Answer:
5/7
Step-by-step explanation:
We have two points ( 2,-2) and (9,3)
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 3- -2)/( 9-2)
= ( 3+2)/(9-3)
= 5/7
-15+5x= 20
5x= 35
x= 7
20= -15+5x
35= 5x
7 = x
Answer:
80/81
Step-by-step explanation:
If a head is twice as likely to occur as a tail, then the probability of getting heads is 2/3 and the probability of getting tails is 1/3.
The probability of getting at least 1 head involves 4 scenarios:
1) 1 Head and 3 Tails
2) 2 Heads and 2 Tails
3) 3 Heads and 1 Tail
4) 4 Heads
Instead of calculate all these scenarios, you could calculate the opposite scenario: 4 Tails. The sum of all possible scenarios is 1, so:
P(at least one head) + P(no heads) = 1
Then, P(at least one head) = 1 - P(no heads)
The probability of 4 tails is:
P(no heads) = P(TTTT) = (1/3)(1/3)(1/3)(1/3)=1/81
Then, P(at least one head) = 1 - 1/81=80/81
Answer:
Step-by-step explanation:
Each signal unit cubes are 1 cm to each side
the dimensions of the large cube is 4 by 6 by 3 width height and depth
a) volume of the cube Vol = area of the base times height
area of the base = the width times the depth
Volume = Base Depth
= Width x Depth x Height
= 4 x 3 x 6
= 12 x 6
Vol = 72 cm ³
b ) the volume of the smaller cuboid has different dimensions
the smaller cube is 2 by 2 by 1 width height and depth
Volume = Base Depth
= Width x Depth x Heigh
= 2 x 2 x 1
Vol smaller cuboid = 4
How many smaller cubes can be made?
The obvious answer might be to straight up divide the large cube volume by the smaler cuboid volume. That might work IF all of the cuboid dimensions divide evenly into the cube dimensions.
Number of cuboid = Volume of the cube / Volume of the cuboid
= 72 / 4
= 18
Check this answer by dividing the dimension of the cube by the cuboid
4 by 6 by 3
2 by 2 by 1
(4/2) by (6/2) by (3/1)
2 by 3 by 3 = 2 x 3 x 3 = 18
