ABCD is a rectangle. Find the length of each diagonal.AC=3(x-3)
BD=x+3

AC=___
BD=___

The probability of at most three boys in ten births is approximately 0.17139, or about 17.14%.

What is Probability?

It is a branch of mathematics that deals with the occurrence of a random event.

This is a binomial probability problem with n = 10 (number of births) and p = 0.5 (probability of a boy or a girl).

We want to find the probability of at most three boys in ten births, which is equivalent to finding the probability of 0, 1, 2, or 3 boys.

To calculate this probability, we can use the binomial probability formula:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 0.00098 + 0.00977 + 0.04395 + 0.11719

= 0.17139

Therefore, the probability of at most three boys in ten births is approximately 0.17139, or about 17.14%.

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Answer:

Step-by-step explanation:

This is a binomial distribution

The probability of at most 3 boys=

P(exactly 0 boys)+P(exactly 1 boy)+P(exactly 2 boys)+P(exactly 3 boys)

.171875

Answer:

Knowing that those vectors start at the point (0,0) we can "think" them as lines.

As you may know, two lines are parallel if the slope is the same, then we can find the "slope" of the vectors and see if it is the same.

A) the vectors are: (√3, 1) and (-√3, -1)

You may remember that the way to find the slope of a line that passes through the points (x1, y1) and (x2, y2) is s = (y2 - y1)/(x2 - x1)

Because we know that our vectors also pass through the point (0,0)

then the slopes are:

 (√3, 1) -----> s = (1/√3)

 (-√3, -1)----> s = (-1/-√3) =  (1/√3)

The slope is the same, so the vectors are parallel.

Part B:

The vectors are: (2, 3) and (-3, -2)

the slopes are:

(2, 3) -----> s = 3/2

(-3, -2)----> s = -2/-3 = 2/3

the slopes are different, so the vectors are not parallel.

∥v∥=√((6)^2+(-8)^2)=√(36+64)=√100=10. Dividing v by its magnitude, we get the unit vector u=(v/∥v∥)=(6i−8j)/10=(3/5)i−(4/5)j. Therefore, two unit vectors parallel to v are (3/5)i−(4/5)j and −(3/5)i+(4/5)j.

a. Two unit vectors parallel to v=6i−8j can be found by dividing the vector v by its magnitude. The magnitude of v can be calculated using the formula ∥v∥=√(v1^2+v2^2), where v1 and v2 are the components of v in the x and y directions, respectively. In this case, v1=6 and v2=−8. Thus,

b. To find the value of b when v=⟨1/3,b⟩ is a unit vector, we need to calculate the magnitude of v and set it equal to 1. The magnitude of v is given by ∥v∥=√((1/3)^2+b^2). Setting this equal to 1, we have √((1/3)^2+b^2)=1. Squaring both sides of the equation, we get (1/3)^2+b^2=1. Simplifying, we have 1/9+b^2=1. Rearranging the equation, we find b^2=8/9. Taking the square root of both sides, we get b=±(2√2)/3. Therefore, the value of b when v is a unit vector is b=(2√2)/3 or b=−(2√2)/3.

c. To find all values of a such that w=ai−a/3j is a unit vector, we need to calculate the magnitude of w and set it equal to 1. The magnitude of w is given by ∥w∥=√(a^2+(-a/3)^2). Setting this equal to 1, we have √(a^2+(-a/3)^2)=1. Simplifying, we get a^2+(a^2/9)=1. Combining like terms, we have (10/9)a^2=1. Dividing both sides by 10/9, we get a^2=(9/10). Taking the square root of both sides, we have a=±√(9/10). Therefore, the values of a such that w is a unit vector are a=√(9/10) or a=−√(9/10).

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Answer:

Job A - Job D - Job E - Job B - Job C

Step-by-step explanation:

Job A = 2

Job B = 10

Job C = 15

Job D = 6

Job E = 8

SJN (Shortest Job Next) is also known as Shortest Job First. In Shortest Job Next, the job with the shortest time among the available jobs is executed first then followed by the next job having the shortest time till all the jobs are finally executed.

Since all the five jobs are already in the queue: they will be processed based on the job having the shortest CPU time among the available job.

Job A will be processed first since it has smallest time of 2, followed by Job D with a time of 6, followed by Job E with a time of 8, followed by Job B with a time of 10 and finally Job C which is processed last.

Answer:

The answer is A) 6 square yards.

Answer:

4, or it could be 8 but mostly 4

Step-by-step explanation: