Which of the following is an element of this set? a,c,e,g,i,k,m

(a) How many integers from 1 through 1,000 are multiples of 2 or multiples of 9?

DENIUS [597]

Answer:

(a)There are 500 integers from 1 through 1,000 are multiples of 2.

There are 111 integers from 1 through 1,000 are multiples of 9.

(b)0.611

Step-by-step explanation:

Given the set of Integers from 1 through 1000

The least multiple of 2 is 2 and the highest multiple of 2 in the interval is 1000.

To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 2,4,6,... is an Arithmetic Progression,

where first term, a =2, common difference, d =2

Nth term of an A.P,

$U_n= a+(n-1)d\\1000=2+2(n-1)\\1000=2+2n-2\\1000=2n\\n=500$

There are 500 integers from 1 through 1,000 are multiples of 2.

Similarly,

Given the set of Integers from 1 through 1000

The least multiple of 9 is 9 and the highest multiple of 9 in the interval is 999.

To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 9,18,27,... is an Arithmetic Progression,

where first term, a =9, common difference, d =9

Nth term of an A.P,

$U_n= a+(n-1)d\\999=9+9(n-1)\\999=9+9n-9\\999=9n\\n=111$

There are 111 integers from 1 through 1,000 are multiples of 9.

(b)Probability that an integer selected at random is a multiple of 2 or a multiple of 9.

There are a total of 1000 numbers between from 1 through 1,000

n(S)=1000

n(Multiples of 2)=500

n(Multiples of 9)=111

Therefore:

$P(\text{Multiples of 9}) \:OR\: P(\text{Multiples of 2})=\frac{111}{1000} + \frac{500}{1000} \\=\frac{611}{1000} \\=0.611$

7 0

3 years ago

If you multiply 5(2x+3+4y), the answer is ______

Volgvan

Answer:

You don't even need to do the whole question. Just look at 5 times 2x. which is 10x then u get your answer

6 0

3 years ago

Read 2 more answers

X^2-5x=14 solve for x

elixir [45]

Answer:

x=7, -2.

Step-by-step explanation:

x^2-5x=14

x^2-5x-14=0

factor out the trinomial,

(x-7)(x+2)=0

zero property,

x-7=0, x+2=0,

x=0+7=7,

x=0-2=-2

8 0

3 years ago

Read 2 more answers

write the restrictions that should be imposed on the variable for each of the following function. then find, explicitly, the dom

matrenka [14]

By using the rules that the value inside square root can’t be negative and the denominator value can’t be zero, the domain for the given function is a) x<-1 and x>1 b) p≤1/2 c) s>-1.

I found the complete question on Chegg, here is the full question:

Write the restrictions that should be imposed on the variable for each of the following function. Then find, explicitly, the domain for each function and write it in the interval notation a) f(x)=(x-2)/(x-1) b) g(p)=√(1-2p) c) m(s)= (s^2+4s+4)/√(s+1)

Ans. We know that a number is not divisible by zero and number inside a square root can not be negative. In both the cases the outcome will be imaginary.

a) For this case the denominator x-1 can not be zero. So, x ≠1 and the domain is x<-1 and x>1.

b) For this case the value inside square root can’t be negative. So, p can’t be greater than 1/2 the domain is p≤1/2.

c) For this case also the value inside square root can’t be negative and the denominator value can’t be zero. So, s can’t equal or less than -1 and domain is s>-1.

Learn more about square root here:

brainly.com/question/3120622

#SPJ4

3 0

2 years ago

Dennis needs to fix a leaky roof on his house but does not own a ladder. He thinks that a 25-foot ladder will be

Mars2501 [29]

Answer:

Step-by-step explanation: 2/8 =h/2

3 0

3 years ago