What is D(50) − (D(15) ∪ D(20))?

(a) The probability that the system functions on a rainy day is the probability that at least 4 out of the 6 components function, with each component having a probability of 0.7 of functioning.

We can calculate this probability using the binomial distribution:

P(system functions on a rainy day) = P(X ≥ 4), where X ~ Binomial(n=6, p=0.7)

Using a calculator or statistical software, we find:

P(system functions on a rainy day) = 0.8482

(b) The probability that the system functions on a non-rainy day is the probability that at least 4 out of the 6 components function, with each component having a probability of 0.9 of functioning. Again, we can use the binomial distribution:

P(system functions on a non-rainy day) = P(X ≥ 4), where X ~ Binomial(n=6, p=0.9)

Using a calculator or statistical software, we find:

P(system functions on a non-rainy day) = 0.9970

(c) To find the probability that the system will function tomorrow, we need to use the law of total probability. Let R be the event that it rains tomorrow and NR be the event that it doesn't rain tomorrow. Then:

P(system functions tomorrow) = P(system functions on a rainy day)P(R) + P(system functions on a non-rainy day)P(NR)

Using the probabilities from parts (a) and (b), and the fact that P(R) = 0.2 and P(NR) = 0.8, we can calculate:

P(system functions tomorrow) = (0.8482)(0.2) + (0.9970)(0.8) = 0.9746

Therefore, the probability that the 4 out of 6 systems will function tomorrow is 0.9746, assuming a 0.2 probability of rain.

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Answer:

Step-by-step explanation:10299

The summation of permutations of the n-1 rolls that contain at least one 6.

Permutation refers to the arrangement of a set of objects in a specific order or sequence. It is a mathematical concept that involves counting the number of ways in which a set of objects can be ordered or arranged.

However, we need to exclude the sequences that already contain a 6 before the nth roll. These sequences do not belong in event E n . Therefore, we need to find the number of permutations of the n-1 rolls that contain at least one 6.

Let's first consider the case where there is exactly one 6 in the sequence. We have n-1 slots for the rolls, and we need to choose one of them to be a 6. There are (n-1) ways to choose the position of the 6, and the remaining (n-2) slots can be filled with any of the remaining 5 numbers. Therefore, there are

=> [tex](n-1) * 5^{n-2}[/tex]

ways to have exactly one 6 in the sequence.

Now let's consider the case where there are two 6s in the sequence. We have n-1 slots for the rolls, and we need to choose two of them to be 6s. There are (n-1) choose 2 ways to choose the positions of the 6s. For the remaining (n-3) slots, we can fill them with any of the remaining 4 numbers. Therefore, there are

=> [tex](n-1 choose 2) * 4^{n-3}[/tex]

ways to have exactly two 6s in the sequence.

We can continue this pattern for the case where there are k 6s in the sequence. There are (n-1) choose k ways to choose the positions of the k 6s. For the remaining (n-k-1) slots, we can fill them with any of the remaining 6-(k+1) = 5-k numbers. Therefore, there are

=> [tex](n-1 choose k) * (5-k)^{n-k-1}[/tex]

ways to have exactly k 6s in the sequence.

To get the total number of outcomes in event E n , we need to sum up the number of outcomes for each possible number of 6s in the sequence. Therefore, we have:

[tex]|E n | = 6^{(n-1) - (n-1)} * 5^{(n-2) + (n-1 choose 2)} * 4^{(n-3)} - ... + (-1)^{(n-1) * (n-1 choose n-1)} * 1^{(n-n)}[/tex]

This is a formula for the total number of outcomes in event E n .

We use permutations to count the number of ways to arrange the rolls, and we use the principle of inclusion-exclusion to exclude the sequences that contain a 6 before the nth roll.

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Answer:

Step-by-step explanation:

1.

The points (0, 0), (0, 3), (4, 0): A. points are vertices of a right triangle.

The points (1, 2), (3, 0), (3, 3): B. points are not vertices of a right triangle.

The midpoint between the two points (2, 2) and (6, 4) is [4, 3].

The midpoint between the two points (2, 3) and (4, 1) is [3, 2].

The company's sales in 1997 is equal to $610,000.

