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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

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3 years ago
Se puede pasar 11/20 a fraccion mixta?​
Shtirlitz [24]
<h2>¡Hola!</h2>

La fracción 11/20 no puede ser una fracción mixta ya que es una fracción propia es decir el numerador es menor al denominador.

Digamos que si usaramos el recíproco de la fracción si se podría pasar a mixta ya que en ese caso seria impropia.

Solo las fracciones impropias pueden ser mixtas.

Por ejemplo si invertimos la fracción :

\:\: \: \: \:  \: \: \:  \boxed{ \bold{\frac{20}{11} = 1 \:  \:  \frac{9}{11} }}

Así que no la fracción 11/20 no puede ser una fracción mixta.

#Spj1

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2 years ago
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