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2 years ago

In a data set, the proportion of items that are in a particular category is called the.

Mathematics

1 answer:

Neporo4naja [7]2 years ago

8 0

In a data set, the proportion of items that are in a particular category is called the Relative Frequency

<h3>What is Relative Frequency ?</h3>

Frequency mean how often an event can occur , an relative frequency means how many times that event will occur with respect to the total number of events.

For determining Relative frequency , we need to know the frequency for a particular event and the total number of event.

The proportion of items that are in a particular category is called the <u>Relative Frequency</u>.

To know more about Relative Frequency

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A tv originally cost 400$ how much is the final cost of the tv if the sales tax is 8%

weeeeeb [17]

Multiply 400 by 8% and add it to 400:

400 x 0.08 = 32

400 + 32 = 432

Answer: $432

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3 years ago

An item is priced at $14.64. if the sales tax is 7% what does the item cost including sales tax?

Hitman42 [59]

7% of 14.64 is 1.02 est.

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3 years ago

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3 years ago

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Use a triple integral to find the volume of the tetrahedron T bounded by the planes x+2y+z=2, x=2y, x=0 and z=0

Tanzania [10]

Answer:

Volume of the Tetrahedron T = $\frac{1}{3}$

Step-by-step explanation:

As given, The tetrahedron T is bounded by the planes x + 2y + z = 2, x = 2y, x = 0, and z = 0

We have,

z = 0 and x + 2y + z = 2

⇒ z = 2 - x - 2y

∴ The limits of z are :

0 ≤ z ≤ 2 - x - 2y

Now, in the xy- plane , the equations becomes

x + 2y = 2 , x = 2y , x = 0 ( As in xy- plane , z = 0)

Firstly , we find the intersection between the lines x = 2y and x + 2y = 2

∴ we get

2y + 2y = 2

⇒4y = 2

⇒y = $\frac{2}{4} = \frac{1}{2}$ = 0.5

⇒x = 2( $\frac{1}{2}$ ) = 1

So, the intersection point is ( 1, 0.5)

As we have x = 0 and x = 1

∴ The limits of x are :

0 ≤ x ≤ 1

Also,

x = 2y

⇒y = $\frac{x}{2}$

and x + 2y = 2

⇒2y = 2 - x

⇒y = 1 - $\frac{x}{2}$

∴ The limits of y are :

$\frac{x}{2}$ ≤ y ≤ 1 - $\frac{x}{2}$

So, we get

Volume = $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}\int\limits^{2-x-2y}_{z=0} {dz} \, dy \, dx$

= $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}{[z]}\limits^{2-x-2y}_0 {} \, \, dy \, dx$

= $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}{(2-x-2y)} \, \, dy \, dx$

= $\int\limits^1_0 {[2y-xy-y^{2} ]}\limits^{1-\frac{x}{2}} _{\frac{x}{2} } {} \, \, dx$

= $\int\limits^1_0 {[2(1-\frac{x}{2} - \frac{x}{2}) -x(1-\frac{x}{2} - \frac{x}{2}) -(1-\frac{x}{2}) ^{2} + (\frac{x}{2} )^{2} ] {} \, \, dx$

= $\int\limits^1_0 {(1 - 2x + x^{2} )} \, \, dx$

= ${(x - x^{2} + \frac{x^{3}}{3} )}\limits^1_0$

= 1 - 1² + $\frac{1^{3} }{3}$ - 0 + 0 - 0

= 1 - 1 + $\frac{1 }{3}$ = $\frac{1}{3}$

So, we get

Volume = $\frac{1}{3}$

7 0

3 years ago

Find all intervals on which the graph of f(x)=(x-1)/(x+3) is concave upward

Yuliya22 [10]

To find concavity we need to find the second derivative.
Use quotient rule to find f'(x)=4/(x+3)^2
Then use chain rule to find f''(x)=-8/(x+3)^3
To find potential inflection points, we need to find all x values where the second derivative is equal to 0 or is undefined.

Set the numerator and denominator equal to 0 and solve.

(x+3)^3=0
x+3=0
x= -3

Now plug a value less than -3 and greater than -3 into the second derivative to find where the concavity is upward (positive number).

Since f''(-4) is positive, that means that f(x) is concave up on the interval (-infinity, -3).

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4 years ago