Using the washer method, the volume is given by the integral
where 3 - 1 = 2 is the distance from <em>y</em> = 3 to the axis of revolution, and similarly (1 + sec(<em>x</em>)) - 1 = sec(<em>x</em>) is the distance from <em>y</em> = 1 + sec(<em>x</em>) to the axis. The integrand is symmetric about <em>x</em> = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.
So the volume is
Answer:
We conclude that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.
Step-by-step explanation:
We are given that a sports statistician claim that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.
The mean winning time of a sample of 30 randomly selected Boston marathon women's open division champions is 2.60 hours. assume the population standard deviation is 0.32 hours.
<em>Let </em><em> = </em><u><em>mean winning times for Boston marathon women's open division champions.</em></u>
So, Null Hypothesis, :
2.68 hours {means that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours}
Alternate Hypothesis, : p < 2.68 hours {means that the mean winning times for Boston marathon women's open division champions is less than 2.68 hours}
The test statistics that would be used here <u>One-sample z test</u> <u>statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean winning time = 2.60 hours
= population standard deviation = 0.32 hours
n = sample of women's open division champions = 30
So, <em><u>test statistics</u></em> =
= -1.37
The value of z test statistics is -1.37.
Now, P-value of the test statistics is given by following formula;
P-value = P(Z < -1.37) = 1 - P(Z 1.37)
= 1 - 0.9147 = <u>0.0853</u>
Since, P-value of the test statistics is more than the level of significance as 0.0853 > 0.05, so <u>we have insufficient evidence to reject our null hypothesis</u> as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.
Answer:
Altogether Gavin and Jim won £95.
Step-by-step explanation:
We are given the following in the question:
Ratio of money won by Gavin and Jim = 5:2
Gavin gets £39 more than Jim.
Let x be the amount of money Won by Jim.
Then, money won by Gavin =
Thus, we can write the equation:
Solving, we get,
Thus, Gavin won £65 and Jim won £26.
Money won altogether =
Thus, altogether Gavin and Jim won £95.
Answer: D. 15
Step-by-step explanation:
Given : The revenue each season from tickets at the theme part is represented by .
The cost to pay the employees each season is represented by .
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15
We will use ratio to determine how much can Fatima afford as a loan for her house.
Let gross income of Fatima = $ x
Amount earned by Fatima monthly= $ 5,375
36 % of 5,375=
$
Maximum amount that can be paid as a loan monthly = $ 1935
Total money that she can pay yearly for house loan if Fatima allowable money for paying loans is $ 1935=
$
Money saved as a down payment = $ 15,000
So, maximum amount loan Fatima can take on a house= 23220 + 15000=$38,220
She is not allowed for loan for house if the cost of house is any of the four options.
(B) 28 % of $ 5375=
$
Maximum amount that Fatima spend on her house monthly= $ 1505
Amount that fatima can spend yearly on her house = 1505× 12 =$18,060
For the four options given , none of the option matches Fatima's expectations.