The answer is D, i.e. the system was solved via elimination
If you multiply the first equation by 5, the system becomes
If you sum the two equations, you get
And so if you substitute the second equation of system A with this new equation, you'll get system B.
8 quarters = (8 x .25) = $2.00
5 dimes = (5 x .10) = $.50
$2.00 + $.50 = $2.50
8 + 5 = 13
Hello :
note 1 :
p(A|B) = p(A∩B)/<span> p(B)
note 2 :
</span> A and B independent: p(A∩B) = p(A)×p(B)
calculate : p(A∩B)
p(A∩B) = p(A|B)×p(B)
p(A∩B) = 0.35 ×0.75 = 0.2625
but : p(A)×p(B) = 0.44×0.75 = 0.33
conclusion :
<span>the events A and B are not independent ?</span>
Answer:
<h2><u><em>
a²+2ab+b²-c²</em></u></h2>
Step-by-step explanation:
Solve:
(a+b+c) (a+b-c)=
(a²+ab-ac+ab+b²-bc+ac+bc-c²)=
a²+ab-ac+ab+b²-bc+ac+bc-c²=
a²+2ab+0ac+b²+0bc-c²=
a²+2ab+b²-c²
Answer:
a. 12 feet b. 12 feet 0.5 inches c. 8.33 %
Step-by-step explanation:
a. How far out horizontally on the ground will it protrude from the building?
Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.
So, by ratios rise/run = 1/12 = 12/x
1/12 = 12/x
x = 12 × 12
x = 144 inches
Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet
b. How long should the ramp be?
The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.
So, L = √(12² + 144²)
= √[12² + (12² × 12²)]
= 12√(1 + 144)
= 12√145
= 12 × 12.042
= 144.5 inches
Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches
c. What percent grade is the ramp?
The percentage grade of the ramp = rise/run × 100 %
= 12 inches/144 inches × 100 %
= 1/12 × 100 %
= 0.0833 × 100 %
= 8.33 %
