A, B and C

Step-by-step explanation:

In the equation: 3y=27x

Making y the subject of the equation, we have:

$y=\frac{27}{3}x\\y=9x$

The constant of proportionality between y and x is 9.

We want to determine which relationships have the same constant of proportionality 9.

Option A

y=9x

The constant of proportionality is 9.

Option B

2y=18x

Divide both sides by 2 to obtain: y=9x

The constant of proportionality is 9.

Option C

x=3, y=1/3

Substitution into y=kx gives:

1/3=3k

k=9

The constant of proportionality is 9.

Option D

x=6, y=2/3

Substitution into y=kx gives:

2/3=6k

k=2/3*6=4

The constant of proportionality is 4.

Option E

When x=2, y=18

Substitution into y=kx gives:

18=2k

k=9

However, when x=4, y=27

Substitution into y=kx gives:

27=4k

k=6.75

This is not a proportional relation since the constant of proportionality is not equal.

The correct options are A, B and C

4 0

2 years ago

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the sc

seraphim [82]

25.96
85.58
89.22
103.78

8 0

3 years ago

Read 2 more answers

The ratio of boys to girls in a class is 5:3. There are 32 students in the class. How many students are boys?

alina1380 [7]

Class ratio of girls to boys is 3:5
So there are 3 girls and 5 boys in 8 students
If there are 32 students, then 3/(3+5) * 32 = 12 girls, and 5/(3+5) * 32 = 20 boys

Hope it helps you?

8 0

2 years ago