1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vova2212 [387]
3 years ago
7

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

Mathematics
1 answer:
DENIUS [597]3 years ago
7 0

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

You might be interested in
During the month of April, Dora kept track of the bugs she saw in her garden. She saw a ladybug on 23 days of the month. What is
Vinvika [58]
D. 23/30 This is saying that out of 30 days, 23 of them she saw a ladybug, which means that each day, there is a 23/30 chance of finding one. 
4 0
3 years ago
Type the number to the left of the rational number in the box to the point it represents on the number
svlad2 [7]

Answer:

I put the numbers first because it was easier for me to do but if it confuses you I can redo it

1. C

2. D

3. F

4. B

5. E

6. A

7 0
2 years ago
Casy is taking pictures outdoors she know that the later in the afternoon she takes a picture
krok68 [10]
Later in the afternoon, the sun would most likely begin to set making quality sunlight pictures, but poor lighting for selfies.
7 0
4 years ago
Simplify 5sqrt 12xm^3 <br> Assume x and m are nonnegative
fredd [130]

Answer:

The right answer to your question is the third option

Step-by-step explanation:

            5 √12xm³

             First find the prime factors of 12

   12   2

     6   2

    3    3

     1             Then 12 = 2² 3

   and m³ = m m²

So    5 √ 2² 3 x m m²

and   5 (2)(m) √ 3xm

         10 m √ 3xm

5 0
3 years ago
Wendy has 5 and 1 over 3 feet of ribbon. How many 2 over 3 foot pieces can Wendy cut from the 5 and 1 over 3 feet of ribbon? Sho
denis-greek [22]

Answer:

Your answer is 8

Step-by-step explanation:

First you have to convert the mixed number into an improper fraction. To do this, multiply the denominator by the whole number. Then add the numerator and put that answer in a fraction over the original. So it would be 3*5=15+1=16/3. So now that the denominators are the same, all you need to do is see how many times 2 goes into 16. 16/2 which is 8. Answer = 8

6 0
3 years ago
Other questions:
  • A candy dish contains 30 jelly beans and 20 gumdrops. Ten candies are picked at random. What is the probability that 5 of the 10
    6·1 answer
  • Jenny makes food for her hummingbird feeders. The food is made up of 1 part sugar and 4 parts water. She uses 34 cup of sugar to
    5·2 answers
  • Find the surface area of the solid shown or described. If necessary, round to the nearest tenth
    5·1 answer
  • What is the median??
    6·2 answers
  • Two sides of a right triangle or 8 and 12 inches. Find the missing side if these are the lengths of the legs
    15·1 answer
  • Select whether each equation has no solution, one solution, or infinitely many solutions
    14·1 answer
  • I need to know this please
    14·2 answers
  • Suppose you deposited $83,000 into this account. How much would the account be worth after 4 days, assuming that the account com
    15·1 answer
  • Inside a personal computer, 5 memory chips fit inside a 1-inch section. How much space do 3 memory chips take up?
    5·2 answers
  • 70. Find the volume:
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!