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2 years ago

Composition of functions Find g (f(x)) for the following problems

Mathematics

1 answer:

beks73 [17]2 years ago

7 0

$f(x)=-3x\qquad g(x)=5x-6\\\\g(f(x))=5(-3x)-6=\boxed{-15x-6}$

$f(x)=x-6\qquad g(x)=x^2+6x-2\\\\g(f(x))=(x-6)^2+6(x-6)-2=x^2-12x+36+6x-36-2=\\\\=\boxed{x^2-6x-2}$

$f(x)=4x+3\qquad g(x)=2x^2-x+1\\\\g(f(x))=2(4x+3)^2-(4x+3)+1=2(16x^2+24x+9)-4x-3+1=\\\\=32x^2+48x+18-4x-3+1=\boxed{32x^2+44x+16}$

$f(x)=2x^2\qquad g(x)=8x^2+3x\\\\g(f(x))=8(2x^2)^2+3(2x^2)=8\cdot4x^4+6x^2=\boxed{32x^4+6x^2}$

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Can someone please help with the last problem

Brut [27]

Answer:

18x +9h

Step-by-step explanation:

Such problems are tedious, but not difficult. The trick is to avoid making mistakes in the algebra.

$\dfrac{f(x+h)-f(x)}{h}=\dfrac{(9(x+h)^2)-(9x^2)}{h}\\\\=\dfrac{9(x^2+2xh+h^2)-9x^2}{h}=\dfrac{18xh+9h^2}{h}=\boxed{18x+9h}$

3 0

2 years ago

Accountants at the Tucson firm, Larry Youdelman, CPAs, believed that several traveling executives were submitting unusually hi

77julia77 [94]

Answer:

a) $Y= 90 +46.50(5) +0.35 (340) =441.50$

b) The accountant should not question the voucher as the request is much higher than expected.

c) We can add the following variables

d) The percentage of variation in the trip cost that can be explained by the model = (0.64)^2 =0.4096 or 40.96%

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Step-by-step explanation:

Part a

For this case we have the multiple regression model given by:

$Y= 90 +46.50 x_1 +0.35 x_2$

Where $x_1$ represent the number of days on the road and $x_2$ the distance traveled in miles.

And we want to find the expected amount from a 340-mile trip that took her out of town for 5 days, so we just need to replace x1= 5 and x2=340 and we got:

$Y= 90 +46.50(5) +0.35 (340) =441.50$

Part b

The expected value taking in count that x1 = 5 and y = 340 is:

$Y= 90 +46.50(55) +0.35 (340) =441.50$

And the difference from the obtained value is : 685-441.50=243.5

So then the correct answer would be:

The accountant should not question the voucher as the request is much higher than expected.

Part c

We can add the following variables

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Part d

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

The coefficient of determination "is a measure used in statistical analysis that assesses how well a model explains and predicts future outcomes. It is indicative of the level of explained variability in the data set".

The percentage of variation in the trip cost that can be explained by the model = (0.64)^2 =0.4096 or 40.96%

6 0

2 years ago

All of the points in the graph are on the same line.<br><br> Find the slope of the line.

geniusboy [140]

Answer:

The slope of the line is $\frac{1}{2}$ .