Answer: He bought 7 pens.
Step-by-step explanation:
21/3 = 7
Answer:
The standard deviation of the age distribution is 6.2899 years.
Step-by-step explanation:
The formula to compute the standard deviation is:
The data provided is:
X = {19, 19, 21, 25, 25, 28, 29, 30, 31, 32, 40}
Compute the mean of the data as follows:
![=\frac{1}{11}\times [19+19+21+...+40]\\\\=\frac{299}{11}\\\\=27.182](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B11%7D%5Ctimes%20%5B19%2B19%2B21%2B...%2B40%5D%5C%5C%5C%5C%3D%5Cfrac%7B299%7D%7B11%7D%5C%5C%5C%5C%3D27.182)
Compute the standard deviation as follows:
![=\sqrt{\frac{1}{11-1}\times [(19-27.182)^{2}+(19-27.182)^{2}+...+(40-27.182)^{2}]}}\\\\=\sqrt{\frac{395.6364}{10}}\\\\=6.28996\\\\\approx 6.2899](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B11-1%7D%5Ctimes%20%5B%2819-27.182%29%5E%7B2%7D%2B%2819-27.182%29%5E%7B2%7D%2B...%2B%2840-27.182%29%5E%7B2%7D%5D%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%5Cfrac%7B395.6364%7D%7B10%7D%7D%5C%5C%5C%5C%3D6.28996%5C%5C%5C%5C%5Capprox%206.2899)
Thus, the standard deviation of the age distribution is 6.2899 years.
Answer:
<em>Part 1 : Equation: ( 3x - 9 ) + 30 + 24 = 180,</em>
<em>Part 2 : Value of x ⇒ 45°,</em>
<em>Part 3 : Measure of Angle U ⇒ 126°</em>
Step-by-step explanation:
~ Part 1 ~
We know that ∑ of angles in a triangle is 180;
m∠ U + m∠ V + m∠ W = 180°,
<em>Equation: ( 3x - 9 ) + 30 + 24 = 180</em>
~ Part 2 ~
Now let us simplify the equation above to solve for x;
3x - 9 + 30 + 24 = 180,
3x - 9 = 126,
3x = 135,
x = 45 degrees ( ° ) ⇒
<em>Value of x ⇒ 45°</em>
~ Part 3 ~
If it is known that m∠ U ⇒ 3x - 9;
m∠ U = 3 * ( 45 ) - 9,
m∠ U = 135 - 9,
m∠ U = 126 degrees ( ° ) ⇒
<em>Measure of Angle U ⇒ 126°</em>
Well,
We would see the rectangular prism cut in half, which, if we looked from the top, would look like a rectangle. That is figure Z.
