Answer: 29.3333333
Step-by-step explanation: multiply
Answer:
see explanation
Step-by-step explanation:
a and b lie on the straight line CA, hence
and b sum to 180°, that is supplementary angles
10-x=C=2πr
(10-x)/(2π)=r
A=π(100-20x+x^2)/(4π^2)
A=(x^2-20x+100)/(4π)
...
x/4=s, x=4s using this in the area of a circle we get:
A=(16s^2-80s+100)/(4π)
A=(4s^2-20s+25)/π
And of course the area of a square is s^2
A=(4s^2+πs^2-20s+25)/π
Answer:
y = negative 2 (x minus one-half)
Step-by-step explanation:
The equation of a line is given as:
y = mx + c, where m is the slope and c is the intercept on the y axis.
The equation of a line going through (0, 1) and (1, - 1) is calculated using:
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ y-1=\frac{-1-1}{1-0}(x-0)\\ y-1=-2x\\y=-2x+1](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29%5C%5C%20y-1%3D%5Cfrac%7B-1-1%7D%7B1-0%7D%28x-0%29%5C%5C%20y-1%3D-2x%5C%5Cy%3D-2x%2B1)
The solution of two lines is at their point of intersection. The equation of the line that would not have any solution with y = -2x + 1 would be a line that is parallel to y = -2x + 1. Since the two lines would be parallel to each other, their would be no intersection and therefore no solution.
Two lines are said to be parallel to each other if they have the same slope. The slope of y = -2x + 1 is gotten by comparing with y = mx + c, therefore the slope m = -2. From the options the only line with a slope m = -2 is y = -2(x -1/2). Therefore y = -2(x -1/2) is parallel to y = -2x + 1 and would have no solution
Answer:
0.79 ; 0.753
Step-by-step explanation:
Given that:
Students who have spent at least five hours studying GMAT review guides have a probability of 0.85 of scoring above 400 :
≥ 5 hours review = 0.85
Students who do not spend at least five hours reviewing have a probability of 0.65 of scoring above 400
< 5 hours = 0.65
70% (0.7) of business students spend atleast 5 hours review time
A.) probability of scoring above 400
(Proportion who spend atleast 5 hours review time * 0.85) + (Proportion who do not spend atleast 5 hours * 0.65)
Proportion who do not spend atleast 5 hours = (1 - proportion who spend atleast 5 hours) = 1 - 0.7 = 0.3
Hence,
P(scoring above 400) = (0.7 * 0.85) + (0.3 * 0.65) = 0.595 + 0.195
= 0.79
B.) probability that given a student scored above 400, he/she spent at least five hours reviewing for the test.
P(spent ≥5 hours review | score above 400) :
P(spent ≥5 hours review) / P(score > 400)
(0.7 * 0.85) / 0.79
0.595 / 0.79
= 0.753