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4 years ago

The volume of a cone is 37x3 cubic units and its height is x units.

Mathematics

1 answer:

Alla [95]4 years ago

5 0

Answer:

Step-by-step explanation:

The formula for the volume of a cone is ...

V = (π/3)r²h

Filling in the given values and solving for r, we find ...

37x³ = (π/3)r²x

(3·37/π)x² = r² . . . . . . . . divide by the coefficient of r²

x√35.3324 ≈ r ≈ 5.94x

The closest answer choice is 6x.

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Rewrite the expression as a product of two factors 4x + 8

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3 years ago

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Vlad1618 [11]

Answer:

Step-by-step explanation:

#1:

$\frac{18m^2u}{16n^3v^2} \div \frac{24m}{15nu^3}*\frac{8n^2v^3}{30m^3u}$

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#2:

$\frac{24a^2b^3c}{9bc^3}\div\frac{4a^5bc^3}{27a^3b^2c}$

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3 years ago

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Given these what is X if B-X=A

ser-zykov [4K]

Answer:

Step-by-step explanation:

B-X=A

B-A=X

X=B-A

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4 years ago

Test the null hypothesis Upper H 0 : (mu 1 minus mu 2 )equals 0H0: μ1−μ2=0 versus the alternative hypothesis Upper H Subscript a

Law Incorporation [45]

Answer:

The test statistic t is t=2.9037.

The null hypothesis is rejected.

For a significance level of 0.05, there is enough evidence to support the alternative hypothesis.

Step-by-step explanation:

The question is incomplete:

The sample 1, of size n1=25 has a mean of 1.15 and a standard deviation of 0.31.

The sample 2, of size n2=25 has a mean of 0.95 and a standard deviation of 0.15.

This is a hypothesis test for the difference between populations means.

The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is α=0.05.

The difference between sample means is Md=0.2.

$M_d=M_1-M_2=1.15-0.95=0.2$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{0.31^2+0.15^2}{25}}\\\\\\s_{M_d}=\sqrt{\dfrac{0.119}{25}}=\sqrt{0.005}=0.069$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.069}=\dfrac{0.2}{0.069}=2.9037$

The degrees of freedom for this test are:

$df=n_1+n_2-1=25+25-2=48$

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$P-value=2\cdot P(t>2.9037)=0.0056$

As the P-value (0.0056) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

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4 years ago