Answer:
18π ≈ 56.5 meters
Step-by-step explanation:
The length of the arc of a circle is given by the formula ...
s = rθ . . . . where r is the radius, and θ is the central angle in radians
<h3>Application</h3>
You are given the values of r and θ, so you only need to put them into the formula and simplify.
s = (27 m)(2π/3) = 18π m
The length of the arc is 18π meters, about 56.5 meters.
Answer:
7
Step-by-step explanation:
Let’s think about this like a number line.
If we have a number line with the ends of F and H, and G is somewhere in between, it would look something like this.
F———-G———H
We know that FH = 19 and that FG is 12.
This means that GH will be the FH - FG

So FG is 7.
Hope this helped!
Answer:
Step-by-step explanation:
Hello!
Given the linear regression of Y: "Annual salary" as a function of X: "Mean score on teaching evaluation" of a population of university professors. It is desired to study whether student evaluations are related to salaries.
The population equation line is
E(Y)= β₀ + β₁X
Using the information of a n= 100 sample, the following data was calculated:
R²= 0.23
Coefficient Standard Error
Intercept 25675.5 11393
x 5321 2119
The estimated equation is
^Y= 25675.5 + 5321X
Now if the interest is to test if the teaching evaluation affects the proffesor's annual salary, the hypotheses are:
H₀: β = 0
H₁: β ≠ 0
There are two statistic you can use to make this test, a Student's t or an ANOVA F.
Since you have information about the estimation of β you can calculate the two tailed t test using the formula:
~
= 25.1109
The p-value is two-tailed, and is the probability of getting a value as extreme as the calculated
under the distribution 
p-value < 0.00001
I hope it helps!
Answer:
x = 3.
Step-by-step explanation:
2(x + 1) + 1 = 1 - 2(x - 7)
2x + 2 + 1 = 1 - 2x + 14
4x = 1 + 14 - 2 - 1
4x = 12
x = 3.
Imagine first splitting 6 wholes up into fourths. That means that, for each whole (each 1) in 6, we're creating 4 equal slices. This gives us 4 x 6 = 24 total slices, which we call <em>fourths</em>. How many groups of <em>3 fourths </em>(3/4) can you make out of those <em>24 fourths </em>(24/4)? If we throw aside the label <em>fourths</em> for a minute, in general, if we have 24 <em>things</em>, how many groups of 3 <em>things</em> can we make out of those? Well, our answer there would just be 24 ÷ 3 = 8 groups.
The same thing applies to fourths. If we have 24/4, and we divide it by 3/4, we get 24 ÷ 3 = 8 groups again, so our answer is <em />8 3/4-pound packages.