Given:
DE = (6x - 9) cm
EF = (4x + 4) cm
LM = 14 cm
MN = 16 cm
To find:
The value of x.
Solution:
<em>If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.</em>
![$\Rightarrow \frac{DE}{EF} =\frac{LM}{MN}](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5Cfrac%7BDE%7D%7BEF%7D%20%3D%5Cfrac%7BLM%7D%7BMN%7D)
![$\Rightarrow \frac{6x-9}{4x+4} =\frac{14}{16}](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5Cfrac%7B6x-9%7D%7B4x%2B4%7D%20%3D%5Cfrac%7B14%7D%7B16%7D)
Do cross multiplication.
![$\Rightarrow 16( {6x-9})=14 ({4x+4} )](https://tex.z-dn.net/?f=%24%5CRightarrow%2016%28%20%7B6x-9%7D%29%3D14%20%28%7B4x%2B4%7D%20%29)
![$\Rightarrow 96x-144=56 x+56](https://tex.z-dn.net/?f=%24%5CRightarrow%2096x-144%3D56%20x%2B56)
Add 144 on both sides.
![$\Rightarrow 96x-144+144=56 x+56+144](https://tex.z-dn.net/?f=%24%5CRightarrow%2096x-144%2B144%3D56%20x%2B56%2B144)
![$\Rightarrow 96x=56 x+200](https://tex.z-dn.net/?f=%24%5CRightarrow%2096x%3D56%20x%2B200)
Subtract 56x from both sides.
![$\Rightarrow 96x-56x=56 x+200-56x](https://tex.z-dn.net/?f=%24%5CRightarrow%2096x-56x%3D56%20x%2B200-56x)
![$\Rightarrow 40x=200](https://tex.z-dn.net/?f=%24%5CRightarrow%2040x%3D200)
Divide by 40 on both sides, we get
![$\Rightarrow x=5](https://tex.z-dn.net/?f=%24%5CRightarrow%20x%3D5)
The value of x is 5.
Answer:
the amount of sales
Step-by-step explanation:
= 3.60
Solution:
We have the equation:
14.4 ÷ 4 = 3.60
Calculated to 2 decimal places.
Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68
The relative frequency of getting a bag of gold is .......... reasonably close
.32 is close to 30% so
Alison's claim about the theoretical probability is likely to be 2............true
Further, this means that the theoretical probability of getting a magic wand is most likely 3............1 - 30% = 70%