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Elena-2011 [213]
2 years ago
7

If : f(x)=x^2, g(x)=x-1. Find (f×g)(x).​

Mathematics
1 answer:
kramer2 years ago
8 0

Answer:

  • \boxed{ f\cdot{g}(x) = x {}^{3}  - x {}^{2}}

Step by step explanation:

Given that,

f(x) =  {x}^{2}

g(x) = x - 1

Solution:

Solving for (f•g)(x):

= f(x) \cdot g(x)

Now substitute the given values.

= x {}^{2}  \cdot(x - 1)

= x {}^{2} (x - 1)

Apply distributive property:

= (x ^{2}  \cdot x) - x {}^{2}  \cdot 1

  • \boxed{ f\cdot{g}(x) =  x {}^{3}  - x {}^{2}}

Hence,f•g(x) will be x {}^{3}  - x {}^{2}.

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Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the
Ad libitum [116K]

<u>Answer-</u>

<em>The least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable is "y=0.937x+12.765" .</em>

<u>Solution-</u>

The independent variable / input variable= x = Number of years after 2000 ( = year-2000)

The dependent variable / output variable = y = Average cost in thousands of dollars

(The table has been attached herewith.)

To find the regression equation for a group of (x,y) points,

We have to calculate the slope and y-intercept, then we can put those values in the equation y = mx + c ( Slope - Intercept formula)

We know that,

Slope=m=\frac{N\sum xy -\sum x\sum y}{N\sum x^{2}- (\sum x)^{2}}

Putting the values from the table,

m=\frac{(8 \times 1020.206)-(52 \times 150.894)}{(8 \times 3810)-(52^2)}

( ∵ Instead of 150,894 we have to put 150.894 as we have find the line for year and thousands of dollars )

\Rightarrow m =\frac{8161.648-7846.488}{3040-2704} =\frac{315.16}{336}=0.937

Now, for the y-intercept,

c =\frac{\sum y -m(\sum x)}{N}

Putting the values,

c=\frac{150.894-(52 \times 0.937)}{8}=\frac{102.125}{8}=12.765

Now, putting the values of c and m, in the Slope-Intercept formula,

y=0.937x+12.765


3 0
3 years ago
What is 3×10^-2 in standerd notation??
Gemiola [76]

Answer: 0.03

Step-by-step explanation:

7 0
3 years ago
jane is twice as old as Barbara. Michael is 7 years older than Jane. If Michael is 21, which equation could be used to find Barb
dedylja [7]

Step-by-step explanation:

J = 2b

M = J + 7

M = 21

J = 21 - 7

J = 14

B = 7

<em>Equation:</em>

If M is J+7, so then J = 21-7. J is 2*b, so 2*b = 21-7. Then you subtract and divide.

3 0
2 years ago
Help please 24 points.
miss Akunina [59]
Range:5-24
Median: 10
Mean: 8.76 
8 0
3 years ago
Read 2 more answers
Pls answer and show work for brainliest
Zina [86]
15/50 = 0.3
that’s 30%
so 30% of people will not be wearing hats.
30% of 250 = 250 x 0.3
= 75 people
8 0
3 years ago
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