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3 years ago

Find the ordered pair (x,y) that is a solution to the equation.

Mathematics

1 answer:

miv72 [106K]3 years ago

4 0

Answer:

☑ (¼, 0)

Step-by-step explanation:

${ \tt{4x - y = 1}}$

» Assume y is zero:

${ \tt{4x - 0 = 1}} \\ { \tt{4x = 1}} \\ { \tt{x = \frac{1}{4} }}$

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What is the gcf of 48, 64 and 72

ziro4ka [17]

The greatest common factor is 8 because Prime factor is 2 and 4, Number 48 is 4 and 1 Number 64 is 6 and o Number 72 is 3 and 0 which it would all equal 2^3 so 48 = 2^4 times 3 64 = 2^6 and 72 = 2^3 times 3^2 Hope this helps.

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3 years ago

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A population of 120,000 grows 3% per year for 14 years

kobusy [5.1K]

Answer:

181510

Step-by-step explanation:

120,000 x1.03∧14=181510.767

Round the answer down as you can't have 0.767 of a person.

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3 years ago

Solve 4x - 3 = 18. Round to the nearest thousandth.

lorasvet [3.4K]

Answer:

$x=5.250$

Step-by-step explanation:

We have been given an equation $4x-3=18$ . We are asked to solve our given equation.

First of all, we will add 3 to both sides of our equation.

$4x-3+3=18+3$

$4x=21$

Now, we will divide both sides of our equation by 4.

$\frac{4x}{4}=\frac{21}{4}$

$x=5.25$

Upon rounding our answer to nearest thousandth (3 places after decimal) we will get,

$x=5.250$

Therefore, the solution for our given equation is $x=5.250$ .

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3 years ago

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How can you check the solution of an equation?

vichka [17]

In order to check you would plug in the value of x and see if it equals the same thing.
or do the opposite of the equation. it depends on if you are dealing with x or not. so if you have 6-3 is 3 you can do 3+3 is 6

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3 years ago

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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

7 0

3 years ago