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Ket [755]
3 years ago
7

A rectangular prism with a volume of 333 cubic units is filled with cubes with side lengths of \dfrac14 4 1 ​ start fraction, 1,

divided by, 4, end fraction unit. How many \dfrac14 4 1 ​ start fraction, 1, divided by, 4, end fraction unit cubes does it take to fill the prism?
Mathematics
2 answers:
sergey [27]3 years ago
8 0

Answer:

192 unit cubes.

Step-by-step explanation:

Let n represent number of cubes with each side 1/4 unit.

We have been given that a rectangular prism with a volume of 3 cubic units is filled with cubes with side lengths of 1/4 unit. We are asked to find the number of cubes that will fill that prism.

First of all, we will find volume of each cube.

\text{Volume of cube}=\text{Side length}^3

\text{Volume of cube}=(\frac{1}{4}\text{ unit})^3

\text{Volume of cube}=\frac{1^3}{4^3}\text{ unit}^3

\text{Volume of cube}=\frac{1}{64}\text{ unit}^3

The volume of rectangular prism will be equal to volume of n cubes.

\text{Volume of n cubes}=\text{Volume of rectangular prism}

n\times \frac{1}{64}\text{ Unit}^3=3\text{ Unit}^3

n\times \frac{1}{64}=3

n\times \frac{1}{64}\times 64=3\times 64

n=192

Therefore, it will take 192 unit cubes to fill the prism.

LekaFEV [45]3 years ago
4 0

Answer:

192 cubes

Step-by-step explanation:

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Answer:

1.0472

Step-by-step explanation:

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2 years ago
Which of the following is not true about the standard error of a statistic?
aniked [119]

Answer:

Only option d is not true

Step-by-step explanation:

Given are four statements about standard errors and we have to find which is not true.

A. The standard error measures, roughly, the average difference between the statistic and the population parameter.

-- True because population parameter is mean and the statistic are the items.  Hence the differences average would be std error.

B. The standard error is the estimated standard deviation of the sampling distribution for the statistic.

-- True the sample statistic follows a distribution with standard error as std deviation

C. The standard error can never be a negative number. -- True because we consider only positive square root of variance as std error

D. The standard error increases as the sample size(s) increases

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5 0
3 years ago
What is the value of the expression?
KengaRu [80]

Answer:

<h2>B. -3.2</h2>

Step-by-step explanation:

4\!\!\!\!\diagup^1\cdot\dfrac{-6.4}{8\!\!\!\!\diagup_2}=-\dfrac{6.4}{2}=-3.2

8 0
3 years ago
A​ hot-air balloon is 140 ft140 ft above the ground when a motorcycle​ (traveling in a straight line on a horizontal​ road) pass
luda_lava [24]

Answer:

Step-by-step explanation:

Given

Balloon velocity is 14 ft/s upwards  

Distance between balloon and cyclist is 140 ft

Velocity of motor cycle is 88 ft/s

After 10 sec  

motorcyclist traveled a distance of d_c=88\times 10=880 ft

Distance traveled by balloon in 10 s

d_b=14\times 10=140 ft

net height of balloon from ground =140+140=280 ft[/tex]

at t=10 s

distance between cyclist and balloon is z=\sqrt{280^2+880^2}

z=923.47 ft

now suppose at any time t motorcyclist cover a distance of x m and balloon is at a height of h m

thus z^2=(88t)^2+(14t+140)^2

differentiating w.r.t time

\Rightarrow z\frac{\mathrm{d} z}{\mathrm{d} t}=14\cdot \left ( 14t+140\right )+88\cdot \left ( 88t\right )

\Rightarrow at\ t=10 s

\Rightarrow \frac{\mathrm{d} z}{\mathrm{d} t}=\frac{14\cdot \left ( 14t+140\right )+88\cdot \left ( 88t\right )}{z}

\Rightarrow \frac{\mathrm{d} z}{\mathrm{d} t}=\frac{14\times 280+88^2\times 10}{923.471}

\Rightarrow \frac{\mathrm{d} z}{\mathrm{d} t}=\frac{81,360}{923.471}=88.102\ ft/s

3 0
3 years ago
Solve integral (2x-5)⁷ dx​
trapecia [35]

Answer: 128x^7dx-2240x^6dx+16800x^5dx-70000x^4dx+175000x^3dx-262500x^2dx+218750xdx-7812

Step-by-step explanation:

1) Expand : (2x-5\right)^7dxquad 128x^7dx-2240x^6dx+16800x^5dx-70000x^4dx+175000x^3dx-262500x^2dx

2) Distribute Parentheses

3) Apply your minus/plus rules

+(-a)= -a

128x^7dx-2240x^6dx+16800x^5dx-70000x^4dx+175000x^3dx-262500x^2dx+218750xdx-78125dx

4 0
3 years ago
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