Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, - 6) and (x₂, y₂ ) = (2, - 3) ← 2 points on the line
m = = , thus
y = x + c ← is the partial equation
To find c substitute either ot the 2 points into the partial equation
Using (2, - 3), then
- 3 = + c ⇒ c = - 3 - = -
y = x - ← equation of line
If "a" and "b" are two values of x-coordinate, and "m" is the midpoint between them, it means the distance from one end to the midpoint is the same as the distance from the midpoint to the other end
... a-m = m-b
When we add m+b to this equation, we get
... a+b = 2m
Solving for m gives
... m = (a+b)/2
This applies to y-coordinates as well. So ...
... The midpoint between (x1, y1) and (x2, y2) is ((x1+x2)/2, (y1+y2)/2)
_____
Jennifer had (x1, y1) = (-4, 10) and (x2, y2) = (-2, 6). So her calculation would be
... midpoint = ((-4-2)/2, (10+6)/2) = (-6/2, 16/2) = (-3, 8)
Brandon had (x1, y1) = (9, -4) and (x2, y2) = (-12, 8). So his calculation would be
... midpoint = ((9-12)/2, (-4+8)/2) = (-3/2, 4/2) = (-1.5, 2)
Answer: There is one solution to the given equation.
Step-by-step explanation: We are given to find the number of solutions to the following equation :
Since the given equation is linear in one variable x, so it will have only one solution.
The solution of equation (i) is given by
Thus, there is one solution to the given equation.
Answer: the interval of heights that represents the middle 95% of male heights from this school is between 66 inches and 76 inches.
Step-by-step explanation:
Let x be a random variable representing the heights of males from this school. With the mean and standard deviation given, then the Empirical Rule says the that
1) About 68% of the x values lie between 1 standard deviation below and above the mean.
2) About 95% of the x values lie between 2 standard deviations below and above the mean.
3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.
From the information given,
mean = 71 inches
Standard deviation = 2.5 inches
We want to determine where 95% of x values lies. This is 2 standard deviations from the mean Therefore,
2 standard deviations = 2 × 2.5 = 5 inches
The heights are
71 - 5 = 66 inches and
71 + 5 = 76 inches
Divide the total cost by all 5 panes to get the cost of 1 pane:
14.25/5 = 2.85
Then multiply by 2:
2.85 * 2 = $5.7