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3 years ago

Emily wants to make a rectangular model with a height of one cube

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

4 0

Answer:

Three cubes

Step-by-step explanation:

The cubes have to be indistinguishable and all orientations of one cube are also have to be indistinguishable.

All ways of connecting two cubes result in the same shape. So answer is larger than two.

After connecting two cubes, there are ten faces where the third cube can be attached, and two faces which are connected, accounting for all 12 faces of two cubes.

Of the 10 exposed faces, exactly two are on opposite ends, both leading to the same straight line figure. The other 8 faces all lead to an L shape, and all L shapes can be rotated to be identical.

Hence, three cubes can only make a straight shape or an angled shape.

Four cubes can make a straight shape, a L shape, a Γ shape (but flipping it over through 3 dimensions makes L and Γ identical), a T shape, and a square shape. That is either four or five different objects depending on if they can be lifted from the table. Anyway, it is more than two.

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In the diagram below, R is located at (24,0), N is located at (12,18), T is located at (12,6), and E is located at (18,15). Assu

julsineya [31]

The midpoint of a segment divides the segment into equal halves

The coordinates of K are: $\mathbf{K = (12,12)}$
The coordinates of I are: $\mathbf{I = (24,24)}$
The coordinates of B are: $\mathbf{B = ( 30,33 )}$

The given parameters are:

$\mathbf{R =(24,0)}$

$\mathbf{N =(12,18)}$

$\mathbf{T =(12,6)}$

$\mathbf{E =(18,15)}$

K is the midpoint of N and T.

So, we have:

$\mathbf{K = (\frac{N_x + T_x}{2},\frac{N_y + T_y}{2})}$

This gives

$\mathbf{K = (\frac{12 + 12}{2},\frac{18+ 6}{2})}$

$\mathbf{K = (12,12)}$

E is the midpoint of T and I.

So, we have:

$\mathbf{E = (\frac{I_x + T_x}{2},\frac{I_y + T_y}{2})}$

This gives

$\mathbf{(18,15) = (\frac{I_x + 12}{2},\frac{I_y+ 6}{2})}$

Multiply through by 2

$\mathbf{(36,30) = (I_x + 12,I_y+ 6)}$

By comparison

$\mathbf{I_x + 12 = 36.\ I_y + 6 =30}$

So, we have:

$\mathbf{I_x= 24.\ I_y =24}$

Hence, the coordinates of I are:

$\mathbf{I = (24,24)}$

I is the midpoint of E and B.

So, we have:

$\mathbf{I = (\frac{E_x + B_x}{2},\frac{E_y + B_y}{2})}$

This gives

$\mathbf{(24,24) = (\frac{18 + B_x}{2},\frac{15 + B_y}{2})}$

Multiply through by 2

$\mathbf{(48,48) = (18 + B_x,15 + B_y)}$

By comparison

$\mathbf{18 + B_x = 48,\ 15 + B_y = 48 }$

So, we have:

$\mathbf{B_x = 30,\ B_y = 33 }$

Hence, the coordinates of B are:

$\mathbf{B = ( 30,33 )}$

Read more about midpoints at:

brainly.com/question/18068617

7 0

2 years ago

A tree casts a 25 foot shadow. At the same time of day, a 6 foot man standing near the tree casts a 9 foot shadow. What is the a

kirza4 [7]

Ratio of height of the man to the length of the shadow = 6:9 = 2:3
Ratio of height of the tree to the length of its shadow = x:25 = 2:3
x/25 = 2/3
x = (25 x 2)/3 = 50/3 = 16.67

Therefore the approximate height of the tree to the nearest foot is 17 feet.

7 0

3 years ago

Read 2 more answers

A museum conducts a survey of its visitors in order to assess the popularity of a device which

Natali5045456 [20]

Answer:

The appropriate null hypothesis is $H_0: p \geq 0.2$

The appropriate alternative hypothesis is $H_1: p < 0.2$

The p-value of the test is 0.1057 > 0.05, which means that there is not sufficient evidence that fewer than 20% of the museum visitors make use of the device, and so, it should not be withdrawn.

ii:

The p-value of the test is 0.1057

Step-by-step explanation:

Question i:

The device will be withdrawn if fewer than 20% of all of the museum’s visitors make use of it.

At the null hypothesis, we test if the proportion is of at least 20%, that is:

$H_0: p \geq 0.2$

At the alternative hypothesis, we test if the proportion is less than 20%, that is:

$H_1: p < 0.2$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.2 is tested at the null hypothesis:

This means that $\mu = 0.2, \sigma = \sqrt{0.2*0.8} = \sqrt{0.16} = 0.4$ .

The device will be withdrawn if fewer than 20% of all of the museum’s visitors make use of it. Of a random sample of 100 visitors, 15 chose to use the device.

This means that $n = 100, X = \frac{15}{100} = 0.15$

Test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.15 - 0.20}{\frac{0.4}{\sqrt{100}}}$

$z = -1.25$

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.15, which is the p-value of z = -1.25.

Looking at the z-table, z = -1.25 has a p-value of 0.1057.

The p-value of the test is 0.1057 > 0.05, which means that there is not sufficient evidence that fewer than 20% of the museum visitors make use of the device, and so, it should not be withdrawn.

Question ii:

The p-value of the test is 0.1057

7 0

3 years ago

Can someone assist me with these Algreba questions olease?

Delicious77 [7]

the answer have to be would be (-3, 1)

4 0

3 years ago

Equations that equal 12

crimeas [40]

I hope this helps you

12=3.4=3.2^2