Answer:
y = 1/3
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
2x - 9y = 11
<em>x</em> = 7
<u>Step 2: Evaluate</u>
- Substitute in <em>x</em>: 2(7) - 9y = 11
- Multiply: 14 - 9y = 11
- [Subtraction Property of Equality] Subtract 14 on both sides: -9y = -3
- [Division Property of Equality] Divide -9 on both sides: y = 1/3
Answer:
The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%
Step-by-step explanation:
Confidence interval for the proportion of people who own a tablet:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
For this problem, we have that:
![n = 150, \pi = \frac{120}{150} = 0.8](https://tex.z-dn.net/?f=n%20%3D%20150%2C%20%5Cpi%20%3D%20%5Cfrac%7B120%7D%7B150%7D%20%3D%200.8)
99% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.7159](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.8%20-%202.575%5Csqrt%7B%5Cfrac%7B0.8%2A0.2%7D%7B150%7D%7D%20%3D%200.7159)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.8841](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.8%20%2B%202.575%5Csqrt%7B%5Cfrac%7B0.8%2A0.2%7D%7B150%7D%7D%20%3D%200.8841)
Percentage:
Multiply the proportion by 100.
0.7159*100 = 71.59%
0.8841*100 = 88.41%
The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%
Given:
The ratio of the measures of the sides of a triangle is 3:4:5.
Its perimeter is 48 inches.
To find:
The scale factor as a decimal, and the measure of each side of the triangle.
Solution:
Let x be the scale factor. Then the measures of sides of the triangle are 3x, 4x and 5x.
The perimeter of the triangle is 48 inches. It means the sum of all sides of the triangle is 48 inches.
![3x+4x+5x=48](https://tex.z-dn.net/?f=3x%2B4x%2B5x%3D48)
![12x=48](https://tex.z-dn.net/?f=12x%3D48)
Divide both sides by 12.
![x=\dfrac{48}{12}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B48%7D%7B12%7D)
![x=4](https://tex.z-dn.net/?f=x%3D4)
Now, the measures of sides are:
![3x=3(4)](https://tex.z-dn.net/?f=3x%3D3%284%29)
![3x=12](https://tex.z-dn.net/?f=3x%3D12)
Similarly,
![4x=4(4)](https://tex.z-dn.net/?f=4x%3D4%284%29)
![4x=16](https://tex.z-dn.net/?f=4x%3D16)
And,
![5x=5(4)](https://tex.z-dn.net/?f=5x%3D5%284%29)
![5x=20](https://tex.z-dn.net/?f=5x%3D20)
Therefore, the scale factor is 4 and the measures of sides are 12, 16 and 20.