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allochka39001 [22]
2 years ago
13

A bird flies up and then down again, approximately following the

Mathematics
1 answer:
BaLLatris [955]2 years ago
4 0

Answer:

  • 112.5 ft

Step-by-step explanation:

The maximum is achieved at vertex of parabola.

The x- coordinate of the vertex is determined by x = - b/(2a).

  • x = - 15/(-0.5*2) = 15

The maximum height is the corresponding y- coordinate

  • y = - 0.5(15²) + 15(15) = 112.5 ft
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A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specime
MrRissso [65]

Answer:

We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.

We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.

Step-by-step explanation:

We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;

1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.

Let \mu = <u><em>true average percentage of organic matter</em></u>

So, Null Hypothesis, H_0 : \mu = 3%      {means that the true average percentage of organic matter in such soil is 3%}

Alternate Hypothesis, H_A : \mu \neq 3%      {means that the true average percentage of organic matter in such soil is something other than 3%}

The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;

                         T.S.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean percentage of organic matter = 2.481%

             s = sample standard deviation = 1.616%

            n = sample of soil specimens = 30

So, <u><em>the test statistics</em></u> =  \frac{2.481-3}{\frac{1.616}{\sqrt{30} } }  ~ t_2_9

                                     =  -1.76

The value of t-test statistics is -1.76.

(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we have <u><em>sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.

(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have <u><em>insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.

8 0
3 years ago
When dividing 918 by 4.2, what number should the divisor be multiplied by in order to make it a whole number?
Alexandra [31]
B. Because the divisor, 4.2, has only value in the ones and tenths places, so we only have to multiply by 10 to get to 42, which is the whole number you need.
8 0
3 years ago
Read 2 more answers
State the open intervals over which the function is (a) increasing, (b) decreasing or (c) constant
ipn [44]

Answer:

a. [-3, 4]

b. (-inf, -3]

c. [4, inf)

Step-by-step explanation:

Our intervals will represent the x-values

We know that since there's an arrow pointing to the left of the line that it goes on infinitely

Same thing when the arrow is going to the right

Then we can just looking at the x-values on the graph for the intervals where it starts and stops

Hope this helps

Best of luck

3 0
2 years ago
The sales tax in the town where Amanda lives is 8%. Amanda paid $40 in sales tax on a new stereo. What was the price of the ster
dusya [7]
$500, 40 divided by 8=5, 5x100= 500
6 0
2 years ago
In which picture is point A at 34?
tekilochka [14]
There’s no picture..
5 0
3 years ago
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