There is one zero in the ten thousands place.
There is another zero in the hundreds place.
Both of them have the value of zero.
Answer:
6 I think
Step-by-step explanation:
7 + 5(x - 3) = 22
7 + 5x - 15 = 22
7 + 5x = 37
5x = 30
x = 6
{ 6 }
Answer:
√3 is irrational
Step-by-step explanation:
The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.
<h3 /><h3>Location of point C</h3>
With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC <em>never passes through a point with integer coordinates</em>. (Any point with integer coordinates would be on a line with rational slope.)
<h3>Equilateral triangle</h3>
The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.
The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...
![\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Ccos%2860%5E%5Ccirc%29%26%5Csin%2860%5E%5Ccirc%29%5C%5C-%5Csin%2860%5E%5Ccirc%29%26%5Ccos%2860%5E%5Ccirc%29%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%27%5C%5Cy%27%5Cend%7Barray%7D%5Cright%5D)
Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...
cos(60°)·x + sin(60°)·y
will be irrational.
As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.
Answer:
Dinner: $45
Dinner after discount: $29.25
Tax after discount: $31.59
Tip before the discount: 6.75
Total cost: 38.34
Step-by-step explanation:
Hope it helps! :) (double check my work to be sure)
Answer:
Only option d is not true
Step-by-step explanation:
Given are four statements about standard errors and we have to find which is not true.
A. The standard error measures, roughly, the average difference between the statistic and the population parameter.
-- True because population parameter is mean and the statistic are the items. Hence the differences average would be std error.
B. The standard error is the estimated standard deviation of the sampling distribution for the statistic.
-- True the sample statistic follows a distribution with standard error as std deviation
C. The standard error can never be a negative number. -- True because we consider only positive square root of variance as std error
D. The standard error increases as the sample size(s) increases
-- False. Std error is inversely proportional to square root of n. So when n decreases std error increases