If 5x+3y=12 and 4x-5y=17, what is the value of y?
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Answer:
The 95% confidence interval for the difference of means is (7.67, 16.33).
The estimate is Md = 12.
The standard error is sM_d = 2.176.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1 (this year's sales), of size n1=36 has a mean of 53 and a standard deviation of 12.
The sample 2 (last year's sales), of size n2=49 has a mean of 41 and a standard deviation of 6.
The difference between sample means is Md=12.
The estimated standard error of the difference between means is computed using the formula:
The degrees of freedom are:
The critical t-value for a 95% confidence interval and 83 degrees of fredom is t=1.989.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference of means is (7.67, 16.33).
Answer:
y = 3x + 18
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 9, - 9) and (x₂, y₂ ) = (- 6, 0)
m = =
= 3, thus
y = 3x + c ← is the partial equation of the line
To find c substitute either of the 2 points into the partial equation
Using (- 6, 0), then
0 = - 18 + c ⇒ c = 0 + 18 = 18
y = 3x + 18 ← equation of line