1/2x+3y=4 for x when y=6
2 answers:
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Answer:
a ) y = 1 and x = -1
d) y = 5 and x = -1/2
Step-by-step explanation:
<h2><u>Substitution method</u></h2><h2><u>Question a</u></h2>y = x+ 2
y = 2x + 3
<em>we can make the first formula in terms of x , so we can place in into the second formula</em>
y = x + 2
x = y - 2
now put y - 2 where x is in the second equation
y = 2x + 3
y = 2(y - 2) + 3
y = 2y - 4 +3
now solve
4 - 3 = 2y -y
y = 1
since y = 1 we can find what x is by putting into the first formula
y = x +2
x = y - 2
x = (1) -2
x = -1
<h3><u>hence y = 1 and x = -1 </u></h3><h3><u /></h3><h2><u>Question d</u></h2>y = 2x + 6
y = 4 - 2x
<em>we can make the first formula in terms of x , so we can place in into the second formula</em>
y = 2x + 6
y - 6 = 2x
x = (y-6)/ 2
now place (y-6)/2 where x is in the second formula
y = 4 -2x
y = 4 - 2 ()
now solve
the multiplication by 2 and division by 2 are cancelled out
hence making the simplified equation as:
y = 4 - y + 6
2y = 4 + 6
2y = 10
y = 5
now place this into the first equation
y = 2x + 6
y - 6 = 2x
x = (y-6)/ 2
x = (5-6)/2
x = -1/2
<h3><u>hence y = 5 and x = -1/2</u></h3>
Answer:
Since the p value is lower than the significance level we have enough evidence to conclude that the true means are different at 5% of significance
Step-by-step explanation:
Data given
sample mean for group 1
sample mean for group 2
sample size for group 1
sample size for group 2
sample deviation for group 1
sample deviation for group 2
Solution
We want to check if the two means are equal so then the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
And the statistic is given by:
And replacing we got:
The degrees of freedom are given by:
And the p value would be:
Since the p value is lower than the significance level we have enough evidence to conclude that the true means are different at 5% of significance