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Zina [86]
3 years ago
11

Use the elimination method to solve the system of equations. 5x - 2y = 9 and 3x + 4y = -5

Mathematics
2 answers:
Nana76 [90]3 years ago
6 0

Answer: Y = -2 and x = 1

Simplify:

10x − 4y = 18

3x + 4y = -5

Substitute and then the final answer is shown above.

yaroslaw [1]3 years ago
4 0

Answer:

(1,-2)

Step-by-step explanation:

2(5x-2y=9) = 10x-4y=18

                    3x+4y=-5

4 cancels out then u add everything together

now u have 13x=13 the u divide 13x on both sides and you'll get x=1

now u plug xin to what ever equation u want i pick 3x+4y=-5

now u have 3(1)+4y=-5 then 3+4y=-5 then u subtract 3 on both sides and you get -8

now u have 4y=-8 then u divide and u get y=-2

x=1      y=-2

(1,-2)

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An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had
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Answer:

Q1 z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the that means have no difference

Q2  CI 95 %  =  (  0,056 ;  0,164 )

Step-by-step explanation:

Sample information for people under 18

n₁  =  500

x₁ =  180

p₁  =  180/ 500    p₁  =  0,36    then  q₁  =  1 -  p₁     q₁ =  0,64

Sample information for people over 18

n₂  =  600

x₂  =  150

p₂  =  150 / 600   p₂ =  0,25   then   q₂  =  1 - p₂   q₂ =  1 - 0,25   q₂ = 0,75

Hypothesis Test

Null hypothesis                        H₀              p₁  =  p₂

Alternative Hypothesis           Hₐ              p₁  ≠  p₂

The alternative hypothesis indicates that the test is a two-tail test.

We will use the approximation to normal distribution of the binomial distribution according to the sizes of both samples.

Testin at CI =  95 %    significance level is  α = 5 %   α  =  0,05  and

α/ 2  =  0,025   z (c) for that α  is from z-table:

z(c) = 1,96

To calculate   z(s)

z(s)  =  ( p₁  -   p₂ ) / EED

EED = √(p₁*q₁)n₁  +  (p₂*q₂)/n₂

EED = √( 0,36*0.64)/500  +  (0,25*0,75)/600

EED = √0,00046  +  0,0003125

EED = 0,028

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Then

z(s)  =  0,11 / 0,028

z(s) = 3,93

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z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the idea of equals means

Q2  CI  95 %   =  (  p₁  -  p₂  ) ±  z(c) * EED

CI 95%  =  ( 0,11   ±  1,96 * 0,028 )

CI 95%  = (  0,11  ±  0,054 )

CI 95 %  =  (  0,056 ;  0,164 )

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