Part A:
Significant level:
<span>α = 0.05
Null and alternative hypothesis:
</span><span>h0 : μ = 3 vs h1: μ ≠ 3
Test statistics:
P-value:
P(-0.9467) = 0.1719
Since the test is a two-tailed test, p-value = 2(0.1719) = 0.3438
Conclusion:
Since the p-value is greater than the significant level, we fail to reject the null hypothesis and conclude that there is no sufficient evidence that the true mean is different from 3.
Part B:
The power of the test is given by:
Therefore, the power of the test if </span><span>μ = 3.25 is 0.8105.
Part C:
</span>The <span>sample size that would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9 is obtained as follows:
Therefore, the </span>s<span>ample size that would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9 is 16.</span>
Answer:
The equation representing the total distance would be A. 105x + 90.
The time the truck has travelled would be 8 hours while the time traveled by the train would be 6 hours.
Step-by-step explanation:
Firstly, let's set the time travelled by the train to be x hours.
According to the question, the equation would be 45(x + 2) = 60x, because the truck has travelled 2 more hours than the train.
Hence:
Therefore, the truck has travelled a total of (6 + 2) hours = 8 hours, and the train has travelled for 6 hours.
Also, the equation can be found by adding both equations up:
Hope this helped!
Answer:
x - 4 > -9 or x -4 < 9
Step-by-step explanation:
Let's see the definition of absolute value inequality.
i) If lxl < b, then -b < x < b
ii) If lxl > b, then x > b or x < -b
We are given the inequality lx - 4l<9
Here we have to use the first case.
Using the above definition of inequality, we can write the given inequality as follows:
-9 < (x - 4) < 9
So the third option is correct.
x - 4 > -9 or x -4 < 9
She bought 30 more red apples than green apples.
Susan bought 40 red apples and 10 green apples.
Hope that helps!
Answer: (f·g)(x) = -5x³ - 31x² + 62x + 18
(f·g)(-1) = -70
(fog)(x) = 25x² - 130x + 155
(fog)(-1) = 310
<u>Step-by-step explanation:</u>
f(x) = x² + 8x + 2 g(x) = -5x + 9
(f·g)(x) = (x² + 8x + 2)(-5x + 9)
= -5x³ + 9x²
- 40x² + 72x
<u> - 10x + 18</u>
= -5x³ - 31x² + 62x + 18
(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18
= -5(-1) - 31(1) - 62 + 18
= 5 - 31 - 62 + 18
= -70
****************************************************************************************
(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2
= 25x² - 90x + 81
- 40x + 72
<u> + 2</u>
= 25x² - 130x + 155
(fog)(-1) = 25(-1)² - 130(-1) + 155
= 25 + 130 + 155
= 310
<em>It wasn't clear if you wanted multiplication or composition so I solved both.</em>