Alan, Bill, and Calvin are playing a game with collectible cards. At the moment, Alan has 11 less than 2 1/2 times the number of
cards Bill has. Calvin has 1 more than 1 1/2 times the number of cards Bill has. If Alan and Calvin have the same number of cards, the number of cards Bill has is ______ . The number of cards Alan and Calvin each have is _____ . If Alan, Bill, and Calvin have all the cards in the deck, then the deck has ____ cards.
1 answer:
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Answer:
The height of the arch at its center is 250/9 or about 27.78 feet.
Step-by-step explanation:
We can write an equation to model the parabolic arch.
Let the left-most point of the arch be the origin (0, 0).
Since the bridge has a span of 100 feet, the right-most point must be (0, 100).
We can use the factored form of a quadratic:
Where <em>p</em> and <em>q</em> are the <em>x-</em>intercepts.
Our <em>x-</em>intercepts are <em>x </em>= 0 and <em>x </em>= 100. Hence:
At a point 40 feet from the center, the height of the arch is 10 feet.
The center is <em>x</em> = 50. So, a point 40 feet from the center can be either <em>x</em> = 10 or <em>x</em> = 90.
So, for instance, when <em>x</em> = 10, <em>y</em> = 10. Substitute and solve for <em>a: </em>
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So:
The same value will result if we let <em>x</em> = 90 and <em>y</em> = 10.
Hence, our equation is:
The height of the arch at its center will be when <em>x</em> = 50. Hence:
Answer:
The 95% confidence interval for the true mean resale value of a 5-year-old car of this model
(11,688.68 , 12,511.32)
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given sample size 'n' = 17
mean of the sample x⁻ = 12,100
Standard deviation of the sample (S) = 800
The 95% confidence interval for the true mean resale value of a 5-year-old car of this model
<u><em>Step(ii):-</em></u>
<u><em>Degrees of freedom ν =n-1 = 17-1 =16</em></u>
<u><em></em></u><u><em></em></u>
The 95% confidence interval for the true mean resale value of a 5-year-old car of this model
(12,100 - 411.32 , 12,100 + 411.32)
(11,688.68 , 12,511.32)