Find an equation of the tangent plane to the given parametric surface at the specified point.
r(u, v) = u2 i + 9u sin v j + u cos v k; u = 2, v = 0

The correct next step Amy could take is to factor (x^2 - 16) on the left side of the equation to yield (x + 4)(x – 4)(x + 2) = 0.

The equation is given as:

\(\mathbf{(x^2 - 16)(x + 2) = 0}\)

The possible next steps are:

1. Expand the equation as follows

\(\mathbf{x^3+2x^2-16x-32 = 0}\)

2. Express x^2 -16 as a difference of two squares as follows

\(\mathbf{(x + 4)(x- 4)(x + 2) = 0}\)

However, the correct step in this case is to factor x^2 - 16 as a difference of two squares to give \(\mathbf{(x + 4)(x- 4)(x + 2) = 0}\)

This is so, because the question says Amy is trying to solve for variable x.

This step will ensure that she gets the possible values of x, unlike expanding the whole equation .

Hence, the correct next step is \(\mathbf{(x + 4)(x- 4)(x + 2) = 0}\)

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Answer: 78.54

Step-by-step explanation: pi X radius squared!!

Answer:

Slope of the line m =-2

Step-by-step explanation:

Explanation:-

Given that the points are (10,14) and (8,18)

Slope of the line

    \(m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }\)

    \(m = \frac{18-14 }{8-10 } = \frac{4}{-2} = -2\)

Slope of the line m =-2

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

the value of P(A∩B) in terms of x and y is xy.

The correct option is D. xy.

To determine the value of P(A∩B) in terms of x and y, we can use the definition of conditional probability and the fact that P(A∩B) = P(A|B) * P(B).

Given that P(A|B) = x and P(B) = y, we can substitute these values into the equation:

P(A∩B) = P(A|B) * P(B)

        = x * y

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a) The mode of the list is 7

b) The median of the list is 7.

c) The mean is 5.4

d) The range is 7

What is the Mean, Mode and Median?

Mean: The mean is the average of a set of numbers, calculated by adding up all the numbers and dividing by the total number of numbers in the set.

Mode: The mode is the most frequently occurring number in a set of numbers.

Median: The median is the middle value in a set of numbers when the set is sorted in ascending or descending order.

a) Mode: The mode of the list is 7, as it is the number that occurs most frequently (3 times).

b) Median: To find the median, the list must first be sorted in ascending order:

1, 2, 3, 4, 5, 7, 7, 7, 8, 8

The median of the list is 7.

c) Mean: The mean is found by adding up all the numbers in the list and dividing by the total number of items:

(3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8)/10 = 54/10 = 5.4

d) Range: The range is the difference between the largest and smallest numbers in the list:

8 - 1 = 7

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Answer:

Step-by-step explanation:

Conclusion:

Therefore, 3/10 + 21/100 equals 51/100 as a fraction.

Hoped this helped.

\(BrainiacUser1357\)

0.51000 which as smaller is 0.51

Step-by-step explanation:

simplify 21/ 100 then add 3/10 + 21/100 then simplify 3/10 then you would do 3×10+21/100 which equals 51/100

a collection of 65 coins contains one with two heads. the remainder of the coins are fair. if a coin, selected randomly from the collection, turns up heads 6 times in 6 tosses, 1/65 is the probability it’s a two-headed coin

Definition of probability

(1) : the chance that a given event will occur. (2) : the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

We know that one coin in a collection of 65 has two heads. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row. We calculate the probability that it is the two-headed coin.

We calculate  the number of possible combinations:

C₁⁶⁵= 65!/1!(65-1)!

     = 65

Number of favorable combinations is 1.

Therefore, the probability is

P=1/65.

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The probability that the dog is still lost at the end of the second day is 0.41

To solve this problem, we can use Bayes' theorem, which allows us to update the probability of an event based on new information.

Let A be the event that the dog is in forest A, and B be the event that the dog is in forest B. Let F be the event that the dog is found within two days.

