Answer:
-x/x^2-1
Step-by-step explanation:
-x^2+x/x^3-x^2-x+1
x(-x+1)/(x+1)(x-1)(x-1)
-x/x^2-1
A standard deck of cards has 52 cards. Half of the deck has red cards and half has black cards. So the first probability would be 26/52, or 1/2 (simplified, it's half the deck).
Then you put the card back and choose a 3. There are 4 cards with the number 3 in the deck. So it's 4/52.
Then you multiply both the probabilities
26/52 x 4/52 =
= 1/26
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 %
The first question is this: the smallest square is square A, and that is 9 units. and square E is two times that, and so on.
Square A's side length is 9 units and the area is 81.
Square E's side length is 18 and the area is 324.
Square C's side length is 27 and the area is 729.
Square B's side length is 36 and the area is 1,296.
Square D's side length is 45 and the area is 2,025
