6/54-x = 5/x <br>x=____<br><br><br><br>

Finding an irrational number between which given pair of numbers supports the idea that irrational numbers are dense

Fittoniya [83]

Answer:

3.33 and 1/3

Step-by-step explanation:

"Dense" here means that there are infinite irrational numbers between two rational numbers. Also, there are infinite rational numbers between two rational numbers. That's the meaning of dense. Actually, that can be apply to all real numbers, there always is gonna be a number between other two.

But, to demonstrate that irrationals are dense, we have to based on an interval with rational limits, because the theorem about dense sets is about rationals, and the dense irrational set is a deduction from it. That's why the best option is 2, because that's an interval with rational limits.

8 0

3 years ago

A company compiles data on a variety of issues in education. In 2004 the company reported that the national college freshman-to

nasty-shy [4]

Answer:

1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

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

And we have :

$\mu_p = 0.66$

$\sigma_{p}= \sqrt{\frac{0.66(1-0.66)}{500}}= 0.0212$

Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).

Step-by-step explanation:

For this case we know that we have a sample of n = 500 students and we have a percentage of expected return for their sophomore years given 66% and on fraction would be 0.66 and we are interested on the distribution for the population proportion p.

We want to know if we can apply the normal approximation, so we need to check 3 conditions:

1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

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

And we have :

$\mu_p = 0.66$

$\sigma_{p}= \sqrt{\frac{0.66(1-0.66)}{500}}= 0.0212$

And we can use the empirical rule to describe the distribution of percentages.

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).

8 0

3 years ago

at the county fair , 12% of the pepole who attended received free water bottels . if 1,500 people receive dfree water bottles ,

sweet-ann [11.9K]

12500 people went to fair

<h3><u>Solution:</u></h3>

Given that at the county fair , 12% of the people who attended received free water bottles

1,500 people received free water bottles

To find: number of peoples went to fair

Let "a" be the number of peoples went to fair

From given information,

12% of the people who attended received free water bottles and 1,500 people received free water bottles

Which means 12% of total people is equal to 1500

12% of total people = 1500

12 % of "a" = 1500

$\frac{12}{100} \times a = 1500\\\\a = 1500 \times \frac{100}{12}\\\\a = \frac{150000}{12} = 12500$

Thus 12500 people went to fair

3 0

3 years ago

Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 9-inch perimeter A = sq. in.

Alona [7]

Answer:

$3.9 in^2$

Step-by-step explanation:

The area of a triangle is given by

$A=\frac{1}{2}bh$

where

b is the base

h is the height

Here we have an equilateral triangle, which has the 3 sides of the same length.

Let's call L the length of one side.

We know that the perimeter of the triangle is

p = 9 in

The perimeter is the sum of the three sides, so:

$p=L+L+L=3L$

Therefore, we find the length of the side:

$L=\frac{p}{3}=\frac{9}{3}=3 in$

Therefore the length is the base of the triangle,

$b=L$

The height can be calculated by considering half triangle: the hypothenuse is equal to L, while one side is equal to half the base (b/2), therefore the height is given by Pythagorean's theorem:

$h=\sqrt{L^2-(\frac{b}{2})^2}=\sqrt{3^2-(\frac{3}{2})^2}=2.6 in$

Therefore, the area of the triangle is:

$A=\frac{1}{2}(3)(2.6)=3.9 in^2$

5 0

3 years ago

Leonard earns $8.75 per hour working at a bowling alley. Last weekend, he worked for 5.4 hours. How much money did Leonard earn

sertanlavr [38]

Answer:

$47.25

Step-by-step explanation:

Earnings = (rate of pay)(number of hours worked)

Here,

Earnings last weekend = ($8.75/hr)(5.4 hrs) = $47.25

4 0

3 years ago

6/54-x = 5/x x=____​

6/54-x = 5/x x=____