What is this ratio in simplest form? 16:64 A.1:4 B.2:8 C.4:1 D.8:32

We define the relation =m (read "equal mod m") on Z x Z to be the set: {(p,q): m|(p-q)}. Please show work.

Slav-nsk [51]

Step-by-step explanation:

a) Give two pairs which are in the relation $\equiv \mod 4$ and two pairs that are not.

As stated before, a pair $(x,y)\in \mathbb{Z}\times\mathbb{Z}$ is equal mod m (written $x\equiv y\mod m$ ) if $m\mid (x-y)$ . Then:

x=0 and y=4 is an example of a pair $\equiv \mod 4$
x=0 and y=1 is an example of a pair $\not \equiv \mod 4$

b) Show the $\equiv \mod m$ is an equivalence relation.

An equivalence relation is a binary relation that is reflexive, symmetric and transitive.

By definition $\equiv \mod m$ is a binary relation. Observe that:

Reflexive. We know that, for every m, $m\mid 0$ . Then, by definition, $x\equiv x \mod m$ .
Symmetry. It is clear that, given x,y and m such that $m\mid (x-y)$ , then $m\mid (y-x)$ . Therefore $x\equiv y \mod m \iff y\equiv x \mod m$
Transitivity. Let x,y,z and m such that $x\equiv y \mod m$ and $y\equiv z \mod m$ . Then, $m\mid (y-x)$ and $m\mid (z-y)$ . Therefore:

$m\mid [(y-x)+(z-y)] \implies m\mid (z-x) \implies x\equiv z \mod m$ .

In conclusion, $\equiv \mod m$ defines an equivalence relation.

6 0

3 years ago

A 13 card hand is dealt from a well-shuffled standard 52-card deck. What is the probability that 4 red cards and 9 black cards a

GaryK [48]

The probability that 4 red cards and 9 black cards are dealt is 0.0735.

Let E be the event that 4 red cards and 9 black cards are dealt.

According to the given question.

Number of card hand that is dealt from a well-shuffled standard 52- card deck is 13

Total number of red cards in a well shuffled card deck = 26

Total number of black cards in a well shuffled card = 26

Now, the number of ways to dealt 13 cards = $^{52} C_{13}$

Number of ways to dealt 9 black cards = $^{26}C_{9}$

And, the number of ways to dealt 4 red cards = $^{26} C_{4}$

As, we know that the probability of an event is calculated by taking the ratio of the favorable outcomes to the total number of outcomes.

Therefore, the the probability that 4 red cards and 9 black cards are dealt is given by

P(E) = $\frac{^{26}C_{9}\times \ ^{26}C_{4} }{^{52}C_{13} }$

⇒ P(E) = $\frac{\frac{26!26!}{9!4!17!22!} }{\frac{52!}{13!39!} }$

⇒ P(E) = 0.0735

Hence, the probability that 4 red cards and 9 black cards are dealt is 0.0735.

Find out more information about probability here:

brainly.com/question/14530583

#SPJ4

3 0

2 years ago

Maria, an experienced shipping clerk, can fill a certain order in 11 hours. Felipe, a new clerk, needs 13 hours to do the

ch4aika [34]

Answer:Maria rate = 1/13 job/hr

-----

Felipe rate = 1/16 job/hr

----

Together rate = 1/x job/h

Step-by-step explanation: rate + rate = Together rate

1/13 + 1/16 = 1/x

----

16x + 13x = 13*16

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29x = 13*16

x = 7.17 hrs = 7 hr 10 min 12 seconds (time to do the job together)

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Cheers,

Rubberduck100000.

8 0

3 years ago

Please solve question above

Lana71 [14]

Answer

(f ο g)(2)= 1/17 =0.058 and (f+g)(2)= 17.5

Step-by-step explanation:

f(x)=1/x ; f(2)=1/2

g(x)=4x+9 ; g(2)=4(2)+9

As,

1. (f ο g)(x)=f(g(x)) (Composite Function)

(f ο g)(2)=f(g(2))=f(4(2)+9)=f(8+9)=f(17)=1/17

=0.058 (in decimal)

2. (f+g)(x)= f(x)+g(x) (Sum of Functions)

(f+g)(2)=f(2)+g(2)=1/2 +(4(2)+9)=1/2+(8+9)=1/2+17 (taking L.C.M)

=[1+17(2)]/2=(1+34)/2=35/2

=17.5 (in decimal)

8 0

4 years ago

Which of the following shows the correct solution steps and solution to

Andreyy89

C.

$3x + 2 = 17 \\ 3x + 2 - 2 = 17 - 2 \\ \: \: \: \: \: \: \: \: \: 3x = 15 \\ \: \: \: \: \: \: \: \: \: \: \: x = \frac{15}{3} \\ \: \: \: \: \: \: \: \: x = 5$

6 0

3 years ago