We want to calculate P(F'), the probability that the dog is still lost at the end of the second day. We can use the law of total probability to express this as

P(F') = P(F'|A) × P(A) + P(F'|B) × P(B)

where P(F'|A) is the probability of not finding the dog within two days given that the dog is in forest A, P(F'|B) is the probability of not finding the dog within two days given that the dog is in forest B, and P(A) and P(B) are the prior probabilities of the dog being in forest A and forest B, respectively.

Using the information given in the problem, we can calculate

P(F'|A) = 1 - 0.5 = 0.5 (the probability of not finding the dog in forest A within two days is 1 - 0.5 = 0.5)

P(F'|B) = 1 - 0.8 = 0.2 (the probability of not finding the dog in forest B within two days is 1 - 0.8 = 0.2)

P(A) = 0.7 (the prior probability of the dog being in forest A)

P(B) = 0.3 (the prior probability of the dog being in forest B)

Plugging these values into the formula above, we get

P(F') = 0.5 × 0.7 + 0.2 × 0.3 = 0.41

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The given question is incomplete, the complete question is:

Oscar has lost his dog; there is a 70% probability it is in forest A and a 30% chance it is forest B. If the dog is in forest A and Oscar looks there for a day, he has a 50% change of finding the dog. If the dog is in forest B and Oscar looks there for a day, he has an 80% chance of finding the dog. what is the probability that the dog is still lost at the end of the second day?

Answerham=136

Step-by-step explanation:

ham=x,,cheese=3x....=544...4x=544  which makes  x to be 136 which is the no of hamburgers

The coordinates of the point P along the directed line segment AB are (3, -2).

In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have the following;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(5(6) + 3(2))/(5 + 3)],  [(5(1) + 3(7))/(5 + 3)]

P(x, y) = [(30 - 6)/(8)],  [(5 - 21)/8]

P(x, y) = [24/8],  [(-16)/(8)]

P(x, y) = [3, -2]

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Answer:

irrational

Step-by-step explanation:

Answer:

p = 3

Step-by-step explanation:

We have a right triangle with both legs equal, whose hypotenuse is 3 times the root of 2.

We know both legs are equal because we have identical opposite angles in this right rectangle.

If we apply the Pythagorean theorem, we obtain:

\(p^2+p^2=(3\sqrt{2})^2=9\cdot 2=18\\\\2p^2=18\\\\p^2=18/2=9\\\\p=\sqrt{9}\\\\p=3\)

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m.

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m. This is because the conjunction "and" (∧) is used to connect two statements that must both be true in order for the overall statement to be true. In this case, both s (It is sunny today) and m (I will bring my umbrella) must be true in order for the statement to be true.

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(B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."


The logical operator ∧ (conjunction) connects two propositions and represents the idea of "and." Therefore, s∧m means "It is sunny today and I will bring my umbrella." This is the logical expression that represents the statement given in the question.


To summarize, the correct answer is (B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."
Main Answer: The correct logical expression is (B) s∧m.

In the given statement, "Despite the fact that it is sunny today, I will bring my umbrella," both propositions s (It is sunny today) and m (I will bring my umbrella) are true at the same time. The logical expression that represents this is s∧m, which means "s AND m" are both true.

The statement "Despite the fact that it is sunny today, I will bring my umbrella" is best represented by the logical expression (B) s∧m, as it shows that both s and m are true.

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The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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The digit 3 in the number 17039 represents the value of 3 in the tens place. The place value system is a way to understand the value of each digit in a number. In this case, each digit in the number 17039 has a specific place value, starting from the rightmost digit, which is the ones place, then the tens place, followed by the hundreds place and so on. In the number 17039, the digit 3 is located in the tens place which represent 3 x 10 = 30. To understand the value of any digit in a number, you can multiply the digit by its corresponding place value.

Answer:

The digit 3 in the number 17039 represents the value of 3 in the tens place

Step-by-step explanation:

Answer:

zero

The x‐axis or any line parallel to the x‐axis has a slope of zero.

Step-by-step explanation:

The Y corodinate on X -axis is constant (zero). So the slope of X-axis is 0. Therefore the answer is zero

Answer:

Step-by-step explanation:

You want to know if the fractions (2 1/2)/(6.5) and (5/8)/(1 5/8) are in a proportional relationship, and the simplest form of each.

