Answer:
19
Step-by-step explanation:
<em>1</em><em>3</em><em>×</em><em>3</em><em>=</em><em> </em><em>3</em><em>9</em>
<em>1</em><em>4</em><em>.</em><em>5</em><em>×</em><em>4</em><em>=</em><em> </em><em>5</em><em>8</em>
<em>5</em><em>8</em><em>-</em><em>3</em><em>9</em><em>=</em><em> </em><em>1</em><em>9</em>
Answer:
It should be A if im not corect
Step-by-step explanation:
False
on the left, there is 2 negatives, which cannot result in a negative number on the right
Answer: The ladder is sliding down the wall at a rate of ![5\dfrac{17}{50}\ ft/sec](https://tex.z-dn.net/?f=5%5Cdfrac%7B17%7D%7B50%7D%5C%20ft%2Fsec)
Step-by-step explanation:
Since we have given that
Length of ladder = 25 foot
Distance from the wall to the bottom of ladder = 15 feet
Let base be 'x'.
Let length of wall be 'y'.
So, by pythagorus theorem, we get that
![x^2+y^2=25^2\\\\15^2+y^2+625\\\\225+y^2=625\\\\y^2=625-225\\\\y^2=400\\\\y=\sqrt{400}\\\\y=20\ feet](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D25%5E2%5C%5C%5C%5C15%5E2%2By%5E2%2B625%5C%5C%5C%5C225%2By%5E2%3D625%5C%5C%5C%5Cy%5E2%3D625-225%5C%5C%5C%5Cy%5E2%3D400%5C%5C%5C%5Cy%3D%5Csqrt%7B400%7D%5C%5C%5C%5Cy%3D20%5C%20feet)
![\dfrac{dy}{dx}=-4\ ft/sec](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D-4%5C%20ft%2Fsec)
Now, the equation would be
![x^2+y^2=625\\](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D625%5C%5C)
Differentiating w.r.t x, we get that
![2x\dfrac{dx}{dt}+2y.\dfrac{dy}{dt}=0\\\\2\times 15\dfrac{dx}{dt}+2\times 20\times -4=0\\\\30\dfrac{dx}{dt}-160=0\\\\\dfrac{dx}{dt}=\dfrac{160}{30}=5.34\ ft/sec](https://tex.z-dn.net/?f=2x%5Cdfrac%7Bdx%7D%7Bdt%7D%2B2y.%5Cdfrac%7Bdy%7D%7Bdt%7D%3D0%5C%5C%5C%5C2%5Ctimes%2015%5Cdfrac%7Bdx%7D%7Bdt%7D%2B2%5Ctimes%2020%5Ctimes%20-4%3D0%5C%5C%5C%5C30%5Cdfrac%7Bdx%7D%7Bdt%7D-160%3D0%5C%5C%5C%5C%5Cdfrac%7Bdx%7D%7Bdt%7D%3D%5Cdfrac%7B160%7D%7B30%7D%3D5.34%5C%20ft%2Fsec)
Hence, the ladder is sliding down the wall at a rate of ![5\dfrac{17}{50}\ ft/sec](https://tex.z-dn.net/?f=5%5Cdfrac%7B17%7D%7B50%7D%5C%20ft%2Fsec)
Answer:
A: 14/65
Step-by-step explanation:
Let A be the event of pulling a blue marble first, there are 28 blue marbles
Let B be the event of pulling a red marble second, there are 12 red marbles
There are 40 total marbles in the bag.
So
P(A) = 28/40
Since he pulls two marbles with out replacement, there is one less marble in the bag when he pulls the second marble, so there are only 39 marbles left, so
P(B) = 12/39
When calculating the probability of multiple events, you multiply their probabilities together, so we have
P(A then B) = (28/40)(12/39) = 336/1560
Now reduce the fraction...
112/520
28/130
14/65