9514 1404 393
Answer:
(c) dZ/dt = 11/√544, so moving away at about 0.47 m/s
Step-by-step explanation:
The (x, y) coordinates of the car are related by the fact that they are on a circle centered at (12, 7) with a radius of 5. Then their rates of change are related by the derivative of the circle equation with respect to time.
(x -12)^2 + (y -7)^2 = 25
2(x -12)x' +2(y -7)y' = 0
y' = -(x -12)/(y -7)x'
At the time and point of interest, we have ...
y' = -(15 -12)/(11 -7)(1) = -3/4
__
The distance (z) to the observer is given by the Pythagorean theorem:
z^2 = (x -0)^2 +(y -2)^2
and its rate of change with time is ...
2z·z' = 2(x-0)x' +2(y -2)y'
The distance d at the point of interest is ...
z = √((15 -0)^2 +(11 -2)^2) = √(225 +81) = √306 = 3√34
So, the rate of change of distance to the observer at the time and point of interest is ...
z' = (x(x') +(y -2)y')/z
z' = ((15)(1) +(11-2)(-3/4))/(3√34) = (33/4)/(3√34)
z' = 11/√544 ≈ 0.47 . . . m/s
Answer:
£199.95
Step-by-step explanation:
100% - 69% = 31%
31% of £645
= 31/100 × £645
= 0.31 × £645
= £199.95
= £199.95 is the final answer as it cannot be rounded off to 2 DP.
Answer:
1) = 9³
2) = 4*4*4*4*4
= 4 to the fifth power
Step-by-step explanation:
Answer:
x = 4
Step-by-step explanation:
Step 1: Write equation
9x - 8(x - 6) = 52
Step 2: Solve for <em>x</em>
- Distribute -8: 9x - 8x + 48 = 52
- Combine like terms: x + 48 = 52
- Subtract 48 on both sides: x = 4
Step 3: Check
<em>Plug in x to verify it's a solution.</em>
9(4) - 8(4 - 6) = 52
36 - 8(-2) = 52
36 + 16 = 52
52 = 52
Answer:
a)Null hypothesis:
Alternative hypothesis:
b) A Type of error I is reject the hypothesis that 
is equal to 40 when is fact ![\mu is equal to 40c) We can commit a Type II Error, since by definition "A type II error is the non-rejection of a false null hypothesis and is known as "false negative" conclusion"Step-by-step explanation:Assuming this problem: "Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, [tex]\mu](https://tex.z-dn.net/?f=%5Cmu%20is%20%3Cstrong%3Eequal%20to%2040%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3Ec%29%20We%20can%20commit%20a%20Type%20II%20Error%2C%20since%20by%20definition%20%22A%20type%20II%20error%20is%20the%20non-rejection%20of%20a%20false%20null%20hypothesis%20and%20is%20known%20as%20%22false%20negative%22%20conclusion%22%3C%2Fp%3E%3Cp%3E%3Cstrong%3EStep-by-step%20explanation%3A%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3EAssuming%20this%20problem%3A%3C%2Fstrong%3E%20%22Some%20college%20graduates%20employed%20full-time%20work%20more%20than%2040%20hours%20per%20week%2C%20and%20some%20work%20fewer%20than%2040%20hours%20per%20week.%20We%20suspect%20that%20the%20mean%20number%20of%20hours%20worked%20per%20week%20by%20college%20graduates%2C%20%5Btex%5D%5Cmu)
, is different from 40 hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is 43 hours and that the standard deviation is 4 hours. Based on this information, answer the questions below"
Data given
represent the sample mean
population mean (variable of interest)
s=4 represent the sample standard deviation
n represent the sample size
Part a: System of hypothesis
We need to conduct a hypothesis in order to determine if actual mean is different from 40 , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Part b
In th context of this tes, what is a Type I error?
A Type of error I is reject the hypothesis that is equal to 40 when is fact [tex]\mu is equal to 40
Part c
Suppose that we decide not to reject the null hypothesis. What sort of error might we be making.
We can commit a Type II Error, since by definition "A type II error is the non-rejection of a false null hypothesis and is known as "false negative" conclusion"
