Answer:
The slope of the line is .
Step-by-step explanation:
We are given the line in standard form:
We need to get this into slope-intercept form in order to determine the slope of the line.
Slope-intercept form is , where <em>m</em> is our slope and <em>b</em> is the y-intercept.
Therefore, we need to get:
converted to:
Therefore, by solving the equation in slope-intercept form, we see that <em>m</em> equals 9/14, so our slope is .
Answer:
so the limits are 2 and 9
Step-by-step explanation:
We want to express as a integral. To do this, we have to identify
as a Riemann Sum that approximates the integral. (taking the limit makes the approximation equal to the value of the integral)
In general, to find a Riemann sum that approximates the integral of a function f over an interval [a,b] we can the interval in n subintervals of equal length and approximate the area (integral) with rectangles in each subinterval and them sum the areas. This is equal to
, where
is a selected point of the subinterval.
In particular, if we select the ending point of each subinterval as the , the Riemann sum is:
.
Now, let's identify this in .
The integrand is x² so this is our function f. When k=n, the summand should be because the last selected point is b. The last summand is
thus b=9 and b-a=7, then 9-a=7 which implies that a=2.
To verify our answer, note that if we substitute a=2, b=9 and f(x)=x² in the general Riemann Sum, we obtain the sum inside the limit as required.
Answer:
The probability that the next spin will land on blue is 0.12.
Step-by-step explanation:
The result of the several spins are as follows:
Color Frequency
Red 18
Blue 9
Green 18
Yellow 19
Purple 12
TOTAL 76
Compute the probability that the next spin will land on blue as follows:
Thus, the probability that the next spin will land on blue is 0.12.