Answer:
140
Step-by-step explanation:
Answer:
0.4060
Step-by-step explanation:
To calculate the sample proportion, phat, we take the ratio of the number of preferred outcome to the total number of trials ;
Phat = number of times coin lands on head (preferred outcome), x / total number of trials (total coin flips), n
x = 406
n = 1000
Phat = x / n = 406/ 1000 = 0.4060
Answer:
Unnnnnnnnnnnnnnnnnnnnnnnnbnbnnnn
Answer: Sergio's expression is incorrect because he can not simplify 3-6x and Leon's expression is incorrect because he did not multiply 3 by -1.
Step-by-step explanation:
Here, given expression, 9 - (3 - 6x)
After simplifying this we get the following steps,
Step 1) 9 - (3 - 6x) = 9 - 3 +6x ( by removing parenthesis ) -----(1)
Step 2) 9 - (3 - 6x) = 6 + 6x
Step 3) 9 - (3 - 6x) = 6(1 + x) ( because 6 is common in both term of right side)
Since, when Sergio simplified it he wrote 9−(-3x), which is not matching to the above steps. that, is he is incorrect, because in his explanation he wrote -3x after simplifying 3-6x which can not be solved.
Moreover, the expression of Leon is also not matching to any of the above steps,
Thus he is also incorrect because after removing parenthesis he did not multiply 3 by -1 .
Answer:
The equation of the perpendicular bisector is y = x - 3
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
The rule of the slope is m = , where
- (x1, y1) and (x2, y2) are two points on the line
- The rule of the mid-point is M = ()
- The product of the slopes of the perpendicular lines is -1, that means if the slope of one is m, then the slope of the other is (we reciprocal m and change its sign).
∵ A line passes through points (-1, 5) and (-7, -7)
∴ x1 = -1 ad y1 = 5
∴ x2 = -7 and y2 = -7
→ Use the rule of the slope above to find the slope of the line
∵ m = = = = 2
∴ m = 2
→ Reciprocal the value of m and change its sign to find the slope of
the line perpendicular line
∴ m⊥ =
→ Substitute in the form of the equation above
∵ y = x + b
∵ The ⊥ line is also the bisector of the given line, find the mid-point
of the given line because it is also lying on the ⊥ line
∵ M = () = () = (-4, -1)
∴ M = (-4, -1)
→ Substitute the coordinates of M in the equation of the ⊥ line above
∵ x = -4 and y = -1
∴ -1 = (-4) + b
∴ -1 = 2 + b
→ Subtract 2 from both sides
∴ -3 = b
→ Substitute the value of b in the equation
∴ y = x + -3
∴ y = x - 3
∴ The equation of the perpendicular bisector is y = x - 3