Atyping instructor builds a regression model to investigate what factors determine typing speed for students with two months of instruction. her regression equation looks like: y' = 7x3 + 5x2 + 3x + 11 where: y' = typing speed in words per minute; x3= hours of instruction per week; x2= hours of practice per week; x = hours of typing per week necessary for school or work; a new student is taking 2 hrs of typing instruction per week, will practice 5 hrs per week and must type 2.5 hours per week for work. if the standard error of the estimate is 4, within what range do we have a 95.45% probability that that student's typing speed will be in two months? a. 53.5 and 61.5 words per minuteb. 49.5 and 65.5 words per minutec. 57.5 and 65.5 words per minuted. none of the above

B. 49.5 and 65.5 words per minute

Step-by-step explanation:

95.45% range estimate for the student's typing speed can be calculated using the equation Y±(z×SE) where

Thus, Y±(z×SE) =57.5±(2×4) that is, 95.45%  probability range for the student's typing speed is between 49.5 hours and 65.5 hours

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240