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11 months ago

Why i the product of two rational number alway rational?

1 answer:

8 0

The product of two rational numbers is always rational because (ac/bd) is the ratio of two integers, making it a rational number.

We need to prove that the product of two rational numbers is always rational. A rational number is a number that can be stated as the quotient or fraction of two integers : a numerator and a non-zero denominator.

Let us consider two rational numbers, a/b and c/d. The variables "a", "b", "c", and "d" all represent integers. The denominators "b" and "d" are non-zero. Let the product of these two rational numbers be represented by "P".

P = (a/b)×(c/d)

P = (a×c)/(b×d)

The numerator is again an integer. The denominator is also a non-zero integer. Hence, the product is a rational number.

learn more about of rational numbers here

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Multiply. 32√⋅28√⋅3√⋅6√ Enter your answer, in simplest radical form, in the box.

valkas [14]

Answer:

48√7

Step-by-step explanation:

$\sqrt{32}\cdot\sqrt{28}\cdot\sqrt{3}\cdot\sqrt{6}=\sqrt{(2^5)(2^2\cdot 7)(3)(2\cdot 3)}\\\\=\sqrt{(2^4\cdot3)^2(7)}=2^4\cdot 3\sqrt{7}=\boxed{48\sqrt{7}}$

4 0

3 years ago

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make indepe

Maurinko [17]

Answer:

Mean = 20

Variance = 16

Step-by-step explanation:

Solution:-

- Let X be the number of customers paying with a debit card. X has the binomial distribution with n = 100 trials and success probability p = 0.2

- In general, if X has the binomial distribution with (n) trials and a success probability of (p) then:

P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)

for values of x = 0, 1, 2, ..., n

P[X = x] = 0 for any other value of x.

- The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.

- Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.

X ~ Binomial( n = 100 , p = 0.2 )

- The mean of the binomial distribution is n * p = 20

- The variance of the binomial distribution is n * p * (1 - p) = 16

7 0

3 years ago

ABCD is rectangle on a coordinate grid with side AB parallel to side CD. Side BC is perpendicular to AB. The slip of AB is 3/4.

dybincka [34]

The slope of BC is $\frac{-4}{3}$

Step-by-step explanation:

Let us revise some notes about slopes of lines

If two lines are parallel, then their slopes are equal
If to lines are perpendicular, then the product of their slopes is -1, that means if the slope of one is m, then the slope of the other is $\frac{-1}{m}$

∵ ABCD is a rectangle

∵ AB // CD

∴ The slope of AB = the slope of CD

∵ BC ⊥ AB

∴ The slope of BC × the slope of AB = -1

∵ The slope of AB = $\frac{3}{4}$

- To find the slope of BC reciprocal the slope of AB and reverse its sign

∴ The slope of BC = $\frac{-4}{3}$

The slope of BC is $\frac{-4}{3}$

Learn more:

You can learn more about the slope in brainly.com/question/9801816

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6 0

3 years ago

Felicia invested $25,000 into an account earning 3% interest compounded annually. She makes no other deposits into the account a

madam [21]

The formula is
A=p (1+r)^t
A future value?
P present value 25000
R interest rate 0.03
T time 9 years

A=25,000×(1+0.03)^(9)
A=32,619.33

7 0

2 years ago

Choose the correct slope and y-intercept of the line indicated by this linear equation.

stellarik [79]

The correct answer is m=-2 (slope) and b=4 (y-intercept).

8 0

2 years ago