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Nana76 [90]
3 years ago
6

A teacher collects data on the number of hours, s, his students spend studying and the number of hours, t, they spend watching T

V each day. He finds that there is a negative linear association between s and t that is best modeled by the equation s=−0.5t+3.6 .
What is the meaning of 3.6 in this equation?
Mathematics
1 answer:
Sidana [21]3 years ago
5 0
Since there is a negative correlation, evident by the negative slope of the equation of the line given to be -0.5, if we take t as 0, we get an equation of,
                                            s = 3.6
This means that if a student does not watch television, he or she spends a maximum of 3.6 hours studying. 
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A handbag was purchased for Rs.280/- and sold for Rs.350/- calculate profit%
Llana [10]

Answer:

profit is 25%

Step-by-step explanation:

profit%=sp-cp/cp×100%

=350-280/280×100%

=0.25×100

=25%

7 0
3 years ago
Let X denote the temperature (degree C) and let Y denote thetime in minutes that it takes for the diesel engine on anautomobile
BlackZzzverrR [31]

Answer:

Step-by-step explanation:

Given f_{XY} (x,y) = c(4x + 2y +1) ; 0 < x < 40\,and\, 0 < y

a)

we know that \int\limits^\infty_{-\infty}\int\limits^\infty_{-\infty} {f(x,y)} \, dxdy=1

therefore \int\limits^{40}_{-0}\int\limits^2_{0} {c(4x+2y+1)} \, dxdy=1

on integrating we get

c=(1/6640)

b)

P(X>20, Y>=1)=\int\limits^{40}_{20}\int\limits^2_{1} {\frca{1}{6640}(4x+2y+1)} \, dxdy

on doing the integration we get

                        =0.37349

c)

marginal density of X is

f(x)=\int\limits^2_{0} {\frca{1}{6640}(4x+2y+1)} \, dy

on doing integration we get

f(x)=(4x+3)/3320 ; 0<x<40

marginal density of Y is

f(y)=\int\limits^{40}_{0} {\frca{1}{6640}(4x+2y+1)} \, dx

on doing integration we get

f(y)=\frac{(y+40.5)}{83}

d)

P(01)=\int\limits^{40}_{0}\int\limits^2_{1} {\frca{1}{6640}(4x+2y+1)} \, dxdy

solve the above integration we get the answer

e)

P(X>20, 0

solve the above integration we get the answer

f)

Two variables are said to be independent if there jointprobability density function is equal to the product of theirmarginal density functions.

we know f(x,y)

In the (c) bit we got f(x) and f(y)

f(x,y)cramster-equation-2006112927536330036287f(x).f(y)

therefore X and Y are not independent

4 0
3 years ago
Marisol is preparing a care package to send to her brother. The package will include a board game that weighs 4 lb and several 1
Gelneren [198K]
So what we gotta do is isolate the variable by
writing it out like this
4 1/4 25 those are the numbers where those go are like this
4x - 1/4 < 25 then move on to the next line on here we write out
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8 0
3 years ago
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JulsSmile [24]

Answer:

The last one is the correct answer

5 0
3 years ago
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Find the derivative of f(x) = 12x^2 + 8x at x = 9.
zvonat [6]

Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

(f+g)'=f'+g' Sum rule.

(cf)'=cf' Constant multiple rule.

(x^n)'=nx^{n-1} Power rule.

(x)'=1 Slope of y=x is 1.

f(x)=12x^2+8x

f'(x)=(12x^2+8x)'

f'(x)=(12x^2)'+(8x)' by sum rule.

f'(x)=12(x^2)+8(x)' by constant multiple rule.

f'(x)=12(2x)+8(1) by power rule.

f'(x)=24x+8

Now we need to find the derivative function evaluated at x=9.

f'(9)=24(9)+8

f'(9)=216+8

f'(9)=224

In case you wanted to use the formal definition of derivative:

f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}

Or the formal definition evaluated at x=a:

f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}

Let's use that a=9.

f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}

We need to find f(9+h) and f(9):

f(9+h)=12(9+h)^2+8(9+h)

f(9+h)=12(9+h)(9+h)+72+8h

f(9+h)=12(81+18h+h^2)+72+8h

(used foil or the formula  (x+a)(x+a)=x^2+2ax+a^2)

f(9+h)=972+216h+12h^2+72+8h

Combine like terms:

f(9+h)=1044+224h+12h^2

f(9)=12(9)^2+8(9)

f(9)=12(81)+72

f(9)=972+72

f(9)=1044

Ok now back to our definition:

f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}

f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}

Simplify by doing 1044-1044:

f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}

Each term has a factor of h so divide top and bottom by h:

f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}

f'(9)=\lim_{h \rightarrow 0}(224+12h)

f'(9)=224+12(0)

f'(9)=224+0

f'(9)=224

8 0
3 years ago
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