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KATRIN_1 [288]
3 years ago
12

A rectangular prism has a length of 6cm width of 3cm and a height of 4 1/2 cm.

Mathematics
2 answers:
lapo4ka [179]3 years ago
6 0

I guess it's <br />40.5 hope soo

balu736 [363]3 years ago
6 0

Answer:

To fill the rectangular prism, 648 cubes are needed.

Step-by-step explanation:

It is given that a rectangular prism has a length of 6 cm width of 3 cm and a height of 4 1/2 cm.

The volume of a rectangular prism is

V=length\times breadth \times height

V_1=6\times 3 \times 4\frac{1}{2}

V_1=18 \times \frac{9}{2}

V_1=81

The volume of rectangular prism is 81 cm³.

The volume of a cube is

V=a^3

Where a is the side length.

The volume of a cube with edge 1/2.

V_2=(\frac{1}{2})^3

V_2=0.125

To fill the rectangular prism, the required number of cubes is

n=\frac{V_1}{V_2}

n=\frac{81}{0.125}

n=648

Therefore, to fill the rectangular prism, 648 cubes are needed.

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I want to buy a car that cost 36,718 I also have a 9% sales tax to keep in mind
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How do you calculate it? You start by expressing the density in the units you have. Then you multiply by appropriate conversion factors to get to the units you want. Treat units as though they were any other variable. A value cancels that appears in both the numerator and denominator of a fraction.

\dfrac{56.15\,kg}{0.222\,hh}\cdot \dfrac{1000\,g}{1\,kg}\cdot \dfrac{1\,pw}{1.55\,g}\cdot \dfrac{1\,hh}{238.5\,L}\cdot \dfrac{9.091\,L}{1\,pk}\\\\=\dfrac{56.15\cdot 1000\cdot 9.091\,pw}{0.222\cdot 1.55\cdot 238.5\,pk}\\\\ \approx6220\,\frac{pw}{pk}
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3 years ago
Translate the following phrase to a mathematical expression: a number times fifteen.
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Read 2 more answers
A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations alon
melamori03 [73]

Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.  

X~ Uniform(0,100)

Then the probability mass function is given as follows.

f(x) = P(X=x) = 1/100  \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0  \,\,\,\, \text{otherwise}

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located  70 meters away from city A then the mid point between 20 and 70  is (70+20)/2 = 45 then we can represent D as follows

D(x) =\left\{ \begin{array}{ll}  x  & \mbox{if } 0\leq x \leq 20 \\  x-20 & \mbox{if } 20\leq x < 45\\                70-x & \mbox{if } 45 \leq x \leq 70\\                x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable Y = D(X), Y is a random variable as well, remember that there is a theorem that says that

E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx

Where f(x) is the probability mass function of X. Using the information of our problem

E[Y] = \int\limits_{-\infty}^{\infty}  D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx  \bigg]\\= \frac{51}{4} = 12.75

3 0
3 years ago
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