PLEASE HELP WITH THIS!

Is the number rational or irrational?

skelet666 [1.2K]

1. rational
2. irrational
3. rational
4. irrational

8 0

3 years ago

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Find P(5)-p(3) if P(2x)+P(4x)+P(6x)=24x-6

professor190 [17]

Answer:

P(5) - P(3) = 4

Step-by-step explanation:

Lets explain how to solve the problem

Assume that P(x) is a linear function, that because the sum of P(2x),

P(4x), and P(6x) is linear ⇒ (24x - 6 is linear)

∵ The form of the linear function is y = ax + b

∴ P(x) = ax + b

Substitute x by 2x

∵ P(2x) = a(2x) + b

∴ P(2x) = 2ax + b

Substitute x by 4x

∵ P(4x) = a(4x) + b

∴ P(4x) = 4ax + b

Substitute x by 6x

∵ P(6x) = a(6x) + b

∴ P(6x) = 6ax + b

Add the three functions

∴ P(2x) + P(4x) + P(6x) = 2ax + b + 4ax + b + 6ax + b

Add like terms

∴ P(2x) + P(4x) + P(6x) = 12ax + 3b ⇒ (1)

∵ P(2x) + P(4x) + P(6x) = 24x - 6 ⇒ (2)

Equate (1) and (2)

∴ 12ax + 3b = 24x - 6

By comparing the two sides

∴ 12a = 24 and 3b = -6

∵ 12a = 24

Divide both sides by 12

∴ a = 2

∵ 3b = -6

Divide both sides by 3

∴ b = -2

Substitute these values in P(x)

∵ P(x) = ax + b

∴ P(x) = 2x + (-2)

∴ P(x) = 2x - 2

Now we can find P(5) - P(3)

∵ P(5) = 2(5) - 2 = 10 - 2 = 8

∵ P(3) = 2(3) - 2 = 6 - 2 = 4

∴ P(5) - P(3) = 8 - 4 = 4

* P(5) - P(3) = 4

5 0

3 years ago

A survey is to be conducted in which a random sample of residents in a certain city will be asked whether they favor or oppose t

marshall27 [118]

Answer:

n=269 residents should be sample required to be sure that a 90% confidence interval for the proportion who favor the construction will have a margin of error no greater than 0.05

Step-by-step explanation:

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".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimates proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.64})^2}=268.96$

And rounded up we have that n=269

4 0

3 years ago

If n and k are positive integers and 8*n = 2*k , what is

ziro4ka [17]

Answer: 1/4

Step-by-step explanation:

$8n=2k\\\\4n=k\\\\4=\frac{k}{n}\\\\\frac{n}{k}=\frac{1}{4}$

6 0

1 year ago

Which biconditional is NOT a good definition

ZanzabumX [31]

The answer is: [C]: Two angles form [a] linear pair if and only if the angles are adjacent.
_____________________________
{Your answer choice is correct! Good job!}.
_______________________________________
Explanation:
__________________
Consider the answer choice given in: "Answer choice: [C]" :
_______________________
"Two angles form linear pair if and only if the angles are adjacent."
_____________________________
Then, consider the following:
__________________
1) "Two angles that are supplementary form a linear pair."
Is this true? Yes, but not always. (In other words, "sometimes"). A "linear pair" of angles IS supplementary (by definition); however, NOT ALL supplementary pairs of angles are linear angles. Supplementary pairs of angles must ALSO be ADJACENT in order to be "linear angles" as well.
2) "Two angles that are vertical are adjacent." Is this true? No; this is NEVER true
_____________
As such, this biconditional is NOT a good definition; and by examining all the other answer choices given, we see that this answer choice "C" is correct.
__________________
Consider the other answer choices given:
_________________________________________
Answer choice: [A]: "Two angles are supplementary if and only if the sum of their angles measures 180." ;
 is INCORRECT because it is a good definition:
1) If 2 angles are supplementary, then the sum of their measures is 180 degrees.
2) If the sum of the measures of two angles is 180 degrees, then the angles are supplementary.
___________________________________
Answer choice: [B]: "Two angles are vertical angles only if they are not adjacent to each other and are formed by two intersecting lines.";
is INCORRECT because it is a good definition:
1) If two angles are vertical, then they are nonadjacent angles formed by two intersecting lines.
 2) If two angles are nonadjacent angles formed by two intersecting lines, then the angles are vertical angles.
_____________________________________
Answer choice: [D]: "The sum of two angles is 90 if and only if those angles are complementary" ;
is INCORRECT because it is a good definition:
1) If two angles are complementary, then the sum of their measures is 90 degrees.
 2) f the sum of [the measures of] two angles is 90 degrees, then the angles are complementary.
_______________________________________________

7 0

4 years ago

Read 2 more answers