Let F = sin ( 8 x + 5 z ) i − 8 y e x z k . F=sin⁡(8x+5z)i−8yexzk. Calculate div ( F ) div(F) and curl ( F ) . and curl(F). (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Answer:

0, 14

Step-by-step explanation:

-2, is 8 away from 6, so you add 8 to 6 to reflect it and get 14

The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

This problem can be solved using the binomialdistribution since we have a fixed number of trials (selecting 25 people) and each trial has two possible outcomes (displeased or not displeased).

Let p be the probability of an individual being displeased, which is given as 0.045 (or 4.5% as a decimal).

Then, the probability of an individual not being displeased is:

1 - p = 0.955.

Let X be the number of displeasedpeople in a random sample of 25.

We want to find the probability that at least two people are displeased, which can be expressed as:

P(X ≥ 2) = 1 - P(X < 2)

To calculate P(X < 2), we can use the binomial distribution formula:

where n is the samplesize (25), k is the number of displeasedpeople, and (n choose k) is the binomial coefficient which represents the number of ways to choose k items from a set of n items.

For k = 0, we have:

≈ 0.378

For k = 1, we have:

≈ 0.42

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.798.

Finally, we can calculate,

P(X ≥ 2) = 1 - P(X < 2)

= 1 - 0.798

= 0.202.

Thus,

The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.

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Answer:

Step-by-step explanation:

The correct answer is (B).

Let X = the number of people that are displeased in a random sample of 25 people selected from a population of which 4.5% will be displeased regardless of the situation. Then X is a binomial random variable with n = 25 and p = 0.045.

P(X ≥ 2) = 1 – P(X ≤ 1) = 1 – binomcdf(n: 25, p: 0.045, x-value: 1) = 0.311.

P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)] = 1 – 0C25(0.045)0(1 – 0.045)25 – 25C1(0.045)1(1 – 0.045)24 = 0.311.

Answer:

14 pieces and 34 pieces

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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Step-by-step explanation:

If x is the kilograms of 30% chocolate, and y is the kilograms of 50% chocolate, then:

x + y = 200

0.30x + 0.50y = 0.46(200)

Solving the system of equations with substitution:

0.30x + 0.50(200 − x) = 0.46(200)

0.30x + 100 − 0.50x = 92

8 = 0.20x

x = 40

y = 200 − x

y = 160

The distributor needs 40 kg of 30% chocolate and 160 kg of 50% chocolate.

Final answer:

To obtain 200 kilograms of a 46% fat-content chocolate, the candy distributor needs to mix 40 kilograms of a 30% fat-content chocolate and 160 kilograms of a 50% fat-content chocolate.

Explanation:

This problem can be solved using a basic mixture problem method. Let's name the amount of the 30% fat-content chocolate as 'x' and the amount of the 50% fat-content chocolate as 'y'. The total weight of the resulting chocolate is provided in the problem, 200 kilograms, therefore we know that x + y = 200.

The total fat in the chocolates should be 46% of 200kg, or 92kg. This gives us another equation based on the fat content, 0.3x + 0.5y = 92.

Solving these two equations linearly, we find the values of x and y. The amount of 30% fat content chocolate (x) is 40 kilograms and the amount of 50% fat-content chocolate (y) is 160 kilograms.

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