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Rasek [7]
2 years ago
8

A set of notations (SSS, SAS, ASA and RHS) is used to describe/prove

Mathematics
1 answer:
Olin [163]2 years ago
5 0

Step-by-step explanation:

where are the triangles

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A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y de
strojnjashka [21]

Answer:

a) P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

a= μ-3.16*σ , b= μ+3.16*σ

b) P(Y≥ μ+3*σ ) ≥ 0.90

b= μ+3*σ

Step-by-step explanation:

from Chebyshev's inequality for Y

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

where

Y =  the number of fish that need be caught to obtain at least one of each type

μ = expected value of Y

σ = standard deviation of Y

P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean

k= parameter

thus for

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

P{a≤Y≤b} ≥ 0.90 →  1-1/k² = 0.90 → k = 3.16

then

P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

using one-sided Chebyshev inequality (Cantelli's inequality)

P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)

P{Y≥b} ≥ 0.90  →  1- σ²/(σ²+λ²)=  1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ

then for

P(Y≥ μ+3*σ ) ≥ 0.90

5 0
2 years ago
A group of 55 football players were polled about which synthetic grass they like to play on, Chemstrand or Chemgrass. The data f
cricket20 [7]
From the Venn diagram: 15 players like Chemstrand, 17 players like Chemgrass, 13 players like both Chemstrand and Chemgrass while 10 players like neither Chemstrand nor Chemgrass.

The missing values in the frequency table are x - representing the number of players that like both Chemstrand and Chemgrass, y - representing the number of players that like Chemgrass but do not like Chemstrand and z - representing the number of players likes Chemstrand but do not like Chemgrass.

The number of players that like both Chemstrand and Chemgrass is 13. The number of players that like Chemgrass but do not like Chemstrand is 17. The number of players likes Chemstrand but do not like Chemgrass is 15.

Therefore, x = 13, y = 17 and z = 15
6 0
2 years ago
Read 2 more answers
Clay can run one lap around the track in 1/4 of an hour. How many hours will it take him to run 5 1/3 laps around the track?
Jet001 [13]

Answer: It will take him 1 hour and 35 min

8 0
1 year ago
Charlie is planning a trip to Madrid. He starts with $984.20 in his savings account and uses $381.80 to buy his plane ticket. Th
stepan [7]

Answer:

$24.09

Step-by-step explanation:

you do 984.20-381.80=602.4

then divide 602.4 by 1/4

which 1/4=25.

then you get $24.09

8 0
2 years ago
Read 2 more answers
PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standa
Lunna [17]

Answer:

P = 0.0215 = 2.15%

Step-by-step explanation:

First we need to convert the values of 900 and 975 to standard scores using the equation:

z = \frac{x - \mu}{\sigma}

Where z is the standard value, x is the original value, \mu is the mean and \sigma is the standard deviation. So we have that:

standard value of 900: z = \frac{900 - 750}{75} = 2

standard value of 975: z = \frac{975 - 750}{75} = 3

Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:

z = 2 -> p_2 = 0.9772

z = 3 -> p_3 = 0.9987

We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:

P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215

So the probability is 0.0215 = 2.15%

8 0
2 years ago
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