In order to determine the straight-line distance from your starting point, we would apply Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

c² = a² + b²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

c² = 12² + 2²

c² = 144 + 4

c = √148

c = 12.17 miles.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(6 + 2)/2, (4 + 2)/2]

Midpoint = [8/2, 6/2]

Midpoint = [4, 3]

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(2 + 4)/2, (3 + 1)/2]

Midpoint = [6/2, 4/2]

Midpoint = [3, 2]

By applying the midpoint formula, the sales for 1997 can be calculated as follows;

Sales = (1996 sales + 1998 sales)/Number of years

Sales = ($500,000 + $720,000)/2 years

Sales = $1,220,000/2

Sales = $610,000.

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The female volleyball player is taller in relation to the distribution of heights based on gender.

The mean height of a man is 69 inches and the standard deviation is 2.25 inches. The mean height of a woman is 64 inches and the standard deviation is 2 inches.

To compare the heights of the female volleyball player and the male soccer player, we need to convert their heights to inches.

6 feet 2 inches is equal to 74 inches.

The female volleyball player is 10 inches taller than the mean height for women in the United States, while the male soccer player is 5 inches taller than the mean height for men in the United States.

To determine who is taller in relation to the distribution of heights based on gender, we need to compare the difference between their heights and the mean height for their respective gender in terms of the standard deviation.

For the female volleyball player, the difference is 10 inches - 64 inches (the mean height for women) = 6 standard deviations (since the standard deviation for women is 2 inches).

For the male soccer player, the difference is 10 inches - 69 inches (the mean height for men) = 4.4 standard deviations (since the standard deviation for men is 2.25 inches).

Therefore, the female volleyball player is taller in relation to the distribution of heights based on gender.

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We clearly seen that a little sign mistake here in 'j'.

In the given question  you have computed the cross product of v=i+2j−3k and w=2i−j+2k. You got v×w=i+8j−5k Without actually redoing v×w and we have to tell how can we spot a mistake in my work.

cross product of v and w i.e v×w is orthogonal to v and w

i.e (v×w)×v = 0 = (v×w)×w

Now v×w = i+8j₋5k

v = i+2j−3k

w = 2i−j+2k

then,

(v×w)×v = ( i+8j₋5k)×(i+2j−3k)

(v×w)×v = 1+16+15

(v×w)×v = 32≠0

and

(v×w)×w = ( i+8j₋5k)×(2i−j+2k)

(v×w)×w = 2₋8₋10

(v×w)×w = ₋16≠0

hence given cross product is wrong

Also we clearly seen that a little sign mistake here in 'j'

i.e if (v×w) = ( i₋8j₋5k)

(v×w)×v = ( i₋8j₋5k)×(i+2j−3k)

(v×w)×v = 1₋16+15

(v×w)×v = 0

and

(v×w)×w = ( i₋8j₋5k)×(2i−j+2k)

(v×w)×w = 2+8₋10

Hence, (v×w) = ( i₋8j₋5k)

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Answer: To find the selling price of the karaoke machine with a 49.5% markup, you need to first calculate the amount of the markup. You can do this by multiplying the cost of the machine (52.75) by the markup rate (49.5%) expressed as a decimal:

52.75 * 0.495 = 26.067375

Next, add this markup amount to the cost of the machine:

52.75 + 26.067375 = 78.817375

So, the selling price of the karaoke machine with a 49.5% markup would be $78.82.

Step-by-step explanation:

Answer:

Step-by-step explanation:

10000

Answer:10000

Step-by-step explanation:

dimosure

Answer:

The example that demonstrates the greatest distance traveled is Brenan diving to a depth of -12.76 feet, as it has the highest absolute value.

Answer:

Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.

Step-by-step explanation:

I'm sorry, but I cannot see the graph you are referring to. However, I can still answer some of your questions based on the information provided.

When the diameter of the cylinder is 2 cm, the radius is equal to half the diameter, which is 1 cm.

To express the volume of a cube of side length s as an equation, we use the formula for the volume of a cube:

Volume of cube = s^3

Making a table for the volume of the cube at different side lengths, we get:

Side Length (cm) Volume (cm^3)

        0                                    0

        1                                     1

        2                                     8

        3                                     27

To compare the volume of the cube when the side length is 3 cm and the volume of the cylinder when the diameter is 3 cm, we need to find the radius of the cylinder first.

When the diameter is 3 cm, the radius is half the diameter, which is 1.5 cm. The height of the cylinder is also equal to the radius, so the volume of the cylinder can be found using the formula:

Volume of cylinder = πr^2h

Substituting r = 1.5 cm and h = 1.5 cm, we get:

Volume of cylinder = π(1.5)^2(1.5) ≈ 10.602 cm^3

Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.

The data is analyzed and frequency table is created. The correct option for the histogram is the second option.

