A line in point-slope form has the equation
y = mx + b
where m=slope (increase in y for unit increase in x), and
b=y-intercept (value of y where line cuts y-axis)
The original line is
y=(-1/2)x + 11
so
slope = m = -1/2
Any line perpendicular to a line with slope m has a slope of m1=-1/m
So the slope m1 of the required line
m1 = -1 / (-1/2) = +2
and the required line therefore has an equation of
y=2x+b
Knowing that the line passes through P1=(x1, y1)=(4,-8), we can find b using the point slope form of a line with slope m : (y-y1) = m(x-x1)
where m=+2 as found above.
Substituting values, m=+2, x1=4, y1= -8
y-(-8) = +2(x--4)
simplify
y+8 = 2x-8
=>
y=2x-16 (in point slope form)
Answer:
H0: The new cancer drug increases the mean survival time by 30 days
Ha: The new cancer drug increases the mean survival time by 30 or more than 30 days.
If fail to reject H0 (the null hypothesis), the conclusion is that the new cancer drug increases the mean survival time by 30 days.
Step-by-step explanation:
The null hypothesis is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing. It is expressed using the equality sign.
The alternate hypothesis is also a statement from a population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected. It is expressed using any of the inequality signs.
The test is a two-tailed test because the alternate hypothesis is expressed using more than or equal to.
If I fail to reject H0, it means the test statistic falls within the region bounded by the critical values.
It would therefore be concluded that the new cancer drug increases the mean survival time by 30 days.
Remark
That was well worth doing. Desmos gave you the answer to the graph. Unfortunately I can only give you the correct graph. You will have to figure out from the choices which one is the correct answer -- or edit it so I can see what the rest of the question is.
Graph
The red one is f(x) is x + 3 {x <= -2}
The blue one is f(x) is x^2 - 1 {-2 <x <1} Notice the gap at 2. It is not continuous
The green one is f(x) is log_2(-x + 3) {1 <=x < 3} and there is a gap between the blue and green one.
Answer:
520?
Step-by-step explanation:
I think
