Answer:
15 miles
Step-by-step explanation:
Let's say the dock is at the origin on a coordinate plane and each unit is 1 mile. If the boat travels 9 mile due north, that means that we move up from the origin (0, 0) 9 units to point A (0, 9). Now, this boat moves 12 miles due west, so we will go 12 units to the left of (0, 9) to point B (-12, 9). See the attached drawing (sorry for the crudeness).
Notice that this is a right triangle with legs of 9 and 12. That means the distance from the boat to the dock is just the hypotenuse, so use the Pythagorean Theorem: distance = 
Thus, the answer is 15 miles.
Hope this helps!
Answer:
coefficient is 1/6
Step-by-step explanation:
=-2a/3+5a/6-1/6
= a/6 -1/6
= 1/6(a -1)
coefficient is 1/6
Answer:
see explanation
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 )
here m = - 
, hence
y = - x + c ← is the partial equation
To find c substitute (- 3, - 1) into the partial equation
- 1 = 2 + c ⇒ c = - 1 - 2 = - 3
y = - x - 3 ← is the equation of the line
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 17
For the alternative hypothesis,
µ < 17
This is a left tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 80,
Degrees of freedom, df = n - 1 = 80 - 1 = 79
t = (x - µ)/(s/√n)
Where
x = sample mean = 15.6
µ = population mean = 17
s = samples standard deviation = 4.5
t = (15.6 - 17)/(4.5/√80) = - 2.78
We would determine the p value using the t test calculator. It becomes
p = 0.0034
Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.
The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
