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3 years ago

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The volume of a rectangular prism is given by the formula V=lwh, where I is the length of the prism, w is the width, and h is th

e height. Which expression represents the volume of the following rectangular prism?

2 answers:

irinina [24]3 years ago

8 0

Answer:

Volume = $6x^3+39x^2+54x$

Step-by-step explanation:

Prism is an object which has two bases which are parallel to each other and other faces are parallelograms .

Rectangular prism is a three dimensional figure which has 6 faces which are all rectangles .

Let l be the length of rectangular prism , w be the width of prism and h be the height of prism .

Then volume of rectangular prism is equal to $lwh$ .

We will also use formula: $a(b+c)=ab+ac$

Here,

$l=x+2\\w=3x\\h=2x+9$

Therefore,

volume of rectangular prism is calculated as follows:

$V=\left ( x+2 \right )\left ( 3x \right )\left ( 2x+9 \right )\\=\left ( 3x^2+6x \right )\left ( 2x+9 \right )\\=3x^2\left ( 2x+9 \right )+6x\left ( 2x+9 \right )\\=6x^3+27x^2+12x^2+54x\\=6x^3+39x^2+54x$

antoniya [11.8K]3 years ago

3 0

Answer:

The answer is $6x^{3} +39x^{2}+54x$

Step-by-step explanation:

Volume of the rectangular prism = Length * Width * Height

Length (l) = $x+2$

Width (w) = $3x$

Height (h) = $2x+9$

By substituting these values to the equation above,

Volume of the rectangular prism = $(x+2)*3x*(2x+9)$

= $(3x^{2} +6x)*(2x+9)$

= $6x^{3} +27x^{2} +12x^{2} +54x$

= $6x^{3} +39x^{2}+54x$

Therefore,

The answer is $6x^{3} +39x^{2}+54x$

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The diameters of ball bearings are distributed normally. The mean diameter is 106 millimeters and the standard deviation is 4 mi

Assoli18 [71]

Answer:

Probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.

Step-by-step explanation:

We are given that the diameters of ball bearings are distributed normally. The mean diameter is 106 millimeters and the standard deviation is 4 millimeters.

<em>Firstly, Let X = diameters of ball bearings</em>

The z score probability distribution for is given by;

Z = $\frac{ X - \mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean diameter = 106 millimeters

$\sigma$ = standard deviation = 4 millimeter

Probability that the diameter of a selected bearing is greater than 111 millimeters is given by = P(X > 111 millimeters)

P(X > 111) = P( $\frac{ X - \mu}{\sigma}$ > $\frac{111-106}{4}$ ) = P(Z > 1.25) = 1 - P(Z $\leq$ 1.25)

= 1 - 0.89435 = 0.1056

Therefore, probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.

4 0

3 years ago

Graph this equation y=3sin(2x-5)

OLEGan [10]

Y = 3sin(2x - 5)
y = 3sin(2x - 5)

6 0

3 years ago

Which statement is correct?

Arisa [49]

Answer:

$2.06 \times 10^-^2 = 206$

$1.88 \times 10^-^1 = 18.8$

$206 \times 18.8 = 3,872.8$

$7.69 \times 10^-^2 = 769$

$2.3 \times 10^-^5 = 230,000$

$=\frac{769}{230000}$

= 0.00334

therefore,

3,872.80 > 0.00334

Step-by-step explanation:

Which statement is correct?

(2.06x102x1.88 x 10-1) <7.69x 10

2.3x10-5

(2.06 x 10-2)(1.88 x 10-1) 7.69x 10-

2.3x10-5

7.69 x 10"

(2.06 x 10-2x1.88x10-)>

2.3x10-5

(2.06x 10-2X(1.88x 10-1)-7.69x104

2.3x10-5

Given that;

$2.06 \times 10^-^2 = 206$

$1.88 \times 10^-^1 = 18.8$

$206 \times 18.8 = 3,872.8$

$7.69 \times 10^-^2 = 769$

$2.3 \times 10^-^5 = 230,000$

$=\frac{769}{230000}$

= 0.00334

therefore,

3,872.80 > 0.00334

7 0

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DiKsa [7]

That’s the same thing I’m on

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hoa [83]

Answer:

27,824

Step-by-step explanation:

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3 years ago

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