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11 days ago

$abcd$ is a square. how many squares have two or more vertices in the set $\{a, b, c, d\}$?

Mathematics

2 answers:

AnnZ [9K]11 days ago

7 0

Response:

Detailed explanation:

There are (4 choose 2) = 6 methods to select two points P and Q from the group of four points {A, B, C, D}. With P and Q as adjacent vertices, two squares can be constructed (one next to each side of PQ), and one square can be formed with P and Q acting as opposite vertices. This results in a total of 6 x 3 = 18 squares.

Nevertheless, we need to exclude duplicates. The original square ABCD was counted 6 times, which leads to a final count of actual squares being 18 - 5 = 13.

PIT_PIT [9.1K]11 days ago

7 0

There are four squares whose sides match one of the sides of square abcd.

Additionally, there are four squares that have sides corresponding to the diagonals of square abcd.

Finally, consider the original square

Thus, we have 4 + 4 + 1 = 9 squares <span>that contain at least two vertices within the set {a, b, c, d}.</span>

You might be interested in

A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn w

Zina [9171]

Answer:

The number of standard deviations above the mean is $z_o = 1.4607$

Step-by-step explanation:

The question indicates that:

The average weight of the corn ears from each farm is $\mu=1.26$

The standard deviation for the corn ears from Iowa is $\sigma_1$

The standard deviation for the corn ears from Ohio is

$\sigma_2= 0.01 + \sigma_1$

A randomly chosen ear of corn from Iowa weighs x = 1.39 pounds

The standardized score is z = 1.645

The weight of a randomly chosen ear of corn from Ohio measures $x_1 = 1.39\ pound$

In general, the standardized score of corn weight from Iowa can be mathematically defined as:

$z = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $1.645 = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $\sigma_1 = \frac{ 1.39 - 1.26 }{ 1.64 5}$

=> $\sigma_1 = 0.0790$

Conversely, the standardized score of corn weight from Ohio is expressed as:

$z_o = \frac{ 1.39 - 1.26 }{\sigma_2 }$

=> $z_o= \frac{ 1.39 - 1.26 }{0.01 + \sigma_1 }$

=> $z_o = \frac{ 1.39 - 1.26 }{ 0.089}$

=> $z_o = 1.4607$

A positive value indicates this quantity represents the number of standard deviations above the mean.

4 0

1 month ago

Problem 8-4 A computer time-sharing system receives teleport inquiries at an average rate of .1 per millisecond. Find the probab

Svet_ta [9500]

Response: a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318

Detailed explanation:

In Problem 8-4, the computer time-sharing system experiences teleport inquiries at an average rate of 0.1 per millisecond. We are tasked with determining the probabilities of the inquiries over a specific period of 50 milliseconds:

Given that

$\lambda=0.1\ per\ millisecond=5\ per\ 50\ millisecond=5$

Applying the Poisson process, we find that

(a) at most 12

probability= $P(X\leq 12)=\sum _{k=0}^{12}\dfrac{e^{-5}(-5)^k}{k!}=0.9980$

(b) exactly 13

probability= $P(X=13)=\dfrac{e^{-5}(-5)^{13}}{13!}=0.0013$

probability= $P(X>12)=\sum _{k=13}^{50}\dfrac{e^{-5}.(-5)^k}{k!}=0.0020$

(d) exactly 20

probability= $P(X=20)=\dfrac{e^{-5}(-5)^{20}}{20!}=0.00000026$

(e) within the range of 10 to 15, inclusive

probability= $P(10\leq X\leq 15)=\sum _{k=10}^{15}\dfrac{e^{-5}(-5)^k}{k!}=0.0318$

Thus, a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318

6 0

17 days ago

Solve y=3bx-7x for x

AnnZ [9099]

Y = 3bx - 7x
y = x(3b - 7)

Assuming 3b - 7 ≠ 0, divide both sides by 3b - 7.
$\frac{y}{3b-7} =x$

Solution:
$x= \frac{y}{3b-7}$

6 0

1 month ago

a video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game to

PIT_PIT [9117]

The slope equals $0.10 (since $1.00 per 10 tokens translates to $0.10 per token)

The y-intercept is $60 (the fixed yearly membership fee)

The linear equation is y = 0.10x + 60 (following y = mx + b)

The domain consists of all x values where x ≥ 0 (negative token quantities are impossible)

The range includes all y values with y ≥ 60 (plugging the domain values into the function)

The y-intercept of this function stands at $60

6 0

1 month ago

Read 2 more answers

Given matrix A below, and that A = B, find the value of the elements in B. A = 9 −2 3 2 17 0 3 22 8 b11 = b12 = b13 = b21 = b22

Svet_ta [9500]

Answer:

$b_{11}=9,b_{12}=-2,b_{13}=3,b_{21}=2,b_{22}=17,b_{23}=0,b_{31}=3,b_{32}=22,b_{33}=8$

Step-by-step explanation:

Review the provided matrix

$A=\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right]$

Let matrix B be defined as

$B=\left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{array}\right]$

It is stated that

$A=B$

$\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right]=\left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{array}\right]$

By comparing the corresponding elements from both matrices, we derive

$b_{11}=9,b_{12}=-2,b_{13}=3$

$b_{21}=2,b_{22}=17,b_{23}=0$

$b_{31}=3,b_{32}=22,b_{33}=8$

Consequently, the needed values are $b_{11}=9,b_{12}=-2,b_{13}=3,b_{21}=2,b_{22}=17,b_{23}=0,b_{31}=3,b_{32}=22,b_{33}=8$ .

3 0

1 month ago

Read 2 more answers