Lol just get a calculator and math paper. This is not cool, u aren't in college. Im in 7TH GRADE and I can do this garbage...
The answer is actually choice A
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If we add up the equations straight down we will have 0a+2b = 6
Note how adding the 'a' terms gives us 3a + (-3a) = 3a-3a = 0a. The 0a term is really 0 since 0 times anything is 0. So the 'a' terms will go away
The equation 0a+2b = 6 turns into 0+2b = 6 and that simplifies to 2b = 6
To isolate b, we divide both sides by 2
2b = 6
2b/2 = 6/2
b = 3
We can stop here since only one answer choice has b = 3, which is choice A. However, let's keep going to find the value of 'a'
Plug b = 3 into any equation with 'a' and 'b', then solve for 'a'
3a+4b = 9
3a+4*3 = 9
3a+12 = 9
3a+12-12 = 9-12
3a = -3
3a/3 = -3/3
a = -1
So a = -1 and b = 3 pair up to form (a,b) = (-1,3)
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To check, plug this ordered pair back into both equations
Equation 1:
3a+4b = 9
3*(-1)+4*3 = 9
-3+12 = 9
9 = 9
Equation 1 has been checked out
Equation 2:
-3a-2b = -3
-3(-1)-2(3) = -3
3 - 6 = -3
-3 = -3
this is true as well
So this confirms that the final answer is choice A
Positive because it is increasing
Answer:
No, because the 95% confidence interval contains the hypothesized value of zero.
Step-by-step explanation:
Hello!
You have the information regarding two calcium supplements.
X₁: Calcium content of supplement 1
n₁= 12
X[bar]₁= 1000mg
S₁= 23 mg
X₂: Calcium content of supplement 2
n₂= 15
X[bar]₂= 1016mg
S₂= 24mg
It is known that X₁~N(μ₁; σ²₁), X₂~N(μ₂;δ²₂) and σ²₁=δ²₂=?
The claim is that both supplements have the same average calcium content:
H₀: μ₁ - μ₂ = 0
H₁: μ₁ - μ₂ ≠ 0
α: 0.05
The confidence level and significance level are to be complementary, so if 1 - α: 0.95 then α:0.05
since these are two independent samples from normal populations and the population variances are equal, you have to use a pooled variance t-test to construct the interval:
[(X[bar]₁-X[bar]₂) ±
*
]


[(1000-1016)±2.060*23.57*
]
[-34.80;2.80] mg
The 95% CI contains the value under the null hypothesis: "zero", so the decision is to not reject the null hypothesis. Then using a 5% significance level you can conclude that there is no difference between the average calcium content of supplements 1 and 2.
I hope it helps!