Prove by mathematical induction.<br> 2n<(n+2)!, for n ≥ 0, where n ∈ ℤ

Must show work-Solve the conjunction and describe the solution set. −5 < 2x + 3 < 9

Tema [17]

The solution set of the inequality −5 < 2x + 3 < 9 is (-4,3)

<h3>How to solve the inequality?</h3>

The compound inequality is given as:

−5 < 2x + 3 < 9

Expand the inequality

−5 < 2x + 3 or 2x + 3 < 9

Rewrite as:

2x + 3 > -5 or 2x + 3 < 9

Subtract 3 from both sides

2x > -8 or 2x < 6

Divide both sides by 2

x > -4 or x < 3

Rewrite as:

(-4,3)

Hence, the solution set of the inequality is (-4,3)

Read more about inequality at

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8 0

2 years ago

Suppose that in a large metropolitan area, 73% of all households have cable tv. Suppose you are interested in selecting a group

Darina [25.2K]

Answer:

$P(X \leq 2)=0.000387+0.00628+0.0425=0.0491$

Step-by-step explanation:

1) 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".

2) Solution to the problem

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

$X \sim Binom(n=6, p=0.73)$

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:

$nCx=\frac{n!}{(n-x)! x!}$

For what proportion of groups will at most two of the households have cable tv?

So we want to find this probability:

$P(X \leq 2)=P(X=0)+P(X=1)+P(X=2)$

$P(X=0)=(6C0)(0.73)^0 (1-0.73)^{6-0}=0.000387$

$P(X=1)=(6C1)(0.73)^1 (1-0.73)^{6-1}=0.00628$

$P(X=2)=(6C2)(0.73)^2 (1-0.73)^{6-2}=0.0425$

$P(X \leq 2)=0.000387+0.00628+0.0425=0.0491$

3 0

3 years ago

Create an equation with the indicated number of solutions.

GenaCL600 [577]

An equation that doesn't have a solution would have to end up as something impossible when you solve it all out, like
5=3.

When you simplify your equation out, you get

3x-4=3x+?

Subtract 3x from both sides.

-4=?

From this, you can tell that you need to out something in the ? that will make the equation false, or something that doesn't equal -4.

You could put anything in the ? as long as it is not -4.

Hope this helps!

4 0

3 years ago

The least common denominator of two fractions is 20. If you subtract the two denominations, you get 1. What are the denominators

LekaFEV [45]

Steps
find the Least Common Multiple of the denominators (which is called the Least Common Denominator).

Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator.

Then add (or subtract) the fractions, as we wish!
your denominators stay the same so its 20

6 0

3 years ago

What is a closed line of credit

Vinvika [58]

You may start out with a "line of credit" agreement with a bank that allows you to create relatively small loans by the bank to yourself at a specified interest rate and under other specific terms. Of course you must repay these loans, with interest, and that's how the bank makes its money.

If you fail to repay the bank, the bank may close your account and demand that you immediately repay all the money you owe it. A "closed line of credit" is a pretty sad thing.

7 0

4 years ago

Read 2 more answers

Prove by mathematical induction. 2n<(n+2)!, for n ≥ 0, where n ∈ ℤ