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A hollow metallic cylinder is made from a metallic sheet of 2.4 cm thickness. The inner

butalik [34]

Answer:

The volume of the metal used is 5277.9 cm³.

Step-by-step explanation:

The volume of a cylinder is given by:

$V = \pi r^{2} h$

Where:

r: is the radius

h: is the height = 50 cm

The volume of metal ( $V_{m}$ ) can be found by subtracting the internal volume ( $V_{i}$ ) from the external volume ( $V_{e}$ ):

$V_{m} = V_{e} - V_{i}$

$V_{m} = \pi r_{e}^{2} h - \pi r_{i}^{2} h$

The external radius is given by the sum of the internal radius with the tickness:

$r_{e} = t + r_{i}$

Hence, the volume is:

$V_{m} = \pi*50 cm((2.4 cm + 5.8 cm)^{2} - (5.8 cm)^{2}) = 5277.9 cm^{3}$

Therefore, the volume of the metal used is 5277.9 cm³.

I hope it helps you!

4 0

3 years ago

Martha works at a small jewelry store. She designed 2 rings in the furst hour. Every additional hour, she designs 3 new rings.

andrey2020 [161]

So should be it is 53

4 0

3 years ago

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Stefans bikes renta bikes for $20 plus $7 per hour. shawna paid $69 to rent a bike. for how many hours did she rent the bike?

Katarina [22]

Answer:

7 hours

Step-by-step explanation:

First you subtract 20 from 69, as the starting fee. That leaves you with 49. 49/7 = 7 hours

4 0

3 years ago

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The average high-density lipoprotein (HDL) cholesterol level of adult females is 53 milligrams per deciliter. You want to determ

emmasim [6.3K]

Answer:

$t=\frac{54.1-53}{\frac{1.78}{\sqrt{12}}}=2.14$

$df = n-1= 12-1=11$

$p_v = P(t_{11}>2.14) =0.0278$

Step-by-step explanation:

Data provided

$\bar X=54.1$ represent the sample mean in mg per deciliter of cholesterol level

$s=1.78$ represent the sample standard deviation

$n=12$ sample size

$\mu_o =53$ represent the value that we want to test

t would represent the statistic (variable of interest)

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

System of hypothesis

We need to conduct a hypothesis in order to check if the mean is higher than 53 mg per deciliter, the system of hypothesis would be:

Null hypothesis: $\mu \leq 53$

Alternative hypothesis: $\mu > 53$

The statistic is given by:

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

Calculate the statistic

Replacing into the formula we got:

$t=\frac{54.1-53}{\frac{1.78}{\sqrt{12}}}=2.14$

P-value

We need to find first the degrees of freedom:

$df = n-1= 12-1=11$

The p value for this case since we have a right tailed test is:

$p_v = P(t_{11}>2.14) =0.0278$

6 0

3 years ago

Write this in y=ax^2+b form:<br><br> y=(x-5)^2 - 2

MrMuchimi

Expand (x - 5)^2

(x - 5)^2 = (x - 5)(x - 5)

Multiply all the terms in the first parenthesis to all the terms in the 2nd:

x * x = x^2
x * -5 = -5x
-5 * x = -5x
-5 * -5 = 25

So we have:

x^2 - 5x - 5x + 25

Combine like terms:

x^2 - 10x + 25

Plug it back in:

y = (x - 5)^2 - 2

y = x^2 - 10x + 25 - 2

Combine like terms:

y = x^2 - 10x + 23

3 0

3 years ago

Read 2 more answers