For rectangle
l=3.07m
b=2.24m
so longest side that can be drawn is diagonal of rectangular board
=squareroot l^2+b^2
=squareroot3.07^2+2.24^2
=squareroot9.4249+5.0176
=squareroot14.4425
=3.80
So longest line that can be drawn in rectangular board is 3.80m
Question not correct, so i have attached the correct question.
Answer:
SE = 0.59
Step-by-step explanation:
The mean of the students height is;
x' = (53 + 52.5 + 54 + 51 + 50.5 + 49.5 + 48 + 53 + 52 + 50)/10
x' = 51.35
Now, deviation from the mean for each height;
53 - 51.35 = 1.65
52.5 - 51.35 = 1.15
54 - 51.35 = 2.65
51 - 51.35 = -0.35
50.5 - 51.35 = -0.85
49.5 - 51.35 = -1.85
48 - 51.35 = -3.35
53 - 51.35 = 1.65
52 - 51.35 = 0.65
50 - 51.35 = -1.35
Now, square of the deviations above;
1.65² = 2.7225
1.15² = 1.3225
2.65² = 7.0225
-0.35² = 0.1225
-0.85² = 0.7225
-1.85² = 3.4225
-3.35² = 11.2225
1.65² = 2.7225
0.65² = 0.4225
-1.35² = 1.8225
Sum of the squared deviations;
2.7225 + 1.3225 + 7.0225 + 0.1225 + 0.7225 + 3.4225 + 11.2225 + 2.7225 + 0.4225 + 1.8225 = 31.525
Let's divide the sum by the DF of n - 1 i.e 10 - 1 = 9.
Thus;
31.525/9 = 3.50278
Taking the square root of that gives us the standard deviation.
Thus;
s = √3.50278
s = 1.8716
Formula for standard error is;
SE = s/√n
SE = 1.8716/√10
SE = 0.59
You need to calculate how many times the required difference is of the standard deviation, i.e. the ratio difference / standard deviation.
These are the calculations:
Standard deviation = 0.2 mm
Difference between 25.6mm and the mean = 25.6mm - 25mm = 0.6 mm
Ratio difference / standard deviation = 0.6mm / 0.2 mm = 3.
Then, the answer is that a ball with a diameter of 25.6 mm differs 3 standard deviations from the mean.
Answer:
so that number becomes divisible by 3, 6 and 9.
Step-by-step explanation:
In Number Theory there is a rule of thumb which states that sum of digits of a multiple of 3 equal 3 or a multiple of three. If we know that
, then its sum of digits is:

(Eq. 1)
We have to determine which digits corresponds to multiples of three, there are four digits:
N = 0

(
)
N = 3

(
)
N = 6

(
)
N = 9

(
)
We get the following four distinct options: 154038, 154338, 154638, 154938. Now we find which number is divisible by 6 and 9 by factor decomposition:




It is quite evident that
so that number becomes divisible by 3, 6 and 9.