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Tanzania [10]
3 years ago
9

For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hi

lls bank. each of the four systems detects theft with a probability of .99 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs, at least oneof the four systems will detect it. this probability is equal to:
Mathematics
1 answer:
AleksAgata [21]3 years ago
7 0
The probability any one system works is 0.99
So the probability of any one system failing is 1-0.99 = 0.01, so basically a 1% chance of failure for any one system

Multiply out the value 0.01 with itself four times
0.01*0.01*0.01*0.01 = 0.000 000 01
I'm using spaces to make the number more readable
So the probability of all four systems failing is 0.00000001
Subtract this value from 1 to get
1 - 0.00000001 = 0.99999999

The answer is 0.99999999 which is what we'd expect. The probability of at least one of the systems working is very very close to 1 (aka 100%)
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Factor completely.<br> x² - 3x² - 4
Ber [7]

Answer:

-2(x^2+2)

Step-by-step explanation:

1. x^2-3x^2-4
= -2x^2-4
2. -2(x^2+2) factor completely :)

7 0
2 years ago
Read 2 more answers
Which numbers will produce a rational number when multiplied by 1/5
labwork [276]
A rational number times a rational number=rational numberan irrational number times a rational number=irrational number
remember, a rational number is a number that can be written as a/b where a and b are integers and b≠0


A is irrational because the pattern doesn't repeatb is irrational because it's a crazy square rootC is irrationalD is not irrational, it is a fraction 

answer is D

 
3 0
3 years ago
Find the sum of the first 20 terms of an arithmetic sequence with an 18th term of 8.1 and a common difference of 0.25.
il63 [147K]

The sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5

Given,

18th term of an arithmetic sequence = 8.1

Common difference = d = 0.25.

<h3>What is an arithmetic sequence?</h3>

The sequence in which the difference between the consecutive term is constant.

The nth term is denoted by:

a_n = a + ( n - 1 ) d

The sum of an arithmetic sequence:

S_n = n/2 [ 2a + ( n - 1 ) d ]

Find the 18th term of the sequence.

18th term = 8.1

d = 0.25

8.1 = a + ( 18 - 1 ) 0.25

8.1 = a + 17 x 0.25

8.1 = a + 4.25

a = 8.1 - 4.25

a = 3.85

Find the sum of 20 terms.

S_20 = 20 / 2 [ 2 x 3.85 + ( 20 - 1 ) 0.25 ]

         = 10 [ 7.7 + 19 x 0.25 ]

         = 10 [ 7.7 + 4.75 ]

         = 10 x 12.45

         = 124.5

Thus the sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5

Learn more about arithmetic sequence here:

brainly.com/question/25749583

#SPJ1

8 0
1 year ago
Use a calculator to find the value of the trigonometric function to four decimal places. Tan 3.4??? A.0.2555 B.0.0594 C.0.9668 D
r-ruslan [8.4K]
The value of Tan 3.4 is 0.059410947 rounded off to four decimal places would equal to 0.0594, letter B. This is your answer if your calculator is in the degree mode. 

Tangent or Tan is one of the trigonometry functions. It represents TOA in the sohcahtoa mnemonic which means Tan = Opposite / Adjacent 
7 0
3 years ago
Given: -2x &lt; 10. Choose the solution set.
nadya68 [22]

Answer:

C

Step-by-step explanation:

given - 2x < 10 ( divide both sides by - 2 )

Remembering that the symbol is reversed when multiplying/ dividing by a negative quantity.

x > - 5 ← note reversal of symbol

solution is {x | x > - 5 } → C


4 0
3 years ago
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