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Arlecino [84]
3 years ago
9

5. To prevent a flooded basement, a homeowner has installed two special pumps that work automatically and independently to pump

water if the water level gets too high. One pump is
rather old and does not work 28% of the time, and the second pump is newer and does not work 9% of the time. Find the probability that both pumps will fail to work at the same time.
Mathematics
1 answer:
NeX [460]3 years ago
7 0

Answer:

The probability that both pumps will fail to work at the same time is 0.025 or 2.5%.

Step-by-step explanation:

The probability that both pumps will fail to work at the same time is the multiplication of the probabilities that the pomps fail.

That is

  • the probability that the old pump fail = \frac{28}{100}
  • the probability that the newer pump fail = \frac{9}{100}

Then, the probability that both fail at the same time is:

\frac{28}{100} * \frac{9}{100} = 0.025

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There is a rectangle ABCD, with sides AB = CD = 32, and sides and BC = DA = 24. The rectangle is rotated 90° clockwise about C,
Sphinxa [80]

Answer

given,

side of rectangle, AB = CD = 32

                              BC = DA = 24

rectangle is rotated 90° clockwise about C.

then rotated 90° clockwise about D.

Path traveled by the point A for first rotation will be in circle with radius AC.

   D_1 = \dfrac{\theta_1}{360^0}\times \pi \times {AC}^2

      AC = \sqrt{24^2+32^2}

             AC = 40

             θ₁ = 90°

   D_1 = \dfrac{90^0}{360^0}\times \pi \times {40}^2

         D₁ = 1256.64

For the second rotation Point A will move in circular path with radius of AD

   D_2 = \dfrac{\theta_2}{360^0}\pi {AD}^2

             AD = 24

             θ₁ = 90°

   D_2 = \dfrac{90^0}{360^0}\times \pi \times {24}^2

         D₂ = 452.39

total path traveled by the point A

   D = D₁ + D₂

   D = 1256.64 + 452.39

  D = 1709.03

3 0
3 years ago
A deck of cards contain 52 cards. These cards consist of four suits (hearts, spades, clubs, and diamonds) of each of the followi
earnstyle [38]

Answer:

i think 25%

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Determine the recursive function that defines the sequence.
Strike441 [17]
<h2>Answer:</h2>

Option: C is the correct answer.

    C.   f(1)=4\\\\f(n)=5\cdot f(n-1)\ ;\ n\geq 2  

<h2>Step-by-step explanation:</h2>

Recursive Formula--

It is the formula which is used to represent the nth term of a sequence in terms of (n-1)th term of the sequence.

Here we are given a table of values by:

            n            f(n)

            1              4

            2             20

            3             100  

i.e. when n=1 we have:

f(1)=4

Also,

f(2)=20\\\\i.e.\\\\f(2)=5\cdot 4\\\\i.e.\\\\f(2)=5\cdot f(1)

Also,

f(3)=100\\\\i.e.\\\\f(3)=5\cdot 20\\\\i.e.\\\\f(3)=5\cdot f(2)

Hence, the recursive formula is:

f(n)=5\cdot f(n-1)\ for\ n\geq 2

5 0
3 years ago
If a third plane could be drawn which contains both lines a and b, then what must the lines be?
Akimi4 [234]
The line a and line b are parallel to each other since if you draw another line or a third plane and it contains both points both in line a and in line b it means that this third plane passes through to the both lines a and b.  In order to achieve both lines a and b can be passed by the third plane, they should be parallel to each other.
7 0
3 years ago
Read 2 more answers
What does<br> 9 x 2/5 equal​
fomenos

Answer:

3 3/5

Step-by-step explanation:

9/1*2/5=18/5

=3 3/5

3 0
3 years ago
Read 2 more answers
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