Here 30 individual samples are given. We are first categorizing the values in a frequency distribution table. It is shown as an image below.

Temperature          frequency            Relative frequency

    70-74                          5                        5/30 = .166 = 16.6%

    75-79                          4                        4/30 = .133 = 13.3%

   80-84                           7                        7/30 = 0.233 =23.3%

   85-89                          6                        6/30 = 0.2 = 20%

   90-94                         8                        8/30 = 0.266 = 2.66%

From the given histogram the second one represents the data given in the frequency table. It is marked in the image.

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The complete question is included as image

After evaluating f (-2), where f(x )is the piecewise function graphed given, the value of f(-2) = -3.

What is the piecewise function?

A function that is defined piecemeal is one that has numerous subfunctions, each of which applies to a distinct interval in the domain. Instead of being a property of the function itself, piecewise definition is a means to express the function.

Here, we have

The problem asks for f(-2), which is the value of y, that is, the vertical axis, when x, that is, the horizontal axis is -2.

We can see that at x = -2, the function changes the definition, thus it is called a piece-wise function.

To find the numeric value at x = -2, we have to look at the definition with the closed circle, which is at y = -3.

Hence, the value of f(-2) = -3.

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The missing angles in triangle RST and LMN are 121° and 15° respectively.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The Latin word "angulus," which means "corner," is where the term "angle" originates.

Angle position describes how a line interacts with another line or plane. The amount of rotation of the body relative to the reference position is used to calculate the angle of position.

Theta (), the sign used to represent the angular position, can represent the angle in degrees (°), radians (rads), or revolutions.

So, in the triangle RST:

Missing angle:

44 + 15 + x = 180

x = 180 - 59

x = 121°

In triangle LMN:

121 + 44 + x = 180

x = 180 - 165

x = 15°

Therefore, the missing angles in triangle RST and LMN are 121° and 15° respectively.

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10^-2/3 - 5 is the x-intercept of the given equation.

The x-intercept of a function is the point where the function f(x) is equivalent to zero.

Given the function below;

f(x)=3log(x+5)+2

3log(x+5)+2 = 0

Make x the subject of the formula:

3log(x+5) = -2

log(x+5) = -2/3

x + 5 = 10^-2/3

x = 10^-2/3 - 5

Hence the x-intercept of the graph of f(x)=3log(x+5)+2 is 10^-2/3 - 5

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The values of all 9 angles shown were found using the property of a kite they are:

m∠1=55°

m∠2=35°

m∠3=35°

m∠4=90°

m∠5=55°

m∠6=67°

m∠7=67°

m∠8=23°

m∠9=23°

What is an angle ?

In Kite figure, it is given that:

∠2+∠3 = 70°

Since they are equal so ∠2=∠3=35

∠8+∠9 = 46°

Since they are equal so ∠8=∠9=23°

∠5 = 180-∠3-∠4 = 180-35-90=55°

Similarly, ∠1 = 55°

∠6+∠7 = 180-∠8-∠9 = 180-46 = 134°

Since they are equal

∠6=∠7 = 67°

Therefore, all 9 angles were calculated using property of a kite.

m∠1=55°

m∠2=35°

m∠3=35°

m∠4=90°

m∠5=55°

m∠6=67°

m∠7=67°

m∠8=23°

m∠9=23°

In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The rays or line segments are called the sides or legs of the angle, and the distance between the sides at the vertex is called the angle's measure.

Angles are typically measured in degrees or radians, and they can be classified by their measures as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), straight (exactly 180 degrees), reflex (greater than 180 degrees and less than 360 degrees), or full (exactly 360 degrees).

Kites have several properties related to their angles, including:

Two pairs of opposite angles in a kite are congruent. That is, the angles formed between the pairs of congruent sides are equal.

One diagonal of a kite bisects the other diagonal. This means that the diagonal that connects the non-congruent vertices of the kite divides the other diagonal into two equal segments.

The sum of the measures of the two non-congruent angles in a kite is 180 degrees. This is because the kite can be divided into two congruent triangles by drawing the diagonal that bisects the other diagonal, and the sum of the angles in a triangle is always 180 degrees.

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Answer:

3² +2³= 9+8=17

2¹ - 3²= 2-9=8

Step-by-step explanation:

Answer:

1-7

Step-by-step explanation:

[tex]3^{2}[/tex] + [tex]2^{2}[/tex] (3x3) + (2x2x2) = 9 + 8 = 17

[tex]2^{1}[/tex] - [tex]3^{2}[/tex] = 2 - (3x3) = 2 - 9 = -7

Using a telephone directory as the sampling frame can lead to under-coverage and bias, and it is generally not considered a representative sampling method.

