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3 years ago

Any nonzero integer divided by zero equals zero. True or False and justify.

Mathematics

2 answers:

xz_007 [3.2K]3 years ago

8 0

It is true because any number multiplied by zero will be zero even if it's 1 or 100000000000000

scZoUnD [109]3 years ago

6 0

True, because a nonzero integer is any number other than 0. If you divide 1 by 0, you get 0. It goes on and on, but basically, no number can be divided by zero and still get 1 or 2 etc. Hope I helped

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Ghella [55]

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3 years ago

Given f: ℝ → ℝ and : ℝ → ℝ , for the following, find f(g(x)) and g(f(x)), and state the domain.

horrorfan [7]

Answer:

Remember, $(f\circ g)(x)=f(g(x))$ and the range of g must be in the domain of f.

$f(g(x))=f(x-1)=(x-1)^2-(x-1)=x^2-2x+1-x+1=x^2-3x+2$

$g(f(x))=g(x^2-x)=(x^2-x)-1=x^2-x-1$

The domain of f(g(x)) and g(f(x)) is the set of reals.

$f(g(x))=f(\sqrt{x}-2)=(\sqrt{x}-2)^2-x=\sqrt{x}^2-2*2*\sqrt{x}+2^2-x=-4\sqrt{x}+4$

$g(f(x))=g(x^2-x)=\sqrt{x^2-x}-2$

The domain of f(g(x)) is the set of nonnegative reals and the domain of g(f(x)) is the set of number such that $x^2-x\geq 0$

$f(g(x))=f(\frac{1}{x-1})=(\frac{1}{x-1})^2=\frac{1}{(x-1)^2}$

$g(f(x))=g(x^2)=\frac{1}{x^2-1}$

The domain of f(g(x)) is the set of reals except the 1 and the domain of g(f(x)) is the set of reals except the 1 and -1

$f(g(x))=f(\frac{1}{x-1})=\frac{1}{(\frac{1}{x-1}-1)}=\frac{1}{\frac{2-x}{x-1}}=\frac{x-1}{2-x}$

$g(f(x))=g(\frac{1}{x+2})=\frac{1}{(\frac{1}{x+2}-1)}=\frac{1}{\frac{-x-1}{x+2}}=\frac{x+2}{-x-1}$

The domain of f(g(x)) is the set of reals except 2, and the domain of g(f(x)) is the set of reals except -1.

$f(g(x))=f(log(2(x+3)))=f(log(2x+6))=log(2x+6)-1$

$g(f(x))=g(x-1)=log(2(x-1)+6)=log(2x+4)$

The domain of f(g(x)) is the set of nonnegative reals except -3. The domain of g(f(x)) is the set of nonnegative reals except -2.

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3 years ago

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Zielflug [23.3K]

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Read 2 more answers

A soup company puts 12 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of

lana [24]

Answer:

Option d: n = 36, p = 0.97, x = 36.

Step-by-step explanation:

We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.

We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.

Let X = <u><em>Number of cans that are properly filled</em></u>

The above situation can be represented through binomial distribution;

$P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........$

where, n = number of trials (samples) taken = 36 cans

x = number of success = all cans are properly filled = 36

p = probabilitiy of success which in our question is probability that

can have the correct amount, i.e. p = 97%

So, X ~ Binom (n = 36, p = 0.97)

Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.

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3 years ago