Equivalent fractions can be found by multiplying numerator and denominator by the same number.

  (2 1/2)/(6.5) = 2·(2 1/2)/(2·6.5) = 5/13

  (5/8)/(1 5/8) = 8(5/8)/(8·(1 5/8)) = 5/(8+5) = 5/13

Both fractions are equivalent to 5/13, so their relationship is proportional.

Answer:

C

Step-by-step explanation:

The matrices are conformable for multiplication.

Multiply and sum the product of corresponding elements in row 1 of matrix A with elements in column of matrix B.

AB = \(\left[\begin{array}{ccc}5(2)+2(3)\\3(2)-1(3)\\\end{array}\right]\) = \(\left[\begin{array}{ccc}10+6\\6-3\\\end{array}\right]\) = \(\left[\begin{array}{ccc}16\\3\\\end{array}\right]\) → C

The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37%.

The probability that a haphazardly chosen vagrant pet in a creature covered in Austin is a canine is 11.71%.

The probability that a haphazardly chosen stranded canine in a similar creature cover in Austin is a Chihuahua is 29.37% .

2.76% + 2.86% + 3.44% + 2.65% = 11.71%

11.71/3.44 = .2937

.2937 = 29.37%

Probability is just the way that logical something is to occur.

Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions represented by probability is called statistics.

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Answer:

The independent variable is the depth of the submarine

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

The value of (f - g)(x) is -x - 14

The given parameters are:

f(x) = 4x - 8

g(x) = 5x + 6

To calculate (f - g)(x), we make use of

(f - g)(x) = f(x) - g(x)

So, we have:

(f - g)(x) = 4x - 8 - 5x - 6

Evaluate the like terms

(f - g)(x) = -x - 14

Hence, the value of (f - g)(x) is -x - 14

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Jane needs to work for a certain number of weeks, denoted as w, to save enough money to buy the bicycle. The equation that represents this situation is:

$50 + $40w = $330

To find the value of w, we can solve this equation.

To solve the equation, we need to isolate the variable w on one side of the equation. We can do this by subtracting $50 from both sides:

$40w = $330 - $50

$40w = $280

Next, we divide both sides of the equation by $40 to solve for w:

w = $280 / $40

w = 7

Therefore, Jane needs to work for 7 weeks to save enough money to buy the bicycle.

In order to buy the bicycle, Jane needs to work for 7 weeks. During this time, she will earn $40 each week from babysitting. By the end of the 7th week, she will have accumulated a total of $280 ($40 x 7). Since the bicycle is marked down by 25% after the first week of babysitting, we need to determine how many more weeks Jane must work to reach the full price of $330.

To calculate the additional weeks needed, we first need to determine the discounted price of the bicycle after the first week. A 25% discount on $330 is $82.50 ($330 x 0.25). Therefore, the discounted price of the bicycle after one week of babysitting is $247.50 ($330 - $82.50).

To find out how many more weeks Jane needs to work, we subtract her current savings and the discounted price from the original price of the bicycle:

$330 - $50 - $247.50 = $32.50

Therefore, Jane needs to work for approximately 1 more week to save the remaining $32.50 and buy the bicycle.

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The following can be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other: B. PR and SQ have the same midpoint.

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel opposite sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

(Line segment PR)/2 = (Line segment SQ)/2

Line segment PR = Line segment SQ

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Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

In calculating the mean of this data set  Ashrita did the best job.

The  Mean of the data set is the most commonly used measures of central tendency.

It means the average value of the data set.

one doesn't have to arrange the data in order  for finding it.

The data set value  takes is to add them all together and divide that by the number of the data.

It can be written as

\(,(x_1 + x_2 + x_3 + ..... + x_n) / n\)

Where \(x_1 , x_2 , x_3 , ..... ,x_n\)are the values in the data set

Therefore we can conclude that Ashrita did the best job in calculating the mean of this data set.

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Answer:

6

Step-by-step explanation:

if we always go from right to left it will start with lin segment BC   BD    BA   CD  CA    and DA those are all the posible segments for this line