Part A
(h + t)(x)
(5x - 2 + 4x + 6)(x) First plug in the numbers
(9x + 4)(x) Add h(x) and t(x)
(9x² + 4x) Then multiply it by x
x(9x + 4) Lastly, simplify x out (I'm including both answers because I don't know whether your questions will ask for either one)
Unsimplified Answer: 9x² + 4x Simplified Answer: x(9x + 4)
Part B
(h x t)(x)
(5x - 2)(4x + 6)(x) First step is to of cource, plug in the numbers
(20x² + 30x -8x -12)(x) Next we multiply h(x) and t(x)
(20x² + 22x -12)(x) Simplify it a little
(20x³ + 22x² - 12x) After that, multiply the whole thing by x
(2x)(10x² + 11x - 6) Simplify 2x out of the equation
(2x)(5x - 2)(2x + 3) Lastly, simplify the rest
Unsimplified Answer: (20x³ + 22x² -12x) Simplified Answer: (2x)(5x - 2)(2x + 3)
Part C
h[t(x)]
(5x - 2) [(4x + 6)(x)] Plug in the numbers
(5x - 2)(4x² + 6x) Multiply t(x) and x
(20x³ + 30x² - 8x² -12x) Multiply that by h(x)
(20x³ + 22x² -12x) Simplify a little... Wait! That looks like the answer to Part B! Perhaps we did something wrong, let's go back and alter the third step
(5x -2)(2x)(2x + 3) This time, simplify before multiplying oh wait, that's part B's simplified answer, isn't it.
Well, there's a good explanation for this: Part B and Part C are essentially the same equations, just in slightly different orders!
So, it will have the same answers and Part B! (At least, in theory, I'd recommend checking this for yourself too!)
Unsimplified Answer: (20x³ + 22x² - 12x) Simplified Answer: (2x)(5x-2)(2x+3)
Well, that's a wrap, Parts A, B, and, C with work and explanations; if you find that I made a mistake or did something wrong let me know. I hope this helped, and good luck!
The least squares regression line is y=0.6831x+11.25
Step-by-step explanation:
LSRL is the the Least Squares Regression Line.The formula for regression line is y=mx+b where m is the slope of the line and b is the y-intercept value of the line.
First find the slope, m of the line from the means and standard deviations given
x has a mean of 17.2 g and a standard deviation of 14.0 g
y has a mean of 23.5 g and a standard deviation of 16.4 g
The correlation coefficient in both cases is 0.83, hence the slope m is given by;
m=r(Sy/Sx) where m is the slope of the line, Sy is standard deviation of y values, Sx is standard deviation of x values and r is the correction coefficient.
m= 0.5 * 23.5/17.2 =0.6831
Find the value of b, the y-intercept
b=Y-mX where X and Y are the mean values for x and y respectively
b=23.5-0.6831*17.2
b=23.5-11.75=11.25
The LSRL is y=0.6831x+11.25
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Least Squares regression Line : brainly.com/question/4090838
Keyword : standard deviation, least square regression line
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