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pentagon [3]
2 years ago
7

A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure. If the m

ean lifetime of this type of component is 100 hours and its standard deviation is 30 hours, how many of these components must be in stock so that the probability that the system is in continual operation for the next 2000 hours is at least 0.95?
Mathematics
1 answer:
nekit [7.7K]2 years ago
5 0

Answer:

Step-by-step explanation:

From the given information:

Assuming we have an integer c to represent the components in the stocks.

Thus, the needed probability can be expressed as:

P(X_1+X_2+ ........ X_c \ge 2000)

To break this down, we have:

P(\sum X_i \ge 2000) = P \Bigg(\dfrac{\sum X_i - 100n}{\sqrt{n \ Var (X)}} \ge \dfrac{2000-100 n }{\sqrt{n \times 900}} \Bigg )

P \Bigg(\dfrac{\sum X_i - 100n}{\sqrt{n \ Var (X)}} \ge \dfrac{2000-100 n }{\sqrt{n \times 900}} \Bigg )= P (Z \ge 0.95 ) \ \ \  because  \ Z_{0.05} = -1.65 \\ \\  \\  \dfrac{2000-100 n }{\sqrt{n \times 900}} = -1.65 \\ \\ \\ \dfrac{100\  n-2000  }{\sqrt{900n}} = 1.65  \\ \\ 100 n -1.65 \sqrt{900 n }-2000 = 0

By solving the equation:

n = 23

Thus, relating to the needed condition; n ≥ 23

The needed number of the components that should be in stock should be  at least 23.

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2 years ago
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A sports team came to town. the stadium filled all 10,000 seats at two-level pricing. level 1 tickets are $50 each, and level 2
marissa [1.9K]

x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000. This can be obtained by understanding the question and observing the equations.

<h3>What do the x and y represent in the system?</h3>

Given that total number of seats is 10,000 and there are two levels pricing.

Thus by observing the equation, x + y = 10,000,

10,000 is the sum of 2 variable which obviously will be the number of tickets in level 1 and number of tickets in level 2.

Since there are two level pricing,

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Hence x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000.

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3 0
2 years ago
The shortest side of a polygon of area 196 sq. in. is 4 in. long. Find the area of a similar polygon whose shortest side is 8 in
fenix001 [56]
The correct answer is:  " 784 in² " . 
_________________________________________
                  {or; write as:  " 784 sq. inches " .}.
_________________________________________
      When the side is doubled (in this case, 4 is doubled; 4 * 2 = 8} ; the area is increased by 2² times; that is, by 4 times;  so, the area is:
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7 0
3 years ago
Read 2 more answers
Thank you now help please
swat32
If it is #17 this:

the class sold 45 sandwiches and collected $150.75, all you need to do is divide.

150.75/45
= 3.35

$3.35 per sandwitch


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3 years ago
Which is the rationalized form of the expression. A, B , C, or D?
grin007 [14]

Answer:

C

Step-by-step explanation:

Multiply the top and bottom, both by sqrtx-sqrt5. This is in order to rationalize the denominators.

You get answer C.

3 0
2 years ago
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