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Gemiola [76]
3 years ago
10

Let x and y be any numbers at all with x ≤ y. Show that the number of integers between x and y is [y] - [x] +1.That is show that

the number of integers between x and y is = (the floor of y) - (the ceiling of x) +1
Mathematics
1 answer:
ddd [48]3 years ago
5 0

Answer:

the explanation is given below.

Step-by-step explanation:

  • Here what is applied is assumption of range of values of number from say 1 - 100
  • In total, i stopped at 100 on the dot.

from this, the lowest number is 1 and the highest number is 100

  • hence the range of the numbers = Difference between Highest and Lowest
  • range = 100 - 1 = 99, the 99 gotten as the range is indicative that a number has been missing.

  • In order to make up the 100, an integer is added to the difference = 99, i.e 99 is added to 1 to make up the 100.

  • Furthermore, if 0 is exclusively out when numbers are counted up 100 with 0 inclusive, in such case, the first and last number are excluded from the counting. as such the integers will be {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20.........., 99} since both 0 and 100 are not included.

  • Here, if we try to get the range = highest - lowest = 99 - 1 = 98, it implies that to make up the 99, an integer is added to the result of the difference = 98+1 = 99

  • As such, the number of integers between two numbers is the difference between the highest and the lowest number plus 1 i.e highest - lowest + 1 = y - x +1 = (the floor of y) - ( the ceiling of x) + 1
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When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 55 bat
aleksley [76]

The probability of accepting this shipment is 98%.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Almost all such shipments will be accepted because the probability of having a sample with more than 3 defective batteries is very low.

The shipment will be accepted if at most 3 batteries don't meet specifications.

This can be modeled as a binomial distribution, where the sample size is n=55 and the probability of not meeting the specifications of any battery is p=0.02.

The shipment will be accepted if D ≤ 3.

The probability of this event is:

P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)

P(D=X) = n!/(x!(n-x)!) pˣ(1-p)ⁿ⁻ˣ

P(D=0) = 55!/(0!(55-0)!) 0.02⁰(1-0.02)⁵⁵⁻⁰ = 1× 1 × 0.32 = 0.32

P(D=1) = 55!/(1!(55-1)!) 0.02¹(1-0.02)⁵⁴ = 54 × 0.02 × 0.33= 0.35

P(D=2) = 55!/(2!(55-2)!) 0.02²(1-0.02)⁵³ = 55 ×27 × 0.0004 × 0.34= 0.20

P(D=3) = 55!/(3!(55-3)!) 0.02³(1-0.02)⁵² = 25740× 0.0000008 × 0.35= 0.07

Then,

P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)

P( D ≤ 3) = 0.32 + 0.35 + 0.20 + 0.07

P( D ≤ 3) = 0.98

Hence, the probability of accepting this shipment is 98%.

To learn more about the probability from the given link

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4 0
1 year ago
In 1985 there were 275 cell phone subscribers in the small town of China grove. Subscribers increased by 40% each year after 198
emmasim [6.3K]
1985year ->275cell phones->100%
1994year -> x cell phones ->100%+360%
40% • (1994-1985)= 40% • 9= 360%

275 cell phone 100%
X cell phones. 100+360%=460%
x=275•460%/100%
x=12420/100
x=1265
99% sure this is a correct answer


x=275 • 460%/100%
x=12,420/100
x=1265

1994-1985= 9 yrs • 40%= 360%

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