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3 years ago

Simplify the expression -3(x+3)+4x

Mathematics

2 answers:

Korolek [52]3 years ago

8 0

Answer:

x - 9

Step-by-step explanation:

In this case, "simplify" directs that you 1) carry out the indicated multiplication and 2) combine like terms.

-3(x+3)+4x = -3x - 9 + 4x = x - 9

m_a_m_a [10]3 years ago

7 0

Answer: x-9

Step-by-step explanation: To get rid of the parentheses you must distribute or multiply the -3 to all the numbers inside the parentheses.

-3(x+3)+4x

-3x-9+4x

Then we combine like terms which will give us our answer.

-3x-9+4x

x-9

Since this is an expression and not an equation there will <em>not </em>be a result. We are only simplifying the expression.

So the final answer is

<em><u>x-9 Hope this helps!</u></em>

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3 years ago

There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f

Ann [662]

Answer:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated population proportion for this case is:

$\hat p = \frac{350}{500}=0.7$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

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3 years ago

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Answer:

I guess I could be ur friend

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3 years ago

Read 2 more answers

Find the value of x for which the function y = x5-x³ + x² - 1 has a local minimum.

melisa1 [442]

The given function presents a local minimum in the coordinates (0,-1).

<h3>Factoring</h3>

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.

For solving this question, the given equation should be rewritten from the factoring.

$x^5-x^3+x^2-1=\left(x+1\right)^2\left(x-1\right)\left(x^2-x+1\right)=0$ . Then, you have 3 equations.

From the Zero Factor Principle, you can write

Equation 1

(x+1)²=0

x+1=0

x= -1

Equation 2

x-1=0

x=1

Equation 3

x²-x+1=0

$x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\ \\ x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{3}i}{2\cdot \:1}$

From these points it is possible to plot a graph and you can see that the local minimum presents the coordinates (0,-1).