Answer:
2 is the absolute mean deviation
Step-by-step explanation:
absolute mean deviation is
the average of the differences of the data from the average
8, 8, 4, 12
1. take the average
8+8+4+12=32 -> 32/4 = 8
2. subtract each number from this average
8 - 8 = 0
8 - 8 = 0
4 - 8 = 4 (there are no negative answers)
12 - 8 = 4
3. take the average of these subtractions
0+0+4+4=8 -> 8/4 = 2
4. answer: 2 is the absolute mean deviation
Answer:
82.
Step-by-step explanation:
Let the largest number of be 'a'.
Let the middle number be 'b'.
Let the smallest number be 'c'.
From the question given above,
The sum of the three numbers is 223. This can be written as:
a + b + c = 223 .... (1)
The largest number is 13 more than the smallest number. This can be written as:
a = c + 13 ..... (2)
The sum of the largest number and the smallest number is 7 more than twice the middle number. This can be written as:
a + c = 2b + 7..... (3)
Summary:
a + b + c = 223 .... (1)
a = c + 13 ..... (2)
a + c = 2b + 7..... (3)
Substitute the value of a in equation 2 into equation 3. This is illustrated below:
a + c = 2b + 7
a = c + 13
c + 13 + c = 2b + 7
2c + 13 = 2b + 7
Make b the subject
2c + 13 – 7 = 2b
2c + 6 = 2b
2(c + 3) = 2b
Divide both side by 2
b = 2(c + 3) / 2
b = c + 3 ..... (4)
Substitute the value of a in equation 2 and the value of b in equation 4 into equation 1. This is illustrated below:
a + b + c = 223
a = c + 13
b = c + 3
(c + 13) + (c + 3) + c = 223
c + 13 + c + 3 + c = 223
3c + 16 = 223
Collect like terms
3c = 223 – 16
3c = 207
Divide both side by 3
c = 207/3
c = 69
The smallest number (c) is 69
Substitute the value of c into equation 2 to obtain the largest number (a). This is illustrated below:
a = c + 13
c = 69
a = 69 + 13
a = 82
Therefore, the largest number (a) is 82
30 x 28= 840
It's would beat 840 times in half an hour.
Answer:
![\sqrt{13}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D)
Step-by-step explanation:
We are given an isosceles triangle. We need to remember the important rule that the base angles are equal. In this question we need to find the value of 'x' using a perpendicular height of 3 and a base length of 4. In this question we can half the triangle in half to help us find the value of x. Also we need to use Pythagoras theorem to help us find 'x'. Pythagoras states that a² + b² = c² so we want to find the hypotenuse of the triangle. If we half the triangle we get 2 triangle both with a base length of 2 and a perpendicular height of 3 so,
⇒ State Pythagoras theorem
→ a² + b² = c²
⇒ Substitute in the values
→ 3² + 2² = c²
⇒ Simplify
→ 9 + 4 = c²
⇒ Simplify further
→ 13 = c²
⇒ Square root both sides to find the value of 'c'
→
= c
The value of x is the square root of 13