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Sergio039 [100]
3 years ago
12

If using the method of completing the square to solve the quadratic equation

Mathematics
1 answer:
jenyasd209 [6]3 years ago
4 0

You add half of the coefficient of x and square it.

What you do on one side,you must do it on the other.

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Suppose a sample of 100 families of four vacationing at Niagara Falls resulted in sample mean of $282.45 spent per day and a sam
Juli2301 [7.4K]

Given Information:

Mean = μ = $282.45

Standard deviation = σ = $64.50

Sample size = n = 100

Confidence level = 95%

Required Information:  

95% Confidence interval = ?

Answer:

95% Confidence interval = ($269.81, $295.09)

Step-by-step explanation:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

What is Confidence Interval?

The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.  

The confidence interval is given by

CI = \bar{x} \pm MoE\\

Where \bar{x} is the mean and MoE is the margin of error given by

MoE = z_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\

Where σ is the standard deviation, n is the sample size and z_{\alpha/2} is the z-score corresponding to 95% confidence level.

z_{\alpha/2} = 1 - 0.95 = 0.05/2 = 0.025\\\\z_{0.025} = 1.96

MoE = 1.96\cdot \frac{64.50}{\sqrt{100} } \\\\MoE = 1.96\cdot 6.45\\\\MoE = 12.64\\

Finally, the confidence interval is

CI = \bar{x} \pm MoE\\\\CI = 282.45 \pm 12.64\\\\CI = 282.45 - 12.64 \: and \: 282.45 + 12.64\\\\CI = \$269.81 \: and \:\:\$295.09\\

Therefore, we are 95% sure that the true population mean amount spent per day by a family of four visiting Niagara Falls is within the interval of ($269.81, $295.09)

3 0
3 years ago
The observation deck is about 20 m above sea level. From the observation deck, the angle of depression of the boat is 6 degrees.
Leno4ka [110]
 θ\ 6 degrees
     \
       \     so the θ= 180-90-6 =84 degrees so we need to find x  
20m   \      tan (84)=x/20 
  ____  \      x=20 tan(84) 
      x         x=190.287   
7 0
3 years ago
2x+2(1960/x)=200 please help for math hw
sp2606 [1]

Two solutions:

1. x =(100-√2160)/2=50-6√ 15 = 26.762

2. x =(100+√2160)/2=50+6√ 15 = 73.238

3 0
3 years ago
Solve<br> plz -4p-2r-15p
IrinaVladis [17]

Answer:

-2r-19p

Step-by-step explanation:

-4p-2r-15p

add like terms

-2r-19p

3 0
3 years ago
Estimate 864/54 by first rounding each number so that it has only 1 nonzero digit.
KiRa [710]

Answer:

18

Step-by-step explanation:

6 0
3 years ago
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