Answer:
Where is the statement mate
Answer:
both are true
Step-by-step explanation:
have a great day
Prime numbers are numbers that have only one factor pair; 1 and themselves.
Let's start from 21.
21 = 1 x 21, 3 x 7.
This has two factor pairs, this is not prime.
Let's try 22.
22 = 1 x 22, 2 x 11.
This also has two factor pairs, this is not prime.
Let's try 23.
1 x 23.
This is a prime number, as it only has one factor pair; 1 and itself.
23 is your prime number.
I hope this helps!
Answer:
The answer is below
Step-by-step explanation:
Let us assume the rate of printing in machine A is x per hour and the rate for machine B is y. Given that machine B prints at half the rate of machine A, therefore:
y = (1/2)x (1)
Also, both machine produces 200 newspaper printouts, and both operate at different times for a total of 4 hours. Therefore:
200/x + 200/y = 4 (2)
Put y = (1/2)x in equation:
![\frac{200}{x}+\frac{200}{(\frac{1}{2} )x}=4\\ \\ \frac{200}{x}+\frac{400}{x}=4\\\\Multiply\ through\ by\ x:\\\\200+400=4x\\\\4x=600\\\\x=150](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7Bx%7D%2B%5Cfrac%7B200%7D%7B%28%5Cfrac%7B1%7D%7B2%7D%20%29x%7D%3D4%5C%5C%20%5C%5C%20%5Cfrac%7B200%7D%7Bx%7D%2B%5Cfrac%7B400%7D%7Bx%7D%3D4%5C%5C%5C%5CMultiply%5C%20through%5C%20by%5C%20x%3A%5C%5C%5C%5C200%2B400%3D4x%5C%5C%5C%5C4x%3D600%5C%5C%5C%5Cx%3D150)
Put x = 150 in equation y:
y=(1/2)150 = 75
Therefore the rate of machine A is 150 newspapers per hour while that of machine B is 75 newspapers per hour
Answer:
a
![\= x = 82](https://tex.z-dn.net/?f=%5C%3D%20x%20%20%3D%20%2082%20)
b
![s = 9.64](https://tex.z-dn.net/?f=s%20%3D%20%209.64%20)
Step-by-step explanation:
From the question we are told that
The data is 87 91 86 82 72 91 60 77 80 79 83 96
Generally the point estimate for the mean is mathematically represented as
![\= x = \frac{\sum x_i }{n}](https://tex.z-dn.net/?f=%5C%3D%20x%20%20%3D%20%20%5Cfrac%7B%5Csum%20%20x_i%20%7D%7Bn%7D)
=> ![\= x = \frac{87 +91 + 86 + \cdots + 96}{12}](https://tex.z-dn.net/?f=%5C%3D%20x%20%20%3D%20%20%5Cfrac%7B87%20%2B91%20%2B%2086%20%2B%20%5Ccdots%20%20%2B%2096%7D%7B12%7D)
=>
Generally the point estimate for the standard deviation is mathematically represented as
![s = \sqrt{\frac{ \sum ( x_i - \= x )^2 }{ n -1 } }](https://tex.z-dn.net/?f=s%20%3D%20%20%5Csqrt%7B%5Cfrac%7B%20%5Csum%20%28%20x_i%20%20-%20%5C%3D%20x%20%29%5E2%20%7D%7B%20n%20-1%20%7D%20%7D)
=> ![s = \sqrt{\frac{ ( 87 - 82 )^2 +( 91 - 82 )^2 + \cdots + ( 96 - 82 )^2 }{ 12 -1 } }](https://tex.z-dn.net/?f=s%20%3D%20%20%5Csqrt%7B%5Cfrac%7B%20%28%2087%20-%2082%20%20%29%5E2%20%2B%28%2091%20-%2082%20%20%29%5E2%20%2B%20%5Ccdots%20%2B%20%28%2096%20-%2082%20%20%29%5E2%20%20%7D%7B%2012%20-1%20%7D%20%7D)
=> ![s = 9.64](https://tex.z-dn.net/?f=s%20%3D%20%209.64%20)