Answer: 709
Step-by-step explanation:
The formulas we use to find the required sample size :-
1. 
, where 
= population standard deviation,
E = Margin of error .
z* = Critical value
2. 
, where p= prior estimate of population proportion.
3. If prior estimate of population proportion is unavailable , then we take p= 0.5 and the formula becomes
Given : Margin of error : E= 3% =0.03
Critical value for 95% confidence interval = z*= 1.96
A study conducted several years ago revealed that the percent of junior executives leaving within three years was 21%.
i.e. p=0.21
Then by formula 2., the required sample size will be :
[Round to the next integer.]
Hence, the required sample size of junior executives should be studied = 709
So for this you need to set them equal to each other! 3x+100=5x-160
now you combine like terms and solve!
Look at the picture.
Corresponding Angles are equal.
Alternate Angles are equal.
Consecutive Angles add up to 180°.
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3a and 45 are Consecutive Angles. Therefore
3a + 45 = 180 |subtract 45 from both sides
3a = 135 |divide both sides by 3
<h3>a = 45.</h3>
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(2c - 1) and 45 are Corresponding Angles. Therefore
2c - 1 = 45 |add 1 to both sides
2c = 46 |divide both sides by 2
<h3>c = 23.</h3>
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3a and (12b + 3) are Alternate Angles. Therefore
3(45) = 12b + 3
135 = 12b + 3 |subtract 3 from both sides
132 = 12b |divide both sides by 12
<h3>b = 11.</h3>
He will need 17 inches of ribbon.
The diagonal splits the square into two right triangles. We can then use the Pythagorean theorem to find the length of the diagonal (the hypotenuse of the triangle):
12² + 12² = x²
144 + 144 = x²
288 = x²
Take the square root of both sides:
√288 = √x²
16.97 = x
17≈x
The solution x=1/5 is a solution to the first option.
5*1/5=1
hope this helps!
