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3 years ago

27

Mathematics

1 answer:

larisa [96]3 years ago

5 0

Answer:

The original nimber is 67.

Step-by-step explanation:

Let the two digits be x and y.

According to the question.

The sum of two digits of a two digit number is

x + y = 13

or, x = 13 - y

And, a two digit number can be written as

x × 10 + y

when the digits are reversed, the number can be written as

y × 10 + x

the original number increases by 9. i.e.

y x 10 + x = x × 10 + y + 9

Replacing value of x by 13 - y,

y × 10 + 13 - y = 10(13 - y) + y + 9

10y + 13 - y = 130 - 10y + y + 9

9y + 13 = 139 - 9y

18y = 139 - 13

18y = 126

y = 126/18

y = 7

So, x = 13 - y

= 13 - 7

= 6

The original number is x × 10 + y = 6 x 10 + 7 = 67.

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Divide.<br> (4x4 - 4x2 – x-3) = (2x2 – 3)

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Given:

Division problem:

$(4x^4-4x^2-x-3)\div (2x^2-3)$

To find:

The solution for the given division problem.

Solution:

We have,

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Here, 4x^4-4x^2-x-3 is the dividend and (2x^2-3) is divisor.

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$\underline{\quad -x\quad}$ (After subtraction)

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$\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}$

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4 years ago

Read 2 more answers

At a used dealership, let X be an independent variable representing the age in years of a motorcycle and Y be the dependent vari

GarryVolchara [31]

Answer:

a) Selling price y= a + b (age x)

a= 728.025

b= -38.217

Selling price y = 728.025 - 38.217 age x

SSE=8280.25

Step-by-step explanation:

The regression model can be written as

y=a+bx

Here y=selling price and x is age.

So, the regression model will be

Selling price y= a + b (age x)

We have to find the values of "a" and "b"

$b=\frac{nsumxy-(sumx)(sumy)}{nsumx^{2} -(sumx)^2}$

sumx=5+10+12+14+15=56

sumy=500+400+300+200+100=1500

sumxy=5*500+10*400+12*300+14*200+15*100=14400

sumx²=5²+10²+12²+14²+15²=690

n=5

$b=\frac{5(14400)-(56)(1500)}{5(690) -(56)^2}$

b=-12000/314

b=-38.217

ybar=a+bxbar

a=ybar-bxbar

ybar=sumy/n=1500/5=300

xbar=sumx/n=56/5=11.2

a=300-(-38.217)(11.2)

a=300+428.025

a=728.025

Selling price y = a - b(age x)

Selling price y = 728.025 - 38.217 age x

SSE known as sum of square of error can be calculated as

SSE=sum(y-yhat)²

y 500 400 300 200 100

x 5 10 12 14 15

yhat= 728.025 - 38.217 age x 536.940 345.855 269.421 192.987 154.770

y-yhat -36.940 54.145 30.579 7.013 -54.770

(y-yhat)² 1364.56 2931.68 935.08 49.18 2999.75

SSE=sum(y-yhat)²

SSE=1364.56 +2931.68 +935.08 +49.18 +2999.75

SSE =8280.25

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