Let f(x) = 3x - 6 and g(x) = x - 2. Find f/g and it's domain.

Mathematics

1 answer:

Mice21 [21]4 years ago

6 0

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What are the solutions to 0=x^2-x+1?

kumpel [21]

Answer: No solutions

Step-by-step explanation:

There are no solutions to 0 = x² - x + 1.

[Method One]

We can solve this by rewriting the equation, but it is quicker to graph it when there are no solutions. See attached.

[Method Two]

I said we can solve this by solving an equation, here it is. We will use the quadratic formula since the equation given is already in the proper form.

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

$\displaystyle x=\frac{1\pm\sqrt{(-1)^2-4(1)(1)} }{2(1)}$

$\displaystyle x=\frac{1\pm\sqrt{-3} }{2}$

-> Negative numbers don't have real square roots, so there is no solution

4 0

2 years ago

The mean per capita income is 23,037 dollars per annum with a variance of 149,769. What is the probability that the sample mean

mihalych1998 [28]

Answer:

Probability that the sample mean would be less than 23,013 dollars is 0.2358.

Step-by-step explanation:

We are given that the mean per capita income is 23,037 dollars per annum with a variance of 149,769.

Also, a sample of 134 persons is randomly selected.

Firstly, Let $\bar X$ = sample mean

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean per capita income = 23,037 dollars p.a.

$\sigma$ = standard deviation = $\sqrt{Variance}$ = $\sqrt{149,769}$ = 387 dollars p.a

n = sample of persons = 134

So, probability that the sample mean would be less than 23,013 dollars is given by = P( $\bar X$ < 23,013 dollars)

P( $\bar X$ < 23,013) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{23,013-23,037}{\frac{387}{\sqrt{134} } }$ ) = P(Z < -0.72) = 1 - P(Z $\leq$ 0.72)