A golf ball is hit in not the air represented by the equation y= -3x^2+18x+45. The maximum height the ball will reach is____ fee
1 answer:
Answer:
72 ft
Step-by-step explanation:
Here, we want to get the maximum height the ball will reach
the maximum height the ball will reach is equal to the y-coordinate of the vertex of the equation
So we need firstly, the vertex of the given quadratic equation
The vertex can be obtained by the use of plot of the graph
By doing this, we have it that the vertex is at the point (3,72)
Thus, we can conclude that the maximum height the ball can reach is 72 ft
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Answer:
a. The 95% confidence interval for the difference between means is (0.071, 0.389).
b. There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.
c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.
In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.
In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.
Step-by-step explanation:
The table with the data is:
Sample 1 Sample 2
0.580 0.382
0.711 0.276
0.571 0.570
0.666 0.366
0.598
The mean and standard deviation for sample 1 are:
The mean and standard deviation for sample 2 are:
<u>Confidence interval</u>
We have to calculate a 95% confidence interval for the difference between means.
The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.
The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.
The difference between sample means is Md=0.23.
The estimated standard error of the difference between means is computed using the formula:
The critical t-value for a 95% confidence interval is t=2.365.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference between means is (0.071, 0.389).
<u>Hypothesis test</u>
This is a hypothesis test for the difference between populations means.
The claim is that the fish in this particular polluted lake have signficantly elevated mercury levels.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.
The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.
The difference between sample means is Md=0.23.
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this test are:
This test is a right-tailed test, with 7 degrees of freedom and t=3.42, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.006) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.
<u> </u>
c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.
In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.
In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.