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Svet_ta [14]
1 year ago
10

100 POINTS

Mathematics
2 answers:
ddd [48]1 year ago
8 0

B: nine and one over two ft

Oksana_A [137]1 year ago
8 0

Answer:

The answer is B, 9 1/2

Step-by-step explanation:

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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
5 + 14 x y = 9 x y - 5
Anon25 [30]

Answer:

xy = -2

Step-by-step explanation:

To solve:

5 + 14xy = 9xy - 5

=> First subtract 9xy from each side of "="

5 + 5xy = -5

=> Now, subtract 5 from each side:

5xy = -10

=> Finally divide 5 on each side:

xy = -10/5

xy = -2

Hope this helps!

4 0
2 years ago
Read 2 more answers
A piece of cardboard measures 10 ft by 10 ft. Four equal squares of size x are removed from the corners. After removing the squa
Gnesinka [82]

Answer:

The value of x would be \frac{5}{3}

Step-by-step explanation:

Given,

The dimension of the cardboard = 10 ft by 10 ft,

∵ After removing four equal squares of size x ( in ft ) from the corners,

The dimension of the resultant box would be,

Length = ( 10 - 2x ) ft,

Width = ( 10 - 2x ) ft,

Height = x ft,

The volume of box,

V=(10-2x)\times (10 - 2x)\times x=x(10-2x)^2 = x(100 - 40x + 4x^2)=100x - 40x^2 + 4x^3

Differentiating with respect to x,

V'=100 - 80x + 12x^2

Again differentiating with respect to x,

V''=-80 + 24x

For maxima or minima,

V'=0

\implies 100 - 80x + 12x^2 = 0

\implies 3x^2 - 20x + 25=0

By quadratic formula,

x=\frac{20\pm \sqrt{20^2-4\times 3\times 25}}{6}

x=\frac{20\pm \sqrt{400 - 300}}{6}

x=\frac{20\pm \sqrt{100}}{6}

x=\frac{20\pm 10}{6}

\implies x = \frac{10}{6}=\frac{5}{3}\text{ or } x = 5

For x = 5/3, V'' = negative,

While for x = 5, V'' = Positive,

Hence, the value of x would be 5/3 ft for maximising the volume.

8 0
3 years ago
Martin uses his power saw every 15 seconds.How many times did he use it in one hour ?​
Alina [70]

Answer:

  1. 60<em><u>÷</u></em><em><u>15</u></em><em><u> </u></em><em><u>=</u></em><em><u>4</u></em><em><u> </u></em>

<em><u>Therefore</u></em><em><u> </u></em><em><u>Martin</u></em><em><u> </u></em><em><u>uses</u></em><em><u> </u></em><em><u>his</u></em><em><u> </u></em><em><u>power</u></em><em><u> </u></em><em><u>saw</u></em><em><u> </u></em><em><u>4</u></em><em><u> </u></em><em><u>times</u></em><em><u> </u></em><em><u>in</u></em><em><u> </u></em><em><u>one</u></em><em><u> </u></em><em><u>hour</u></em><em><u> </u></em>

7 0
3 years ago
Read 2 more answers
What is the value of x to the nearest tenth?
Ipatiy [6.2K]

Answer:

35

Step-by-step explanation:

4 0
2 years ago
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