Question:
A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling a number greater than 2.
If there is more than one element in the set, separate them with commas.
Answer:
Step-by-step explanation:
Given
A roll of a 6 sided number cube
Solving (a): The sample space
This implies that we list out all number on the number cube.
So:
Solving (b): Outcomes greater than 2
This implies that we list out all number on the number cube greater than 2 i.e. 3 to 6.
So:
Answer:
-3n
a10= -30
Step-by-step explanation:
the distance between -3 and -6 is 3.
if you multiply 3 by the 1st term, it's just 3, so the 3 needs to be a -3.
For a10, you plug in 10 into the equation which is -3n. and that is -30.
Answer:
The best statement which explains the relationship between lines AB and CD is "They are parallel because their slopes are equal" ⇒ A
Step-by-step explanation:
- Parallel lines have equal slopes and different y-intercepts
- The rule of the slope of a line passes through points (x1, y1) and (x2, y2) is m =
In the given figure
∵ The blue line passes through points A and B
∵ A = (-4, -2) and B = (4, 4)
∴ x1 = -4 and y1 = -2
∴ x2 = 4 and y2 = 4
→ Substitute them in the rule of the slope
∵ m(AB) = 
= 
= 
= 
∴ The slope of line AB is
∵ The green line passes through points C and D
∵ C = (0, -3) and D = (4, 0)
∴ x1 = 0 and y1 = -3
∴ x2 = 4 and y2 = 0
→ Substitute them in the rule of the slope
∵ m(CD) = 
= 
=
∴ The slope of line CD is
∵ The slope of line AB = the slope of line CD
∵ Parallel lines have the same slope
∴ AB // CD
∴ AB and CD are parallel lines
The best statement which explains the relationship between lines AB and CD is "They are parallel because their slopes are equal"
Answer:
Population of dice mice after one year = 2000
Population of wood rats after one year = 1000
The population of deer mice is growing faster than the popular of wood rats
Step-by-step explanation:
The expression for population = dN/dt = rN
Upon integration N = rN²/2
Therefore for population N = 200 and r= 0.1
N after one year = (0.1 x 200²)/ 2 = 2000
Therefore for population N = 100 and r= 0.2
N after one year = (0.2 x 100²)/ 2 = 1000
Hence the population of deer mice is growing faster than the popular of wood rats
Answer:
Scale factor = ½
Step-by-step explanation:
The original image is the preimage = ∆ACB
The new image is the image = ∆DFE
The scale of factor of dilation = image/preimage = DF/AC
DF = 6 cm (given)
AC = 12 cm (given)
Plug in the values into the equation to find the scale factor of dilation:
Scale factor = 6/12
Scale factor = ½
