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2 years ago

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

2 answers:

7 0

There are 4 squares having a side corresponding to a side of square abcd.

There are 4 squares having a side corresponding to the diagonals of square abcd.

And then the original square

Therefore, there are 4 + 4 + 1 = 9 squares <span>having two or more vertices in the set {a, b, c, d}.</span>

Vadim26 [7]2 years ago

7 0

Answer:

Step-by-step explanation:

There are (4 choose 2) = 6 ways to choose two points P and Q from the set of four points {A, B, C, D}. Two squares can be formed with P and Q as adjacent vertices (one on each side of PQ), and one square can be formed with P and Q as opposite vertices. This gives us 6 x 3 = 18 squares total.

However, we must subtract repeats. We see that the original square ABCD is counted 6 times, so the number of actual squares is 18 - 5 = 13.

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The mean clotting time of blood is 7.45 seconds with a standard deviation of 3.6 seconds. what is the probability that an indiv

Usimov [2.4K]

Less than 3 is about 10.75% and greater than 13 is about 6.18%.

To find these percents, you need to find the z-score for each value. Then, use your table to find the correct percent. Be sure to find the side above 13 when you use your chart.

For less than 3:
(3 - 7.45) / 3.6 = -1.24 = The percent below this is 0.1075

For greater than 13:
(13 - 7.45) / 3.6 = 1.54 = The percent above this is 0.0618

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2 years ago

The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas inter

tamaranim1 [39]

Answer:the answer is b

Step-by-step explanation:

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3 0

2 years ago

Read 2 more answers

Chris and Becky are comparing mortgages. The mortgage is for $183,500. If they choose 30 years at 5%, their monthly payment will

soldi70 [24.7K]

Answer:

For 30 years at 5% = $354,625.2

For 20 years at 4.5% = $278,618.4

Step-by-step explanation:

The total payback for each payment is given by the monthly payment multiplied by the total number of months for the payment period (years).

1) For 30 years at 5%

Total number of months in 30 years = 30 x 12 = 360 months

Payback = $985.07 x 360 = $354,625.2

2) For 20 years at 4.5%

Total number of months in 20 years = 20 x 12 = 240 months

Payback = $1160.91 x 240 = $278,618.4

5 0

2 years ago

Read 2 more answers

8. Finley has 152 yellow, red, and blue marbles in a bag. He has seven more red marbles than yellow marbles, and three times as

DochEvi [55]

Let number of yellow marbles = x

Let number of red marbles = y

Let number of blue marbles = z

Given that Finley has 152 yellow, red, and blue marbles in a bag.

So we get equation:

x+y+z=152...(i)

"He has seven more red marbles than yellow marbles" means:

y=x+7...(ii)

"three times as many blue marbles as yellow marbles." means:

z=3x...(iii)

Now we just need to solve those equations to find the answer.

Plug (ii) and (iii) into (i)

x+(x+7)+(3x)=152

x+x+7+3x=152

Which looks similar to choice (B)

5x+7=152

5x=145

x=29

Hence final answer is choice B.

Required equation is

x+x+7+3x=152

Number of yellow marbles = 29

5 0

2 years ago

A construction company is considering submitting bids for contracts of three different projects. The company estimates that it h

julsineya [31]

Answer:

a. $P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

b. $E(x) = 0.3$

c. $S(x)=0.5196$

d. $E=5,000$

Step-by-step explanation:

The probability that the company won x bids follows a binomial distribution because we have n identical and independent experiments with a probability p of success and (1-p) of fail.

So, the PMF of X is equal to:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

Where p is 0.1 and it is the chance of winning. Additionally, n is 3 and it is the number of bids. So the PMF of X is:

$P(x)=\frac{3!}{x!(3-x)!}*0.1^{x}*(1-0.1)^{n-x}\\$

For binomial distribution:

$E(x)=np\\S(x)=\sqrt{np(1-p)}$

Therefore, the company can expect to win 0.3 bids and it is calculated as:

$E(x) = np = 3*0.1 = 0.3$

Additionally, the standard deviation of the number of bids won is:

$S(x)=\sqrt{np(1-p)}=\sqrt{3(0.1)(1-0.1)}=0.5196$

Finally, the probability to won 1, 2 or 3 bids is equal to:

$P(1)=\frac{3!}{1!(3-1)!}*0.1^{1}*(1-0.1)^{3-1}=0.243\\P(2)=\frac{3!}{2!(3-2)!}*0.1^{2}*(1-0.1)^{3-2}=0.027\\P(3)=\frac{3!}{3!(3-3)!}*0.1^{3}*(1-0.1)^{3-3}=0.001$

So, the expected profit for the company is equal to:

$E=-10,000+50,000(0.243)+100,000(0.027)+150,000(0.001)\\E=5,000$

Because there is a probability of 0.243 to win one bid and it will produce 50,000 of income, there is a probability of 0.027 to win 2 bids and it will produce 100,000 of income and there is a probability of 0.001 to win 3 bids and it will produce 150,000 of income.

5 0

2 years ago