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2 years ago

762,508 expanded form using exponents

Mathematics

1 answer:

r-ruslan [8.4K]2 years ago

6 0

762,508 in expanded form using exponents is given as:

$7 \times 10^5 + 6 \times 10^4 + 2 \times 10^3 + 5 \times 10^2 +0 \times 10^1 + 8 \times 10^0$

<h3><u>Solution:</u></h3>

Given that we have to write 762, 508 in expanded form using exponents

Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits

<h3><u>Write 762508 in Expanded form</u></h3>

Let us first find the place value of digits

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Place value of 7 = 700000

In 762508, 7 is in hundred-thousands place

Place value of 6 = 60000

In 762508, 6 is in ten-thousands place.

Place value of 2 = 2000

In 762508, 2 is in thousands place

Place value of 5 = 500

In 762508, 5 is in hundreds place

Place value of 0 = 0 x 10 = 0

In 762508, 0 is in tens place

Place value of 8 = 8

In 762508, 8 is in ones place

Therefore, the expanded form is given as:

700,000 + 60,000 + 2,000 + 500 + 0 + 8

<u><em>Using exponents we can write as,</em></u>

$7 \times 10^5 + 6 \times 10^4 + 2 \times 10^3 + 5 \times 10^2 +0 \times 10^1 + 8 \times 10^0$

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a) For this case we can use the binomial model since we assume independent events and the same probability for each trial is the same p =0.15

b) $P(X=0)=(10C0)(0.15)^0 (1-0.15)^{10-0}=0.1969$

c) $P(X=3)=(10C3)(0.15)^3 (1-0.15)^{10-3}=0.1298$

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And using the result from part a we got:

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Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n p)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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Solution to the problem

Part a

For this case we can use the binomial model since we assume independent events and the same probability for each trial is the same p =0.15

Part b

For this case we want this probability:

$P(X=0)$

And replacing we got:

$P(X=0)=(10C0)(0.15)^0 (1-0.15)^{10-0}=0.1969$

Part c

For this case we want this probability:

$P(X=3)$

And replacing we got:

$P(X=3)=(10C3)(0.15)^3 (1-0.15)^{10-3}=0.1298$

Part d

For this cae we want thi probability:

$P(X \geq 1)$

And we can use the complment rule and we got:

$P(X \geq 1)= 1-P(X$

And using the result from part a we got:

$P(X \geq 1)= 1-P(X$

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