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Aleksandr-060686 [28]

3 years ago

7

A ball is thrown into the air with an initial velocity of 22 meters per second.The quadratic function h(t)=-4.9t2+22t+5.5represe

nts the height of the ball above the ground,in meters, with respect to time t,in seconds.

1 answer:

svetlana [45]3 years ago

7 0

<h3><u>Question:</u></h3>

A ball is thrown into the air with an initial velocity of 22 meters per second.

The quadratic function h(t) = -4.9t2 + 22t + 5.5 represents the height of

the ball above the ground, in meters, with respect to time t, in seconds.

Determine h(3) and explain what it represents.

<h3><u>Answer:</u></h3>

h(3) = 27.4

h(3) = 27.4 means that the ball throw into the air with an initial velocity of 22 meters per second is 27.4 meters above the ground after 3 seconds.

<h3><u>Solution:</u></h3>

The quadratic equation that represents the height of the ball above the ground, h(t), in meters, with respect to time, t, in seconds is given by:

$h(t) = -4.9t^2+22t+5.5$

To find h(3), substitute t = 3 into given quadratic equation and solve for it

Plug in t = 3 in h(t)

$h(3) = -4.9(3)^2+22(3)+5.5\\\\\text{Simplify the above expression }\\\\h(3) = -4.9 \times 9 + 66 + 5.5\\\\h(3) = -44.1+66+5.5\\\\h(3) = 27.4$

Thus h(3) = 27.4

h(3) = 27.4 means that the ball throw into the air with an initial velocity of 22 meters per second is 27.4 meters above the ground after 3 seconds.

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The Decision Rule

Fail to reject the null hypothesis

The conclusion

There is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi

Step-by-step explanation:

From the question we are told that

The data is

Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8

Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4

The level of significance $\alpha = 0.05$

Generally the null hypothesis is $H_o : \mu_1 - \mu_2 = 0$

the alternative hypothesis is $H_a : \mu_1 - \mu_2 > 0$

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=> $\= x_1 = 5.56$

Generally the standard deviation of age of cars

$\sigma _1 = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }$

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Generally the sample mean for the age of taxi is mathematically represented as

$\= x_2 = \frac{\sum x_i }{n}$

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Generally the standard deviation of age of taxi

$\sigma _2 = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }$

=> $\sigma _2 = \sqrt{\frac{(8 - 5.85)^2 + (8 - 5.85)^2+ (0 - 5.85)^2 + \cdots + 8}{ 20} }$

=> $\sigma _2 = 2.83$

Generally the test statistics is mathematically represented as

$t = \frac{(\= x_ 1 - \= x_2 ) - 0}{\sqrt{\frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2} } }$

=> $t = \frac{(5.56 - 5.85 ) - 0}{\sqrt{\frac{(3.88)^2}{27} + \frac{(2.83)}{20} }}$

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Generally the degree of freedom is mathematically represented as

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