Given : tan 235 = 2 tan 20 + tan 215
To Find : prove that
Solution:
tan 235 = 2 tan 20 + tan 215
Tan x = Tan (180 + x)
tan 235 = tan ( 180 + 55) = tan55
tan 215 = tan (180 + 35) = tan 35
=> tan 55 = 2tan 20 + tan 35
55 = 20 + 35
=> 20 = 55 - 35
taking Tan both sides
=> Tan 20 = Tan ( 55 - 35)
=> Tan 20 = (Tan55 - Tan35) /(1 + Tan55 . Tan35)
Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1
=> Tan 20 = (Tan 55 - Tan 35) /(1 + 1)
=> Tan 20 = (Tan 55 - Tan 35) /2
=> 2 Tan 20 = Tan 55 - Tan 35
=> 2 Tan 20 + Tan 35 = Tan 55
=> tan 55 = 2tan 20 + tan 35
=> tan 235 = 2tan 20 + tan 215
QED
Hence Proved
Step-by-step explanation:
In this problem, we need to find three rational numbers between 7/12 and 7/11.
First rational no :
Second rational no :
Robert should get D. 8281.25 pesos in exchange.
Explanation:
- Robert is bringing 625 U.S. dollars with him to Mexico. He needs to exchange the money he has with him to Mexico's currency i.e. from U.S. dollars to Mexican pesos.
- The exchange rate is 13.25 Mexican pesos for each U.S. dollar. So 1 U.S. dollar = 13.25 Mexican pesos.
- So to calculate how much 625 U.S. dollars is in pesos we multiply 625 with the exchange rate i.e. 13.25 pesos 625 U.S dollars = 625 × 13.25 = 8281.25 Mexican pesos.
<h3>Option D</h3><h3>The expression can be used to find the price of a $400 telescope after a 32% markup is: 400 + 400 (0.32 )</h3>
<em><u>Solution:</u></em>
Given that,
Price of telescope = $ 400
Mark up = 32 %
To find: Cost after mark up
The formula used is:
<h3>Cost after mark up = Price of telescope + 32 % of Price of telescope</h3>
Therefore,
Cost after mark up = 400 + 32 % of 400
Thus cost after mark up is $ 528 and expression is 400 + 400 (0.32 )
A) In order to create a sampling plan, you need to follow the following 5 steps:
1) Define the sample population: who are the customers you want to contact?
The costumers who bought a new car on a certain year.
2) Define the size of population: how many customers are you going to contact?
Of the 30000 customers who bought a car, you want to contact 1000 customers.
3) Define the contact options: how are you going to contact the customers?
You have a list of names and addresses, therefore you can send a questionnaire via mail.
4) Form a sampling frame: what is the time or contact frame to get in touch with your customers?
You will send the questionnaires and you will wait two months for the answer.
5) Define the analysis method: is yours a qualitative or quantitative research?
In your case, you want a quantitative research and therefore a probabilistic sampling.
B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.
C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
P = 13 / 1000
= 0.013
Therefore,
N = <span>0.013 </span>× 30000
= 390
Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.
