1st you add up all the marbles so we got 15 so the answe will be out of 15 then next we add up nhe number of yellow and purple marbles 5+3= 8 so the answe will be 8/15
Answer:
$43.20
Step-by-step explanation:
Subtract the tax to find the actual sale price then multiply by 4. 12-1.20=10.80.... 10.80*4=43.30
Answer: A. H0: Mean= 5 and Ha: Mean is not equal to 5.
Step-by-step explanation:
Definitions:
- Null hypothesis
is a statement describing population parameters according to the objective of the study. It takes "≤,≥,=" signs.
- Alternative hypothesis
is a statement opposite to the null hypothesis elaborating population parameters according to the objective of the study. It takes ">, <, ≠" signs.
Given: The diameter of a spindle in a small motor is supposed to be 5.8 millimeters.
If the spindle is either too small or too large, the motor will not work properly. so, Mean diameter ≠ 5.8 to work correctly.
i.e. 
So, 
The required null and alternative hypotheses:
H0: Mean= 5 and Ha: Mean is not equal to 5.
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Sum to Product Identities:

<u>Proof LHS → RHS</u>





![\text{Sum to Product:}\qquad \dfrac{\cos 10\bigg[2\cos \bigg(\dfrac{15+25}{2}\bigg)\sin \bigg(\dfrac{15-25}{2}\bigg)\bigg]}{\cos 20\bigg[-2\sin \bigg(\dfrac{15+5}{2}\bigg)\sin \bigg(\dfrac{15-5}{2}\bigg)\bigg]}](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cqquad%20%5Cdfrac%7B%5Ccos%2010%5Cbigg%5B2%5Ccos%20%5Cbigg%28%5Cdfrac%7B15%2B25%7D%7B2%7D%5Cbigg%29%5Csin%20%5Cbigg%28%5Cdfrac%7B15-25%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%7D%7B%5Ccos%2020%5Cbigg%5B-2%5Csin%20%5Cbigg%28%5Cdfrac%7B15%2B5%7D%7B2%7D%5Cbigg%29%5Csin%20%5Cbigg%28%5Cdfrac%7B15-5%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%7D)
![\text{Simplify:}\qquad \qquad \dfrac{\cos 10[2\cos 20\sin (-5)]}{\cos 20[-2\sin 10\sin 5]}\\\\\\.\qquad \qquad \qquad =\dfrac{-2\cos10 \cos 20 \sin 5}{-2\sin 10 \cos 20 \sin 5}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 10}{\sin 10}\\\\\\.\qquad \qquad \qquad =\cot 10](https://tex.z-dn.net/?f=%5Ctext%7BSimplify%3A%7D%5Cqquad%20%5Cqquad%20%5Cdfrac%7B%5Ccos%2010%5B2%5Ccos%2020%5Csin%20%28-5%29%5D%7D%7B%5Ccos%2020%5B-2%5Csin%2010%5Csin%205%5D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Cdfrac%7B-2%5Ccos10%20%5Ccos%2020%20%5Csin%205%7D%7B-2%5Csin%2010%20%5Ccos%2020%20%5Csin%205%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Cdfrac%7B%5Ccos%2010%7D%7B%5Csin%2010%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Ccot%2010)
LHS = RHS: cot 10 = cot 10 