I think you can chose your own points like (0,296) and (2,592)
Step 1 = 3.9 × 0.5 + 4 5/6 ÷ 3 3/7
Step 2 = 3.9 × 0.5 + 29/6 ÷ 24/7
Step 3 = 4.4 + 29/6 × 24/7
Step 4 = 4.4 + 29/1 × 4/7
Step 5 = 4.4 + 111/7
Step 6 =44/10 + 111/7
Step one : Write the problem
Step two : Change the mixed numbers to improper fractions
Step three : Multiplication and Division should be done first. Then simplify.
Step four : Change the division to multiplication and multiply.
Step 6 : Add the remaining fractions
Sorry i didn't know which one so i did the first one. Hope it helps you.
Answer:
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 > 73.293
Step-by-step explanation:
Given: Numbers are 7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 and 73.293
To compare: the two given numbers
Solution:
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 is equal to ![73.385](https://tex.z-dn.net/?f=73.385)
Compare the numbers
and 73.293
Digits at the ones pace and tens place in both the numbers are same.
Observe the digit at the tenth place in both the numbers.
Digit at the tenth place in 73.385 is 3
Digit at the tenth place in 73.293 is 2
As
,
73.385 > 73.293
So,
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 > 73.293
Using the binomial distribution, it is found that the probabilities are given as follows:
a) 0.3185 = 31.85%.
b) 0.7998 = 79.98%.
c) 0.5187 = 51.87%.
<h3>What is the binomial distribution formula?</h3>
The formula is:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem, the parameters are given as follows:
n = 5, p = 0.51.
Item a:
The probability is P(X = 3), hence:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 3) = C_{5,3}.(0.51)^{3}.(0.49)^{2} = 0.3185](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B5%2C3%7D.%280.51%29%5E%7B3%7D.%280.49%29%5E%7B2%7D%20%3D%200.3185)
Item b:
The probability is:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Then:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 0) = C_{5,0}.(0.51)^{0}.(0.49)^{5} = 0.0282](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B5%2C0%7D.%280.51%29%5E%7B0%7D.%280.49%29%5E%7B5%7D%20%3D%200.0282)
![P(X = 1) = C_{5,1}.(0.51)^{1}.(0.49)^{4} = 0.1470](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B5%2C1%7D.%280.51%29%5E%7B1%7D.%280.49%29%5E%7B4%7D%20%3D%200.1470)
![P(X = 2) = C_{5,2}.(0.51)^{2}.(0.49)^{3} = 0.3061](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B5%2C2%7D.%280.51%29%5E%7B2%7D.%280.49%29%5E%7B3%7D%20%3D%200.3061)
![P(X = 3) = C_{5,3}.(0.51)^{3}.(0.49)^{2} = 0.3185](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B5%2C3%7D.%280.51%29%5E%7B3%7D.%280.49%29%5E%7B2%7D%20%3D%200.3185)
So:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0282 + 0.1470 + 0.3061 + 0.3185 = 0.7998.
Item c:
The probability is:
![P(X \geq 3) = 1 - P(X < 3)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%203%29%20%3D%201%20-%20P%28X%20%3C%203%29)
In which:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0282 + 0.1470 + 0.3061 = 0.4813.
Then:
![P(X \geq 3) = 1 - P(X < 3) = 1 - 0.4813 = 0.5187](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%203%29%20%3D%201%20-%20P%28X%20%3C%203%29%20%3D%201%20-%200.4813%20%3D%200.5187)
More can be learned about the binomial distribution at brainly.com/question/24863377
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140 is a composite number. Factor pairs: 140 = 1 x 140, 2 x 70, 4 x 35, 5 x 28, 7 x 20, 10 x 14. Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. Prime factorization: 140 = 2 x 2 x 5 x 7, which can also be written 140 = 2² x 5 x 7