First recognize that the unit rate we're finding is gallons per hour, or
.
rate for Tank 1 = x gallons per hour = <em>a</em> gallons / <em>b</em> hours
rate for Tank 2 = y gallons per hour = <em>c</em> gallons / <em>d</em> hours
Answer:
The coordinates of point k are (-2.8,-3)
Step-by-step explanation:
we shall use the internal division formula to find the coordinates of point k
Mathematically, the formula is as follows;
Let’s call the coordinates of point k (x,y)
(x , y) = mx2 + nx1/(m + n) , my2 + ny1/(m + n)
From the question;
m = 1 , n = 4
x1 = 4, x2= -2
y1 = -7 , y2 = 13
Substituting these values in the equation, we have the following;
1(-2) + 4(4)/(1 + 4) , 1(13) + 4(-7)/(1+4)
(-2+16)/5, (13 -28)/5
= -14/5, -15/5
= (-2.8, -3)
is a quadratic function, so its graph is a parabola.
Notice that the coefficient of x is 0, this always means that the axis of symmetry is the y-axis.
That is, the vertex of the parabola is in the y-axis, so the x-coordinate of the vertex is 0.
for x=0, y=-1. So the vertex is (0, -1)
The coefficient of
is negative. This means that the parabola opens downwards, so the vertex is a maximum.
Answer: (0, -1) , maximum (none of the choices)
C is your answer i hope u got it right
Answer:
The probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
And the standard deviation of the distribution of sample mean is given by,
The information provided is:
<em>μ</em> = 144 mm
<em>σ</em> = 7 mm
<em>n</em> = 50.
Since <em>n</em> = 50 > 30, the Central limit theorem can be applied to approximate the sampling distribution of sample mean.
Compute the probability that the sample mean would differ from the population mean by more than 2.6 mm as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.
