So elimination method is basically adding the equations and canceling out variables.
-6x + 6y = 6
-6x + 3y = -12
The eaiest way to solve is by multiplying the bottom equation by -1.
-6x + 6y = 6
6x - 3y = 12
Now you add the eqautions.
3y = 18
Divde 3 from both sides.
y = 6
Now plug in 6 into any of the original two equations. Lets use the first one.
-6x + 6(6) = 6
-6x + 36 = 6
Subtract 36 from both sides.
-6x = -30
Divide -6 from both sides.
x = 5
So your solution is (5, 6).
I hope this helps love! :)
Answer:

p-value: 0.0367
Decision: Reject H₀
Step-by-step explanation:
Hello!
Hypothesis to test:
H₀:ρ₁-ρ₂=0
H₁:ρ₁-ρ₂>0
The statistic to use to test the difference between two population proportions is the approximation of Z
Z=<u> (^ρ₁-^ρ₂)-(ρ₁-ρ₂) </u> ≈N(0;1)
√ (<u>^ρ₁(1-^ρ₁))/n₁)+(^ρ₂(1-^ρ₂)/n₂))</u>
Z=<u> (0.28-0.15)-0 </u>= 1.79
√ (<u>0.28(1-0.28)/200)+(0.15(1-0.15)/300)</u>
p-value
Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
P(Z>1.79)= 0.0367
Conclusion:
Comparing the p-value against the significance level, you can decide to reject the null hypothesis.
I hope you have a SUPER day!
Answer:
.125
Step-by-step explanation:
The volume of a cube is found by
V = s^3 where s is the side length
V = .5 ^3
V =.125 m^3
The Present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt)/(r/t)
where: P is the monthly payment, r is the annual rate = 7% = 0.07, t is the number of periods in one year = 12 and n is the number of years = 3.
18,000 - 6,098 = P(1 - (1 + 0.07/12)^-(3 x 12)) / (0.07/12)
11,902 = P(1 - (1 + 0.07/12)^-36) / (0.07/12)
P = 0.07(11,902) / 12(1 - (1 + 0.07/12)^-36) = 367.50
Therefore, monthly payment = $367.50
Exponential functions are in the form

, where <em>a</em> is the initial value, <em>b</em> is the growth rate (percent increase) + 1, and <em>x</em> is the number of time periods. Our initial value is 100, and we're given the growth rate + 1 (tripling is the same as increasing by 200%; 200%=2.0; 2.0+1=3). Therefore our function is

.