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Neko [114]
2 years ago
13

A waffle cone has a volume of 31.254 cubic centimeters and a radius of

Mathematics
1 answer:
arlik [135]2 years ago
5 0

Answer:

4.78 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is

V = (1/3)πr²h.  Here, V = 31.254 cm³ and r = 2.5 cm.  

We begin by solving V = (1/3)πr²h for the unknown height, h:

         31.254 cm³              3(31.254 cm³)            93.762 cm³

h = ------------------------  =  --------------------------  =  --------------------  ≈  4.78 cm

            (1/3)πr²                       π(2.5 cm)²               19.635 cm²

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Answer:

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Step-by-step explanation:

\left(\displaystyle \sqrt[3]{x^{-\tfrac 35}}\right)^{\tfrac 58}\\\\\\=\left[ \left(\displaystyle x^{-\tfrac 35} \right)^{\tfrac 13 \right]^{\tfrac 58}\\\\\\=\left( \displaystyle x^{-\tfrac 35}\right)^{\tfrac 5{24}}\\\\\\=x^{ \displaystyle -\tfrac{3}{24}  \right}\\\\\\=x^{\displaystyle -\tfrac 18  }\\\\\\=\dfrac 1{x^{\tfrac 18}}

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Use the given information to find the p​-value. ​Also, use a 0.05 significance level and state the conclusion about the null hyp
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Answer:

We can assume that the statistic is z_{calc}=0.78

p_v = 2* P(z>0.78) = 0.435

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5

Step-by-step explanation:

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 3/5 or not.:  

Null hypothesis:p=3/5  

Alternative hypothesis:p \neq 3/5  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

We can assume that the statistic is z_{calc}=0.78

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:

p_v = 2* P(z>0.78) = 0.435

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of interest is not different from 3/5

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4. Match the polynomial in the left column with its descriptive feature in the
FromTheMoon [43]

Complete question is;

Match the polynomial in the left column with its descriptive feature in the

right column

A.) x³ + 3x² - 2x + 7

B.) 3a³ b ^(6)

C.) 3x⁴ – 9x³ + 5x^(8)

D.) 7a³ b ² + 18ab² c – 9a³

E.) 2x^(5) – 9x³ + 8x^(7)

F.) 4x^(8) – 7x² + 9

G.) x² − 7

I. 9th degree monomial

II. Constant term of −7

III. 7th degree polynomial

IV. Leading coefficient of 4

V. Four terms

VI. 5th degree polynomial

VII. Equivalent to 5x^(8) + 3x⁴ – 9x³

Answer:

A) For polynomial x³ + 3x² - 2x + 7 : Option V - 4 Terms

B) For polynomial 3a³ b ^(6) : option I - 9th degree monomial

C) For the polynomial 3x⁴ – 9x³ + 5x^(8) : Option VII - Equivalent to 5x^(8) + 3x⁴ – 9x³

D) For the polynomial 7a³b² + 18ab²

c – 9a³ : Option VI - 5th degree polynomial.

E) For the polynomial 2x^(5) – 9x³ + 8x^(7) : Option III - 7th degree polynomial.

F) for the polynomial 4x^(8) – 7x² + 9 : Option IV - Leading coefficient of 4

F) For the polynomial x² − 7 : Option II - Constant term of −7

Step-by-step explanation:

A) Most appropriate matching descriptive feature for the polynomial x³ + 3x² - 2x + 7 is Option V - 4 Terms

B) Most appropriate matching descriptive feature for the polynomial 3a³ b ^(6) is option I - 9th degree monomial. This is because the sum of the powers of a and b is 9.

C) Most appropriate matching descriptive feature for the polynomial 3x⁴ – 9x³ + 5x^(8) is Option VII - Equivalent to 5x^(8) + 3x⁴ – 9x³

D) Most appropriate matching descriptive feature for the polynomial 7a³ b ² + 18ab² c – 9a³ is Option VI - 5th degree polynomial. This is because the highest sum of powers attached to a and b in a figure is 2 + 3 = 5.

E) Most appropriate matching descriptive feature for the polynomial 2x^(5) – 9x³ + 8x^(7) is Option III - 7th degree polynomial. This is because the highest power of x is 7.

F) Most appropriate matching descriptive feature for the polynomial 4x^(8) – 7x² + 9 is Option IV: Leading coefficient of 4. This is because the coefficient attached to the largest power of x is 4.

G) Most appropriate matching descriptive feature for the polynomial

x² − 7 is Option II - Constant term of −7

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3 years ago
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