Answer:
Step-by-step explanation:
The quadratic formula would be the following...
![x = \frac{-b (+-)\sqrt{b^{2} - 4ac } }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%28%2B-%29%5Csqrt%7Bb%5E%7B2%7D%20-%204ac%20%7D%20%7D%7B2a%7D)
where the original quadratic equation would be represented as follows
![ax^{2} + bx +c = 0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2B%20bx%20%2Bc%20%3D%200)
Using this information and the information provided in the image we can plug in the quadratic equation values in the image to form the quadratic formula.
![\frac{-(-20)±\sqrt{(-20)^{2} - 4(16)(-6) } }{2(16)}](https://tex.z-dn.net/?f=%5Cfrac%7B-%28-20%29%C2%B1%5Csqrt%7B%28-20%29%5E%7B2%7D%20-%204%2816%29%28-6%29%20%7D%20%7D%7B2%2816%29%7D)
That would be the correct order for the values.
Answer:
Multiply the number and divide by how many numbers were added
Answer:
Length: 139 feet
Width: 104 feet
Step-by-step explanation:
The formula for the perimeter of a rectangle can be given by
. We are given the perimeter of the pool along with the width.
![P = 486](https://tex.z-dn.net/?f=P%20%3D%20486)
![w = l - 35](https://tex.z-dn.net/?f=w%20%3D%20l%20-%2035)
From here, all we have to do is plug back into the original formula:
![486 = 2l + 2(l - 35)](https://tex.z-dn.net/?f=486%20%3D%202l%20%2B%202%28l%20-%2035%29)
Which can be further simplified as:
![486 = 2l + 2l - 70](https://tex.z-dn.net/?f=486%20%3D%202l%20%2B%202l%20-%2070)
![486 = 4l - 70](https://tex.z-dn.net/?f=486%20%3D%204l%20-%2070)
From here, all we have to do is add 70 to both sides of the equation and divide by four:
![556 = 4l](https://tex.z-dn.net/?f=556%20%3D%204l)
![139 = l](https://tex.z-dn.net/?f=139%20%3D%20l)
To make sure that this answer is accurate, we can find that the width of the rectangle should then be 104 (given by 139 - 35). All we have to do is plug back into the original equation:
![P = 2l + 2w](https://tex.z-dn.net/?f=P%20%3D%202l%20%2B%202w)
![P = 2(139) + 2(104)](https://tex.z-dn.net/?f=P%20%3D%202%28139%29%20%2B%202%28104%29)
![P = 278 + 208](https://tex.z-dn.net/?f=P%20%3D%20278%20%2B%20208)
![P = 486](https://tex.z-dn.net/?f=P%20%3D%20486)
And the substitution works, so the length of the rectangle would be 139 feet and the width would be 104 feet.
The answer for the blank space is 21.8
Answer:
0.1994 is the required probability.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 166 pounds
Standard Deviation, σ = 5.3 pounds
Sample size, n = 20
We are given that the distribution of weights is a bell shaped distribution that is a normal distribution.
Formula:
Standard error due to sampling =
![=\dfrac{\sigma}{\sqrt{n}} = \dfrac{5.3}{\sqrt{20}} = 1.1851](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%20%5Cdfrac%7B5.3%7D%7B%5Csqrt%7B20%7D%7D%20%3D%201.1851)
P(sample of 20 boxers is more than 167 pounds)
Calculation the value from standard normal z table, we have,
0.1994 is the probability that the mean weight of a random sample of 20 boxers is more than 167 pounds