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(21 - 16〖sin〗^2 x+8 cosx)/(16 〖cos〗^2 x-29-8 √15 sin⁡x ) = 2

find x
2. ​It is known that the weights of apples from a farm are normally distributed. In order to estimate the mean weight, a random sample of 150 apples is considered and the sample mean and population standard deviation are 6 kg and 0.8 kg respectively.

(a)​Construct a 95% confidence interval estimate for the population mean weight of apples.
​​​​​​​​​​​​ (2 marks)​​​​​​​​​​​​
(b)​The researcher suggests doing the study again so that 98% confidence interval estimate for the population mean weight of apples is (5.8835,6.1165) kg. How large should the sample size be?
​​​​​​​​​​​​ (3 marks)
A right circular cone is inscribed in a cube having a diagonal which
measures 20 square root of 3 cm.

2. What is the volume of the cone?
A right circular cone is inscribed in a cube having a diagonal which
measures 20 square root of 3 cm.

1. What is the altitude of the cone?
The volume of a frustum of a right circular cone is 52π cm3. Its altitude is 3cm and the measure of its lower radius is three times the measure of its
upper radius.

5. What is the radius of the upper base?
6. What is the slant height of the frustum?
7. Find the lateral area of the frustum.
A Leading mobile phone manufacturer is about to introduce a new series, initially they are launching 4 models of the same series. The accompanying table summarizes price and variable costs data, combined fixed costs equal $540,000.
Models
Infinity A Pro Max Infinity A Pro Infinity A Infinity A Lite
Selling Price (in dollars) 500 400 340 220
Material Cost /unit (in dollars) 220 190 150 90
Labor Cost/unit (in dollars) 90 65 65 50
Table 1
a) Develop a joint total revenue function for sales of the four different models.
b) Develop an annual total cost function for manufacturing the four models.
c) Develop the profit function for sales of the four models.
d) Calculate the annual profit if the firm sells 9000, 12000, 45000 and 22000 units, respectively, of the four models?
Go through the statements and identify the thinking style or fallacies linked with these statements. Answer this question with Justifications; Word limit for each part: 50 words.
1.​Karachi met with cold breezes because it rained in Quetta.
2.​This research conclusion states that brand name has a significant impact on brand performance.
3.​The Pakistanis are the best people in the world.
4.​Young people are much more immoral in their behavior than older people.
5.​He was seen talking with a burglar; therefore he is a burglar himself.
Ahmar and Ibad are two good friends and fellow mates; both have been together since elementary school classes and have completed high school together. Now they are preparing for reputed universities. Ahmar is feeling down due to the negative thoughts and he is afraid of being rejected from the top universities. Ibad on the contrary is very energetic, optimistic, well organized and victory oriented.
Requirement: In light of self-esteem, can you explain the reason for two different approaches of two people who had so many things similar to each other. Word limit 500 to 700 words
A committee of 4 women and 2 men is to be selected from 10 women and 5 men. If two of the women \nare feuding and cannot serve on the committee together, in how many ways can the committee be selected?
a.2380
b.2100
c.280
d.1820
All the five questions in an examination must be answered by a student. If it is believed that the order in which the questions are answered has impacts on the performance of the student. In how many different orders can the questions be answered
a.120
b.160
c.100
d.140
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