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pychu [463]
3 years ago
14

Assignment: Show Me the Sets Investigation

Mathematics
1 answer:
Fofino [41]3 years ago
3 0

Answer: Consider a power set \mathbb{R} of real numbers.

The subsets of the power set are as follows:-

1. Natural number(\mathbb{N})={1,2,3,4,5,....}

2.Whole numbers\mathbb{W}={0,1,2,3,4,......}

3.Integers(\mathbb{I})={.......-3,-2,-1,0,1,2,3,....}

4.Rational numbers(\mathbb{Q})=It contains all of the above subsets and fractions (where denominator ≠ 0) ,terminating and repeating decimals.

5.Irrational numbers=It contains numbers which cannot be expressed as the ratio of integers, and they are non-repeating, non-terminating decimals.


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Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st
Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)  

b) n=523 rounded up to the nearest integer  

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".  

\bar X=530 represent the sample mean for the sample  

\mu population mean

s=70 represent the sample standard deviation  

n=48 represent the sample size (variable of interest)  

Confidence =95% or 0.995

Part a

The confidence interval for the mean is given by the following formula:  

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}} (1)  

The degrees of freedom are df=n-1=48-1=47

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,47)".And we see that z_{\alpha/2}=2.01  

Now we have everything in order to replace into formula (1):  

530-2.01\frac{70}{\sqrt{48}}=509.692  

530+2.01\frac{70}{\sqrt{48}}=550.308  

So on this case the 95% confidence interval would be given by (509.592;550.308)  

Part b

The margin of error is given by this formula:  

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (a)  

Assuming that \hat \sigma =s

And on this case we have that ME =6msec, and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=(\frac{z_{\alpha/2} \sigma}{ME})^2 (b)  

The critical value for 95% of confidence interval is provided, z_{\alpha/2}=1.96, replacing into formula (b) we got:  

n=(\frac{1.96(70)}{6})^2 =522.88 \approx 523  

So the answer for this case would be n=523 rounded up to the nearest integer  

3 0
3 years ago
What is 2,117 divided by 3
sweet [91]
The answer is 705.666667. Rounded the answer is about 706. As a fraction it it 705 666667/1000000 (it cannot be simplified any further).
I hope this helps:)
6 0
3 years ago
A horse trot in a circle around it's trainer at the end of a 31 foot long rope. Find the area of the circle that is swept out. R
Mnenie [13.5K]
So, imagine the trainer is in the very middle of the circle and he is holding out a rope that's attached to the horse. The rope here from the trainer to the horse represents the radius of the circle. The horse trots around the trainer (middle point) in a circle.
The formula to find area of a circle is A = pi*r^2 (pi times r squared where r is radius)
We know that the radius of the "circle" here formed as the horse trots around the trainer is 31 (the 31 foot long rope). 
So let r = 31 & plug the value into the formula to find circle area.
A = pi*31^2 = 3019.07054
The area is therefore 3019.07 square feet. (rounded)

3 0
3 years ago
Identify the values of a, b, and c that would be used in the quadratic formula to solve the equation 3x2− 5x + 5 = 0. A. a = 3,
stepan [7]
<span>3x2− 5x + 5 = 0.
a=3 b=-5 c=5

A. a = 3, b = 5, c = 5
B. a = 3, b = −5, c = 5
C. a = 5, b = −5, c = 0
D. a = −3, b = 5, c = −5

answer is B


</span>
6 0
4 years ago
Given that x = 3, y = -2 and z = 0, calculate the value of each of the following algebraic expressions: 2x + y. Answer quick ple
icang [17]
2 times 3+(-2)
6-2
4. Is the cord answer
4 0
3 years ago
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