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kherson [118]
2 years ago
3

Again, the quarterback throws the football, but this time the model y = –16x2 + 35x + 6.5 describes the height (y), in feet, of

the football x seconds after it is thrown. If the ball is not caught, how long will it be in the air?
Mathematics
2 answers:
Aneli [31]2 years ago
7 0

Answer:

Last option

Step-by-step explanation:

soldi70 [24.7K]2 years ago
5 0
The model is:y = - 16 x² + 35 x + 6.5At  x = 0; y ( 0 ) = 6.5 ft.We have to find the zeroes of the parabola:x 1/2 = ( - 35 +/- √(35² - 4 · ( -16 ) · 6.5 ) ) / ( - 32 ) = = ( - 35 */- √1641 ) / ( - 32 ) = = ( - 35 +/- 40.5 ) / ( - 32 ) x 1 = - 0.17x 2 = 2.36The ball will be in the air from x = 0 s  to x = 2.36 s.Answer: 2.36 s.

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A sociologist wants to determine if the life expectancy of people in africa is less than the life expectancy of people in asia.
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Answer:

The sample statistics are attached.

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The alternative hypothesis should be: H_{a}: u_{africa}

The next step is about calculating the<em> t statistics </em>based on the samples. This <em>t test </em>will give the probability value or p-value, which determines if there's enough to reject the null hypothesis. The formula we need to use to find the t-value is: t=\frac{x_{1}-x_{2}  }{\sqrt{\frac{s_{1} ^{2} }{n_{1} } +\frac{s_{2} ^{2} }{n_{2} } } }

Replacing all the values into the formula, we have:

t=\frac{52.4-58.1}{\sqrt{\frac{(7.4)^{2} }{45}+\frac{(8.8)^{2} }{35}  } } \\t=\frac{-5.7}{\sqrt{1.2+2.2} } =\frac{-5.7}{1.8} =-3.2

Therefore, the t-value is -3.2.

Now, we using a level of significance of 0.01, and a degree of freedom (df) of 34, we use the t-table to find the p-value for this results. (df = N -1; in this case, we take the smaller sample, which is 35, giving us 34 of df).

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<em></em>

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Step-by-step explanation:

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soldi70 [24.7K]

Answer:   8 (Pi - sqrt(3))

Discussion:

The area of the shaded region is that of the semicircle minus the area of the triangle..

Area of semicircle = 1/2 * Pi * R^2        

   Where R^2 is the square of the radius of the circle. In our case, R ( = OC)

    = 4 so the semicircle area is

   (1/2) * Pi * (4^2) = (1/2) * Pi * 16 = 8 Pi

Area of triangle.

  First of all, angle ACB is a right angle ( i.e. 90 degrees).

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 so by Pythagoras

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Substituting these in Pythagoras gives

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We are almost done! The area of the triangle is given by

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We conclude the area area of the shaded part is

 8 PI - 8 sqrt(3)   = 8 (Pi - sqrt(3))

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