Compare. Select >, <, or = to make the sentence true.
2 pounds 14 ounces 44 ounces
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What is the reciprocal of
10/9
?
The reciprocal of 10/9 is 9/10.
A grocery store keeps 5 different types of stew in stock. If 4 types of stew are to be included in a special display, in how many different orders can 4 stews be selected and lined up?
orders
The number of ways to select and line up 4 stews out of 5 is given by the permutation formula:
P(5,4) = 5! / (5-4)! = 5! / 1! = 120
Therefore, there are 120 different orders in which 4 stews can be selected and lined up.
Find the equation for the least squares regression line of the data described below.
Colin is a PR agent for an up-and-coming band. He wants to convince the band members that being active on social media is good for their careers. He claims that a large social media following typically translates into ticket sales. To prove his point, Colin looked up information about several successful bands.
He compared the number of social media followers (in millions), x, to the average number of hours it takes these bands to sell out a concert, y.
Followers (in millions) Hours
1.29 162
1.54 165
4.83 126
6.39 129
9.14 113
Round your answers to the nearest thousandth.
y=
x+
Using the least squares regression method, we need to find the equation of a line of the form y = mx + b that best fits the given data. To do this, we need to find the slope (m) and y-intercept (b) of the line.
First, we need to find the means of x and y, denoted by x̄ and ȳ, respectively:
x̄ = (1.29 + 1.54 + 4.83 + 6.39 + 9.14) / 5 ≈ 4.038
ȳ = (162 + 165 + 126 + 129 + 113) / 5 ≈ 139
Next, we need to calculate the deviations of x and y from their respective means:
xi - x̄ yi - ȳ
---------------- -
1.29 - 4.038 162 - 139
1.54 - 4.038 165 - 139
4.83 - 4.038 126 - 139
6.39 - 4.038 129 - 139
9.14 - 4.038 113 - 139
Simplifying the expressions, we get:
xi - x̄ yi - ȳ
----------------- -
-2.748 23
-2.498 26
0.792 -13
2.352 -10
5.102 -26
Next, we need to calculate the product of the deviations for each pair of data points:
(xi - x̄)(yi - ȳ)
-----------------
-63.204
-64.948
-10.296
-23.520
132.452
Using the sum of these products and the sum of the deviations for x, denoted by Σxi and Σyi, respectively, we can find the slope of the regression line:
m = Σ(xi - x̄)(yi - ȳ) / Σ(xi - x̄)²
= (-63.204 - 64.948 - 10.296 - 23.520 + 132.452) / [(1.29 - 4.038)² + (1.54 - 4.038)² + (4.83 - 4.038)² + (6.39 - 4.038)² + (9.14 - 4.038)²]
≈ -8.655
Finally, we can find the y-intercept by substituting the means of x and y, along with our calculated slope, into the equation y = mx + b and solving for b:
139 = (-8.655)(4.038) + b
b ≈ 172.331
Thus, the equation of the least squares regression line is:
y ≈ -8.655x + 172.331
Therefore, Colin can use the equation y ≈ -8.655x + 172.331 to convince the band members that having a social media following typically translates into ticket sales.