Solution
x≤−2 and x<−5
number line for x≤−2
-2,-3,-4.....-n
<---−10-------−9------−8------−7------−6------−5-----−4-------−3------−2
number line for x<−5
-6,-7,-8.....-n
<---−10-------−9------−8------−7------−6
Answer:
0.714
Step-by-step explanation:
Argument
The total number of cards = 5 yellow. 3 blue and 7 red = 15 cards in all.
The probability of choosing a yellow card first is 5/15 = 1/3.
We are now down to 14 cards
There are 3 blue cards.
P(yellow then blue) = 1/3 * 3/14
P(yellow then blue) = 1/14 = 0.0714
Answer:
b1 = 9 cm
Step-by-step explanation:
The formula for area of a trapezoid is
A = 1/2 (b1+b2) *h
We know Area = 135 CM ^2, Height = 10 CM, b2 = 18 cm
Substituting these in
135 = 1/2 (b1+18) *10
Multiply 1/2*10
135 = 5 (b1+18)
Divide both side by 5
135/5 = 5/5 (b1+18)
27 = b1+18
Subtract 18 from each side
27-18 = b1+18-18
9 = b1
For a better understanding of the explanation provided here kindly go through the file attached.
Since, the weight attached is already at the lowest point at time, t=0, therefore, the equation will have a -9 as it's "amplitude" and it will be a Cosine function. This is because in cosine function, the function has the value of the amplitude at t=0.
Now, we know that the total angle in radians covered by a cosine in a given period is 
and the period given in the question is t=3 seconds. Therefore, the angular velocity, 
of the mentioned system will be:
Combining all the above information, we see that the equation which models the distance, d, of the weight from its equilibrium after t seconds will be:
Thus, Option B is the correct option. The attached diagram is the graph of the option B and we can see clearly that at t=3, the weight indeed returns to it's original position.
