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Answer:
Step-by-step explanation:
Sample space 2+5+7+4=18
Answer: The ladder would reach 15.3 ft up the wall
Step-by-step explanation: Please refer to the attached diagram.
If the ladder (represented by line AC) rests on the wall (represented by line AB), it forms an angle of 50 with the ground (at point C). The ground is represented by line BC.
We need to remember that we have one side and one angle given in this question. The given side is the hypotenuse (the side facing the right angle, B in this case) and the given angle is the reference angle. The unknown side which is x, is the opposite as it is facing the reference angle.
Having the opposite and the hypotenuse, we can use the Sine ratio which is,
Sine C = opposite/hypotenuse
Sine 50 = x/20
Checking our table of values or by use of our calculator, sin 50 is 0.766
Sin 50 = x/20
0.766 = x/20
By cross multiplication, we now have our equation rewritten as;
0.766 (20) = x
15.32 = x
Rounded to the nearest tenth,
x = 15.3 ft
Answer:
The smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.
Step-by-step explanation:
The complete question is:
The mean salary of people living in a certain city is $37,500 with a standard deviation of $2,103. A sample of n people will be selected at random from those living in the city. Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income. Round your answer up to the next largest whole number.
Solution:
The (1 - <em>α</em>)% confidence interval for population mean is:
The margin of error for this interval is:
The critical value of <em>z</em> for 90% confidence level is:
<em>z</em> = 1.645
Compute the required sample size as follows:
Thus, the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.