Answer: 401.9
Step-by-step explanation:
Formula for volume of sphere is 4/3πr^3 = 4
r^3 = 64
4/3 x 3.14 = 6.28
6.28 x 64 = 401.92
Rounded to the tenth is 401.9
Answer:
The correct option is b) 1.70
Step-by-step explanation:
Consider the provided information.
The weekly sulfur dioxide emissions follow a normal distribution with a mean of 1000 ppm (parts per million) and a standard deviation of 25.
Thus, μ=1000 and σ = 25
The CEO wants to know if the mean level of emissions is different from 1000.
Therefore the null and alternative hypothesis is:
and ![H_a:\mu \neq1000](https://tex.z-dn.net/?f=H_a%3A%5Cmu%20%5Cneq1000)
The sample size is n = 50 and
ppm.
Now calculate the test statistic by using the formula: ![z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B%5Cbar%20x-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
Substitute the respective values in the above formula.
![z=\frac{1006-1000}{\frac{25}{\sqrt{50}}}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B1006-1000%7D%7B%5Cfrac%7B25%7D%7B%5Csqrt%7B50%7D%7D%7D)
![z=\frac{6}{\frac{25}{\sqrt{50}}}=1.697\approx 1.70](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B6%7D%7B%5Cfrac%7B25%7D%7B%5Csqrt%7B50%7D%7D%7D%3D1.697%5Capprox%201.70)
Hence, the correct option is b) 1.70
Answer: ![x=10.2](https://tex.z-dn.net/?f=x%3D10.2)
Step-by-step explanation:
The triangle shown in the image attached is a right triangle.
Therefore, you can calculate the value of <em>x</em> as you can see below:
![cos\alpha=\frac{adjacent}{hypotenuse}](https://tex.z-dn.net/?f=cos%5Calpha%3D%5Cfrac%7Badjacent%7D%7Bhypotenuse%7D)
In this case, you have that:
<em> adjacent=x</em>
<em> hypotenuse=11</em>
![\alpha=22\°](https://tex.z-dn.net/?f=%5Calpha%3D22%5C%C2%B0)
Therefore, when you substitute values and solve for <em>x</em>, you obtain the following result:
![cos(22\°)=\frac{x}{11}\\\\x=11*cos(22\°)\\x=10.2](https://tex.z-dn.net/?f=cos%2822%5C%C2%B0%29%3D%5Cfrac%7Bx%7D%7B11%7D%5C%5C%5C%5Cx%3D11%2Acos%2822%5C%C2%B0%29%5C%5Cx%3D10.2)
Move all terms not containing z to the right side of the equation.
Z=5
The expression 4a^2c^2 - (a^2-b^2+c^2)^2 has to be factored.
4a^2c^2 - (a^2 - b^2 + c^2)^2
=> (2ac)^2 - (a^2 - b^2 + c^2)^2
=> (2ac - a^2 + b^2 - c^2)(2ac + a^2 - b^2 + c^2)
=> (b^2 - (a^2 - 2ac + c^2))((a^2 + 2ac + c^2) - b^2)
=> (b^2 - (a - c)^2)((a + c)^2 - b^2)
=> (b - a + c)(b + a - c)(a + b + c)(a - b + c)
<span>
The factorized form of 4a^2c^2 - (a^2-b^2+c^2)^2 is (b - a + c)(b + a - c)(a + b + c)(a - b + c)</span>