Answer:
See below in bold,.
Step-by-step explanation:
There are 30-17 = 13 boys in the class.
a. Prob(First is a boy ) = 13/30 and Prob( second is a boy = 12/29).
As these 2 events are independent:
Prob( 2 boys being picked) = 13/30 * 12/29 = 26/145 or 0.179 to the nearest thousandth.
b. By a similar method to a:
Prob ( 2 girls being picked) = 17/30 * 16/29 = 136/435 = 0.313 to the nearest thousandth.
c. Prob (First student is a boy and second is a girl) = 13/30 * 17/29 = 221/870.
Prob ( first student is a girl and second is a boy) = 17/30 * 13/29 = 221/870
These 2 events are not independent so they are added:
Prob( one of the students is a boy) = 2 (221/870 = 221/435 = 0.508 to the nearest thousandth.
Answer:
x∈(-∞,3]
Step-by-step explanation:
2x-6<=5*3-5x
2x-6<=15-5x
+5x +5x
7x-6<=15
+6 +6
7x<=21
:7 :7
x<=3
x∈(-∞,3]
Answer:
y inversely proportional to 1/x
y=4, x=16
4=k/16
k=64
find y when x=8
y=64/8
y=8
Answer:
Check the solution in both equations. The solution is ( − 1, 2). Solve the system by graphing: {− x + y = 12 x + y = 10 . Solve the system by graphing: {2x + y = 6 x + y = 1 . In all the systems of linear equations so far, the lines intersected and the solution was one point.
Hope it helps!!!
Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
