In the figure shown below, OA and OB are radio of the circle with center O. If m

Let A be a set of numbers.

LUCKY_DIMON [66]

Answer:

a. closed under addition and multiplication

b. not closed under addition but closed under multiplication.

c. not closed under addition and multiplication

d. closed under addition and multiplication

e. not closed under addition but closed under multiplication

Step-by-step explanation:

a.

Let A be a set of all integers divisible by 5.

Let $x,y$ ∈A such that $x=5m\,,\,y=5n$

Find $x+y,xy$

$x+y=5m+5n=5(m+n)$

So, $x+y$ is divisible by 5.

$xy=(5m)(5n)=25mn=5(5mn)$

So,

$xy$ is divisible by 5.

Therefore, A is closed under addition and multiplication.

b.

Let A = { 2n +1 | n ∈ Z}

Let $x,y$ ∈A such that $x=2m+1\,,\,y=2n+1$ where m, n ∈ Z.

Find $x+y,xy$

$x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)$

So,

$x+y$ ∉ A

$xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1$

So,

$xy$ ∈ A

Therefore, A is not closed under addition but A is closed under multiplication.

c.

$Let A=\{2,5,8,11,14,...\}$

Let $x=2,y=5$ but $x+y=2+5=7$ ∉A

Also,

$xy=2(5)=10$ ∉A

Therefore, A is not closed under addition and multiplication.

d.

Let A = { 17n: n∈Z}

Let $x,y$ ∈ A such that $x=17n,y=17m$

Find x + y and xy

$x+y=17n+17m=17(n+m)$

$xy=(17m)(17n)=289mn=17(17mn)$

So,

$x+y,xy$ ∈ A

Therefore, A is closed under addition and multiplication.

e.

Let A be the set of nonzero real numbers.

Let $x,y$ ∈ A such that $x=-1,y=1$

Find x + y

$x+y=-1+1=0$

So,

$x+y$ ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

4 0

2 years ago

Use the Distributive Property to expand this expression.

viktelen [127]

Answer:

C is the correct answer

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Covert the measurements 3km 312m

marin [14]

3,312m is your answer

3 0

2 years ago

If 65 percent of the population of a large community is in favor of a proposed rise in school taxes, approximate the probability

xz_007 [3.2K]

Answer: a) 0.99917 b) 0.7054 c) 0.9820

Step-by-step explanation:

Let X denotes the number of people are in favor of a proposed rise in school taxes.

Era re given that p(probability that a person is in favor of a proposed rise )= 0.65

Sample size : n= 100

Mean= np = 100(0.65)=65

Standard deviation: $\sigma=\sqrt{np(1-p)}\\\\=\sqrt{100(0.65)(0.35)}\\\\=4.76969600708\approx4.77$

a) Now, the probability that a random sample of 100 people will contain at least 50 who are in favor of the proposition :

$P(x\geq50)=P(\dfrac{x-\mu}{\sigma}\geq\dfrac{50-65}{4.77})\\\\=P(z\geq-3.144)\\\\=P(z-z)=P(Z$

b) between 60 and 70 inclusive who are in favor;

$P(60$

c) fewer than 75 in favor.

$P(x$

3 0

3 years ago

What is the volume of a sphere with a diameter of 6 m, rounded to the nearest tenth of a cubic meter?

seraphim [82]

Answer:113 cubic meter

Step-by-step explanation:

Diameter=6

Radius=r=6/2

Radius=r=3

π=3.14

Volume of sphere=4/3 x π x r x r x r

Volume of sphere=4/3 x 3.14 x 3 x 3 x 3

Volume of sphere=(4x3.14x3x3x3) ➗ 3

Volume of sphere=339.12 ➗ 3

Volume of sphere=113.04

Volume of sphere =113 cubic meter

6 0

3 years ago