Opposite reciprocal of -8/3

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

What is the lcm of 56 and 136

Citrus2011 [14]

Answer:

$LCM(56,136)=952$

Step-by-step explanation:

To find the LCM of two numbers, factorize both these numbers:

$56=2\cdot 28=2\cdot 2\cdot 14=2\cdot 2\cdot 2\cdot 7=2^3\cdot 7\\ \\136=2\cdot 68=2\cdot 2\cdot 34=2\cdot 2\cdot 2\cdot 17=2^3\cdot 17$

These two numbers have the common factor of $2^3.$

Now multiply this common factor by the remaining factors:

$LCM(56,136)=2^3 \cdot 7\cdot 17=952$

Therefore, the LCM is 952.

8 0

3 years ago

Write the linear inequality shown in the graph.

Korolek [52]

Fist, in the equation y=mx+b, b is the y-intercept. The y-intercept is the poin on the line that crosses the x-axis; the y-intercept is the value of yThese equations follow that format.
Y=mx+b
y $\geq$ 3x-4. <-----In this equation, the slope(m)=3 b= -4.

On the graph, we can see that the line crosses the x-axis at y=-4. Knowing that, we can eliminate the answer choices with +4 in the inequality.

The next step, is to pick an (x,y) coordinate that is in the shaded region and plug it into the remaining 2 inequalities. Which ever inequality is true after you solve it, that is the correct answer.
For example, I'll choose to plug in (-4,4) into the y $\geq$ 3x-4.
y $\geq$ 3x-4.
(4) $\geq$ (3(-4))-4.
(4) $\geq$ (-12)-4.
(4) $\geq$ -16

So, this statement is true becasue -16 is less than positive 4. Therefore, the correct answer would be y $\geq$ 3x-4. Hope that helped! Comment back with any further questions!

6 0

3 years ago

How do i find the shorted distance between the point and the line

m_a_m_a [10]

Answer:

5 units

Step-by-step explanation:

3x + 4y = 8

4y = -3x+8

y = -3/4+2

The shortest distance between a point and a line is the perpendicular line.

Slope of the perpendicular line: 4/3 and point (-3,-2)

b = -2-(4/3)(-3) = 2

Equation of the perpendicular line: y=4/3x+2

y is equal y

4/3x+2= -3/4x+2

4/3x +3/4x = 2-2

x = 0

Plug x=0 into one of the equations to find y

y = 4/3(0) + 2

y = 2

(0,2) and (-3,-2)

Distance = sqrt [(-3-0)^2 + (-2-2)^2]

Sqrt (-3)^2+ (-4)^2

Sqrt 25 = 5

3 0

2 years ago

The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:

Mila [183]

(0,15)(1,45)
slope = (45 - 15) / ( 1 - 0) = 30 mph

7 0

3 years ago