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finlep [7]
3 years ago
8

There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious ap

ples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence?A. (–0.076,0.236)B. (–0.105,0.265)C. (–10.5,26.5)D. (–76,236)E. (−105,265)
Mathematics
1 answer:
Delvig [45]3 years ago
4 0

Answer:

98% confidence interval is (-0.105 , 0.265)

Step-by-step explanation:

n1 = 75          n2 = 75

X1 = 48          X2 = 42

P1 = X1/N1 = 0.64          P2 = X2/N2   = 0.56

98% confidence interval for difference between two proportions is :

P1 - P2  <u>+</u>   Z \sqrt{P1 (1-P1)/n1  + P2 (1-P2)/n1}

= 0.08 <u>+</u> 0.185

= (-0.105 , 0.265)

98% confidence interval is (-0.105 , 0.265)

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Radicales simples ……….
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The expressions with radicals which are variables and numbers raised to a fractional indices are simplified as follows.

13. √(9·x)  = 3·√x

14. √(4·y) = 2·√y

15. √(8·x²) = 2·x·√2

16. √(9·x²) = 3·x

17. √(3·x²) = x·√3

18. √(5·y²) = y·√5

19. √(13·x²) = x·√(13)

20. √(29·y²) = y·√(29)

21. √(64·y²) = 8·y

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<h3>What are radicals expressions?</h3>

A radical expression is one that contains the radical (square root or nth root) sign, √.

13. √(9·x)

√(9·x) = √(3²·x) = 3·√x

  • √(9·x)  = 3·√x

14. √(4·y)

√(4·y) = √(2²·y) = 2·√y

  • √(4·y) = 2·√y

15. √(8·x²)

√(8·x²) = √(4 × 2·x²) = √(2² × 2·x²)

√(2² × 2·x²) = √(2²·x² × 2) = 2·x·√2

  • √(8·x²) = 2·x·√2

16. √(9·x²)

√(9·x²) =  √(3²·x²) = 3·x

  • √(9·x²) = 3·x

17. √(3·x²)

  • √(3·x²) = x·√3

18. √(5·y²)

√5 × √(y²) = √5 × y = y·√5

  • √(5·y²) = y·√5

19. √(13·x²)

√(13·x²) = √(13) × √x² = √(13) × x = x·√(13)

  • √(13·x²) = x·√(13)

20. √(29·y²)

√(29·y²) = √(29) × √(y²) = √(29) × y = y·√(29)

  • √(29·y²) = y·√(29)

21. √(64·y²)

√(64·y²) = √(8²·y²) = √(8²) × √(y²) = 8 × y = 8·y

  • √(64·y²) = 8·y

22. √(125·a²)

√(125·a²) = √(25 × 5 × a²) = √(25) × √5 × √(a²) =  5 × √5 × a

5 × √5 × a  = 5·a·√5

  • √(125·a²) = 5·a·√5

23. ∛(16)

∛(16) = ∛(16) = ∛(8 × 2) =  ∛(2³ × 2) = 2·∛2

  • ∛(16) = 2·∛2

24. √(50·a²·b)

√(50·a²·b) = √(25 × 2 × a² × b) = √(5² × 2 × a² × b) = √(5² × a² × 2 × b)

√((5² × a²) × 2 × b) = 5·a·√(2·b)

  • √(50·a²·b) = 5·a·√(2·b)

Learn more about simplifying expressions with radicals here:

brainly.com/question/13114751

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Step-by-step explanation:

  We can use trigonometry functions to solve for AC. Let the ?, representing AC, be "x" in our mathematical work.

  Since we have the hypotenuse and x is adjacent to the angle given, I am going to use cosine.

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