Step-by-step explanation:
<h2>1)3.25x + -1.5y = 1.25</h2>
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1.5y' to each side of the equation.
3.25x + -1.5y + 1.5y = 1.25 + 1.5y
Combine like terms: -1.5y + 1.5y = 0.0
3.25x + 0.0 = 1.25 + 1.5y
3.25x = 1.25 + 1.5y
<h2>2)13x-6y=10</h2>
13x + -6y = 10
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6y' to each side of the equation.
13x + -6y + 6y = 10 + 6y
Combine like terms: -6y + 6y = 0
13x + 0 = 10 + 6y
13x = 10 + 6y
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<h2>
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We can solve for x or solve for y,
for x
y+6=5x
divide both sides by 5

=x
for y
y+6=5x
minus 6 from both sides
y=5x-6
Answer: x = 5
Step-by-step explanation:
The area of a rectangle is the length times the width. Since the dimensions are given as functions of x, youre going to have to use FOIL to combine them, then set that answer equal to the given value of 72.
l*w = (x+3)*(x+4) = x^2 + 7x +12 = 72
Subtract 72 on both sides. There is a reason why we'll do this instead of subtracting 12. The quadratic formula will help us to solve for x.
x^2 + 7x - 60 = 0
Apply the quadratic formula

We cant have a negative x value because that would result in negative dimensions and a negative area, which is impossible in this context. So you want to add the 17 instead of subtracting it.
x = 5 and x = -12
An alternate way is just factoring the trinomial to:
(x+12)(x-5) = 0
Answer:
Yes, there is enough evidence to say the proportions are the same.
Step-by-step explanation:
Null hypothesis: The proportions are the same.
Alternate hypothesis: The proportions are not the same.
Data given:
p1 = 51% = 0.51
n1 = 200
p2 = 48% = 0.48
n2 = 150
pooled proportion (p) = (n1p1 + n2p2) ÷ (n1 + n2) = (200×0.51 + 150×0.48) ÷ (200 + 150) = 174 ÷ 350 = 0.497
Test statistic (z) = (p1 - p2) ÷ sqrt[p(1-p)(1/n1 + 1/n2) = (0.51 - 0.48) ÷ sqrt[0.497(1-0.497)(1/200 + 1/150)] = 0.03 ÷ 0.054 = 0.556
The test is a two-tailed test. At 0.10 significance level the critical values -1.645 and 1.645
Conclusion:
Fail to reject the null hypothesis because the test statistic 0.556 falls within the region bounded by the critical values.
Answer:
your answer would be .
Step-by-step explanation:
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