Answer:

Step-by-step explanation:
There are a total of 7 + 9 + 2 = 18 balls in the vase, therefore, when not replacing the first ball, there would be 18 · 17 = 306 ways to pull 2 balls. There are 2 ways to choose the first black ball and then 1 way to choose the second black ball so there are 2 · 1 = 2 ways to choose 2 black balls. Therefore, the probability is 2 / 306 =
.
Answer:
x > -24
Step-by-step explanation:
-x/4 < 6
Multiply each side by -4, remembering to flip the inequality
-x/4 *-4> 6*-4
x > -24
Given:
Volume of toy=231 cm³
Diameter of a hemisphere= 7 cm
cone and hemisphere have equal radius.
radius of hemisphere = radius of cone = 3.5 cm
Height of hemisphere= radius of hemisphere= 3.5 cm
Let H be the height of toy
H= height of cone+ height of hemisphere
H = h + r , ( h = height of cone)
H = h + 3.5
volume of toy = volume of cone + volume of hemisphere
Volume of toy= 1/3πr²h + 2/3πr³
Volume of toy=πr²/3(h+2r)
231 = (22/7)×(3.5)² ×(1/3)(h+2×3.5)
231×3 =( 22×3.5×3.5)/7 (h+7)
h+7 = (231×3×7)/(3.5×3.5×22)
h+7 = (3×3)/(.5×.5×2)
h+7= 900 /50= 90/5= 18
h+7= 18
h=18-7
h= 11 cm
Height of toy = h+r
Height of toy = 11+3.5= 14.5
Height of toy =14.5 cm
Hence, the height of the toy = 13.5 cm
Answer:
1. x = +/- 2
- 7
2. x =
+/- 
3. n =
+/- 
Step-by-step explanation:
1. Divide both sides by 2: (x + 7)^2 = 8
Square root both sides: x + 7 = +/- 2
Subtract 7 from both sides: x = +/- 2
- 7
2. Square root both sides: x - 3 = 
Since there is a negative inside the radical, we need to have an imaginary number:
. So, 
Add 3 to both sides: x =
+/- 
3. Divide by -5 from both sides: (n - 2)^2 = -2
Square root both sides: n - 2 = 
Again, we have to use i: 
Add 2 to both sides: n =
+/- 
Hope this helps!