-10. One type of system of equations that results in infinite solutions is one where both sides of the equation are exactly equal. Here, setting the second equation equal to -10 becomes 2y - 4x = -10. This can be rearranged into 2y = 4x - 10. Dividing everything by 2 results in y = 2x - 5, which is exactly what the first equation is. Substituting one equation into another, we get 2x - 5 = 2x - 5, which is a true statement for all values of x.
Answer:
Standard Deviation, σ = 6.5828058860438
Step-by-step explanation:
<u>Data Set:</u> 20, 11, 27, 13, 29, 20
The total numbers in the data set
Count, N = 6
The sum is all values in the data set is added up
20 + 11 + 27 + 13 + 29 + 20
Sum, Σx: 120
The mean is the sim / N
Mean, μ: 20
Answer:
169.56 m³
Step-by-step explanation:
» <u>Concepts</u>
The volume of a cylinder is how much space there is inside the cylinder. The formula to find the volume is πr²h, where r = radius and h = height. Once you get the volume, you have to add <unit>³.
» <u>Application</u>
We are given the radius as three meters and the height as six meters; we also have to use π as 3.14. Now, we just have to plug in these values into the aforementioned formula.
» <u>Solution</u>
Answer:
a)= 2
b) 6.324
c) P= 0.1217
Step-by-step explanation:
a) The mean of the sampling distribution of X`1- X`2 denoted by ux`-x` = u1-u2 is equal to the difference between population means i.e = 2 ( given in the question)
b) The standard deviation of the sampling distribution of X`1- X`2 ( standard error of X`1- X`2) denoted by σ_X`1- X`2 is given by
σ_X`1- X`2 = √σ²/n1 +σ²/n2
Var ( X`1- X`2) = Var X`1 + Var X`2 = σ²/n1 +σ²/n2
so
σ_X`1- X`2 =√20 +20 = 6.324
if the populations are normal the sampling distribution X`1- X`2 , regardless of sample sizes , will be normal with mean u1-u2 and variance σ²/n1 +σ²/n2.
Where as Z is normally distributed with mean zero and unit variance.
If we take X`1- X`2= 0 and u1-u2= 2 and standard deviation of the sampling distribution = 6.324 then
Z= 0-2/ 6.342= -0.31625
P(-0.31625<z<0)= 0.1217
The probability would be 0.1217
Answer:
1. Simplify: (4x2 - 2x) - (-5x2 - 8x).
Solution:
(4x2 - 2x) - (-5x2 - 8x)
= 4x2 - 2x + 5x2 + 8x.
= 4x2 + 5x2 - 2x + 8x.
= 9x2 + 6x.
= 3x(3x + 2).
Answer: 3x(3x + 2)
Step-by-step explanation:
