Slope intercept form of an equation is:
y = mx + b
where m is the slope and b is the t intercept.
First you must determine the slope of the line. This is a ratio of how fast the line travels up or down vs how fast it is moving to the right. Another name for this is rise over run. The equation to find the slope is:
m = (y1 - y2) / (x1 - x2)
now to find b. We can plug in one of the points of the equation into our first equation along with the slope to get out b value.
So if our 2 points were (2, 3) and (3, 4) we could find slope intercept form like this:
m = (2 - 3) / (3 - 4)
m = -1 / -1
m = 1
Now taking point (2, 3)
3 = 1 * 2 + b
1 = b
Finally to plug our m and b into equation for answer:
y = 1x + 1
However, 1 * anything is redundant therefore:
y = x + 1
Convert all numbers into fractions:
-29/6
-31/9
Find a common denominator
-87/18
-62/18
Perform the operation
-149/18
Answer:
The volume of the sphere is 24416.6 cm³
Step-by-step explanation:
To calculate the volume of a sphere we have to use the following formula:
v = volume
r = radius
v = ⁴⁄₃πr³.
To solve this formula we first have to have all the data, as we see we need to calculate the radius, which is calculated by dividing the diameter by 2
r = d/2
r = 36cm/2
r = 18cm
Now that we have all the data we can solve the formula
v = ⁴⁄₃πr³.
v = ⁴⁄₃ * 3.14 * (18cm)³
v = 24416.64 cm³
Round to the nearest tenth
v = 24416.6 cm³
Answer:
133/143
Step-by-step explanation:
Let S be the sample space
Let E be the event of selecting three committee partners with at least one junior partner.
Partners in the law firm include:
Senior partners = 6
Junior partners = 7
Total partners = 13
n(S) = number of ways of selecting 3 partners from 13 = 13C3
n(S) = 13C3 = 13!/(10!3!) = (13x12x11)/(3x2x1) = 286
To get n(E) i.e least 1 junior partner in the selected committee, we may have:
(2 senior and 1 junior) or ( 1 senior and 2 junior) or (3 junior).
Therefore, the required number of way is given below:
= (6C2 x 7C1) + (6C1 x 7C2) + 7C3
= [(6x5)/2 x 7] + [6 x (7x6)/2] + [(7x6x5)/(3x2)]
= 105 + 126 + 35
n(E) = 266
Therefore, the probability P(E) that at least one of the junior partners is on the committee is given below:
P(E) = n(E) /n(S)
P(E) = 266/286
P(E) = 133/143
