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.
Answer:
cos(F) = 9/41
Step-by-step explanation:
The triangles are similar, so you know that ...
... cos(D) = cos(A) = 40/41.
From trig relations, you know ...
... cos(F) = sin(D)
and
... sin(D)² +cos(D)² = 1
So ...
... cos(F) = sin(D) = √(1 -cos(D)²) = √(1 -(40/41)²) = √(81/1681)
... cos(F) = 9/41
_____
The ratio for cos(A) tells you that you can consider AB=40, AC=41. Then, using the Pythagorean theorem, you can find BC = √(41² -40²) = √81 = 9.
From the definition of the cosine, you know cos(C) = BC/AC = 9/41. Because the triangles are similar, you know
... cos(F) = cos(C) = 9/41
Number of ways of choosing two pair of sneakers from three pairs named A, B, C is given by 3C2 (3 combination 2) = 3! / 2!(3 - 2)! = 3! / (2! x 1!) = (3 x 2) / (2 x 1) = 3.
Therefore, the sample space is given by S = {AB, AC, BC}
Answer:
<em>A) The reference angle should be </em><u><em>
,</em></u><em> and the sign of the value should be </em><u><em>negative.</em></u>
Step-by-step explanation:
cos(
)
Remove full rotations of 2π until the angle is between 0 and 2
.
cos(
)
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.
-cos()
The exact value of cos() is 
.
−
All the given points are collinear, so we have ...
AB +BC = AC
BC +CS +SD = BD
The problem statement tells us
BD = AC
BC +CS +SD = AB +BC . . . . . substituting for BD and AC
BC +CS +2 = 4 +BC . . . . . . . . substituting given lengths
CS = 2 . . . . . . . . . . . . . . . . . . . subtract (2+BC)
CS is the radius of Circle C, so its diameter is twice that: 4. The radius of Circle D is the diameter of Circle C plus SD, so is 4 +2 = 6. The diameter of Circle D is twice that: 12.
The diameter of Circle C is 4.
The diameter of Circle D is 12.
