Math Answers

Equation of a Tangent Line: Find the standard (slope-intercept form) equation of the tangent line to the following functions at the specified points. (Show your complete solution, use Method 1)

1. 𝑓(𝑥) = 𝑥² − 4𝑥+1 at point (0,1)
2. 𝑓(𝑥) = 𝑥³+ 2 at point (1,3)
3. 𝑓(𝑥) = 2𝑥⁴+ 3𝑥³ − 2𝑥 + 7 at point (-1,8)
4. 𝑓(𝑥) = √2𝑥 + 7 𝑎𝑡 𝑥 =1

In a study to estimate the proportion of smokers among the residents in a certain city and its suburbs, it is found that 24 of 104 urban residents are smokers, while 34 of 108 suburban residents are smokers.

On an enquiry related to the frequent reporting of mouth cancer cases, it is estimated that around 60% of the patients chewed tobacco. Does this seem to be a valid estimate if, in a random sample of 120 people, 84 were found to be tobacco users?

A newly married couple plans to have two children. Naturally, they are curious about whether their children will be boys or girls. Let B denotes that the child is a boy and G denotes that the child is a girl, BB denotes that the first child is a boy and the second child is a boy and GB denotes that the first child is a girl and the second child is a boy. construct the tree diagram of this experiment. Construct the tree diagram of this experiment?

According to a study conducted by grade 11 students, Php155 is the monthly expense for cellphone loads of high school students on their province. A statistics students claims that this amount has increased since January of this year. Do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of Php165 on cellphone loads? Using 0.05 level of significance, assume that a population standard deviation of Php52.

"\\begin{Bmatrix}\n a \\\\\n b\n\\end{Bmatrix} = 1\/314*\\begin{bmatrix}\n 198 & -26 \\\\\n -26 & 5\n\\end{bmatrix}\\begin{Bmatrix}\n 1230 \\\\\n 6950\n\\end{Bmatrix}"

X= 38; n= 100 - find p =

X= 55; n= 240 - find p=

X= 38; n= 100 find p=

2. The average length of time for students to

have their subjects controlled is 40 minutes. A

new controlling procedure using modern

computing machines is being tried. If a random

sample of 15 students has an average

controlling time of 25 minutes with a standard

deviation of 12.9 minutes under the new

system, test the hypothesis that the average

length of time to control student’s subjects is

less than 40 minutes. Use a level of

significance of 0.10 and assume the

population of controlling times to be normally

distributed.