What is meant by the quadratic formula?

A cylinder has a volume of 360 cubic centimeters. Find the volume of a cone with the same height and diameter as the cylinder.

ratelena [41]

The formula of a volume of a cylinder:

$V_{cylinder}=\pi r^2H$

The formula of a volume of a cone:

$V_{cone}=\dfrac{1}{3}\pi r^2H$

If a cone and a cylinder have the same radius and the same height, then a volume of a cylinder is three times greater than a volume of a cone.

$V_{cylinder}=3V_{cone}\\\\V_{cone}=\dfrac{1}{3}V_{cylinder}$

$V_{cylinder}=360\ cm^3$

$V_{cone}=\dfrac{1}{3}\cdot360\ cm^3=120\ cm^3$

<h3>Answer: The volume of a cone is equal 120 cm³.</h3>

3 0

3 years ago

Nani needs to buy 8 cups of fresh pineapple for a fruit cocktail. The table shows the unit prices (per cup) of pineapple at diff

notka56 [123]

Answer:

She could purchase from stores A, D and E.

Step-by-step explanation:

She needs 8 cups so I multiplied each price by 8;

Store A 0.49(8)=$3.92

Store B 0.51(8)=$4.08

Store C 0.55(8)=$4.40

Store D 0.48(8)=$3.84

Store E 0.45(8)=$3.60

8 0

3 years ago

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A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a populat

eimsori [14]

Answer:

$t=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

$p_v =P(t_{15}>2)=0.0320$

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the true mean is significant higher than 24 years.

Step-by-step explanation:

1) Data given and notation

$\bar X=25$ represent the sample mean

$s=2$ represent the standard deviation for the sample

$n=16$ sample size

$\mu_o =24$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Confidence =0.95 or 95%

$\alpha=0.05$

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean is higher than 24, the system of hypothesis would be:

Null hypothesis: $\mu \leq 24$

Alternative hypothesis: $\mu > 24$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

Calculate the P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=16-1=15$

Since is a one-side upper test the p value would be:

$p_v =P(t_{15}>2)=0.0320$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the true mean is significant higher than 24 years.

3 0

3 years ago

A container in the shape of a rectangular prism holds 297 1/4 cubic inches of dirt. Its base has an area of 20 1/2 square inches

zubka84 [21]

Answer:

5,940 1/8 inches

Step-by-step explanation:

5,940 1/8 inches

3 0

3 years ago

Mr. Marcucci received a bonus of $496 from his employer. He has to pay 33% of his bonus to taxes. How much will Mr. Marcucci pay

tiny-mole [99]

Edit: 33% is not $\frac{1}{3}$ , therefore my solution is wrong. The correct answer is 0.33 x 496, which is $163.68

The following is the original solution, which is incorrect.
33% = $\frac{1}{3}$ . Multiply the bonus of $496 by $\frac{1}{3}$ to get the solution of $\frac{496}{3}$ , or 165 and $\frac{1}{3}$

Therefore the solution is $165.33

7 0

3 years ago

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