Answer:
The 90% confidence interval is (493.1903, 550.2097), and the critical value to construct the confidence interval is 2.0150
Step-by-step explanation:
Let X be the random variable that represents a measurement of helium gas detected in the waste disposal facility. We have observed n = 6 values, 
= 521.7 and S = 31.6368. We will use
as the pivotal quantity. T has a 
distribution with 5 degrees of freedom. Then, as we want a 90% confidence interval for the mean level of helium gas present in the facility, we should find the 5th quantile of the t distribution with 5 degrees of freedom, i.e., 
, this value is -2.0150. Therefore the 90% confidence interval is given by
, i.e.,
(493.1903, 550.2097)
To find the 5th quantile of the t distribution with 5 degrees of freedom, you can use a table from a book or the next instruction in the R statistical programming language
qt(0.05, df = 5)
Answer:
1) 3
2) 1
3) -5
Step-by-step explanation:
The coefficients are the numbers that come before each variable.
The 3 in the first term is in front of the x^2; so the coefficient is 3.
There is no visible number in front of the y in the second term, but there is a y, so we can assume there's at least 1; so the coefficient is 1.
The term in front of x for the third term is -5, so the coefficient is -5.
30
−
(
2
3
)
(
x
3
)
=
30
+
−
8
x
3
=
−
8
x
3
+
30
Answer:
The answers are that a = -5 and b = 1
Step-by-step explanation:
In order to find A and B, we first need to find the equation of the line. We can do this by using two ordered pairs and the slope formula. For the purpose of this activity, I'l use (0, 5) and (-3, 11)
m(slope) = (y2 - y1)/(x2 - x1)
m = (11 - 5)/(-3 - 0)
m = 6/-3
m = -2
Now that we have this we can model this using point-slope form.
y - y1 = m(x - x1)
y - 5 = -2(x - 0)
y - 5 = -2x
y = -2x + 5
Now that we have the modeled equation we can use the ordered pair (a, 15) to solve for a.
y = -2x + 5
15 = -2(a) + 5
10 = -2a
-5 = a
And we can also solve for b using the ordered pair (2, b)
y = -2x + 5
b = -2(2) + 5
b = -4 + 5
b = 1
