When solving the system of equations by graphing, what is the solution of 3x + 2y = 2 and 2x – y=6?
1 answer:
Answer:
answer B: (2,-2)
Step-by-step explanation:
First, write the equations on top of each other:
Then, multiply the the second equation by 2 so that we can use elimination of the y-variable:
Next, use elimination to find the value of "x":
So, your x-value is 2.
Now, substitute your x-value into one of your equations, let's take the second equation, 2x-y=6:
Your y-value is -2.
With all your information gathered, you find that the solution to this system of equation is (2,-2).
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Answer:
A) Null hypothesis;H0: μ ≥ 7
Alternative Hypothesis;Ha: μ < 7
B) t ≈ -1.75
C) 0.025 ≤ p-value < 0.05
D) Do not reject H0 since the p-value is greater than α
E) There is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
Step-by-step explanation:
We are given;
Population mean;μ = 7
Sample mean; x' = 6.7
Sample Standard deviation; s = 2.1
Level of significance; α = 0.01
Sample size; n = 150
A) Now, the hypotheses can be stated as;
Null hypothesis;H0: μ ≥ 7
Alternative Hypothesis;Ha: μ < 7
B) The test statistic will be calculated from the formula;
t = (x' - μ)/(s/√n)
Plugging in the relevant values, we have;
t = (6.7 - 7)/(2.1/√150)
t = -0.3/0.1715
t = -1.7493
t ≈ -1.75
C) From online p-value from t-score calculator attached using t-score of -1.75; DF = 150 - 1 = 149; significance level of 0.01 and one tail, we have;
The p-value = 0.041088
The closest answer among the options is;
0.025 ≤ p-value < 0.05
D) Since the p-value is greater than the significance level of 0.01, thus we will fail to reject the null hypothesis
E) From D above, we will conclude that there is insufficient evidence to suggest that Americans sleep less than the recommended 7 hours of sleep.