Other more representative sampling methods, such as random digit dialing, address-based sampling, or a combination of methods, may be used to obtain a more accurate representation of the population.

Selecting a sample of households from the telephone directory can result in under-coverage and bias for several reasons.

Concept: When random sampling is not used, bias or regular flaws in the way the sample mean the population can occur.

Voluntary reply to samples, in which respondents choose their own respondents, and benefit samples, in which people who live nearby are included in the sample, are particularly biased.

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The maximum sustainable rate of harvest which is possible for the growth of fish P(t)  according to the differential equation " P' = 4P - 4P^2 - h " will be at the harvest rate of h=3.

In order to calculate the maximum sustainable harvest rate possible, we are required to find the equilibrium solutions of the differential equation firstly. Equilibrium solutions occur when P' = 0, so we can set the right-hand side of the differential equation at 0.

4P - 4P² - h = 0

Now a quadratic equation is formed in terms of P, which can be used to obtain P.

P = (1 ± √(1 + h))/2

There are two equilibrium solutions, obtained by these two values of P.

Now, in order to obtain a maximum sustainable harvest rate, we are required to have both equilibrium solutions to as positive ( as negative populations don't make any sense in this context).

Therefore, we have to find the largest value of h for which both of these equations have positive solutions:

(1 + √(1 + h))/2 > 0

(1 - √(1 + h))/2 > 0

On camparing both the inequalities, it can be concluded that the first inequality is always true, since the square root of a positive number is always positive. The second inequality is true when h < 3.

Hence, the maximum sustainable harvest rate is is found to be at h = 3. If the harvesting rate is greater than 3, then there will be no positive equilibrium solutions and the population will eventually be perished.

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The percentage scored by Curry is 39.3% oby halftime.

To find the percentage of his team's points that Curry scored, we can use the following formula:

percentage = (part / whole) x 100

Where

Part = 22 points

Whole = 56 points

Substitute the known values in the above equation, so, we have the following representation

Percentage = (22 / 56) x 100%

Evaluate

Percentage = 39.3%

Hence, Curry scored 39.3% of his team's points by halftime.

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one possible explanation for why there are two different ways of adding up the symbols on the tablet is given below.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The ancient Egyptian number system was based on hieroglyphs, and it used a decimal system with hieroglyphs representing the powers of 10. However, without seeing the specific symbols on the tablet, it is difficult to provide an accurate answer.

Assuming that the tablet is using a basic arithmetic operation such as addition, and each symbol represents a different number,

it is possible that there are two different ways to add up the numbers represented by the symbols on the tablet.

One way to approach this problem is to try to find two different sets of numbers that when added, produce the same result.

For example, if the symbols represent the numbers 2, 3, and 5, then one way to add them up would be:

2 + 3 + 5 = 10

Another way to add them up would be:

3 + 7 = 10

In this case, the symbol for 2 would represent the number 7, and the symbol for 5 would represent the number 3. This would be one possible explanation for why there are two different ways of adding up the symbols on the tablet.

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sorry but without seeing the actual tablet then we cant work it out to get a correct answer

A graphing utility such as Desmos or Wolfram Alpha can be used to graph the function. The graph shows that the maximum value occurs at t = 13 and the minimum value occurs at t = 7, which confirms our calculations.

To find the absolute extrema of the function h(t) = t^2 - 6 on the closed interval [7, 13], we can start by taking the derivative of the function and setting it equal to zero to find any critical points:

h'(t) = 2t = 0

t = 0

However, t = 0 is not in the interval [7, 13], so we only need to check the endpoints of the interval and any other critical points that may lie within the interval.

Since there are no critical points in the interval, we only need to evaluate the function at the endpoints:

h(7) = 7^2 - 6 = 43

h(13) = 13^2 - 6 = 163

Thus, the absolute maximum of h(t) on the interval [7, 13] is 163, which occurs at t = 13, and the absolute minimum is 43, which occurs at t = 7.

To verify our results using a graphing utility, we can graph the function h(t) = t^2 - 6 on the interval [7, 13] and visually observe the maximum and minimum values.

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Answer:

Caca

Step-by-step explanation:

Caca

Context, it is not clear what is meant by "j(0,0)" or what the function's codomain being [tex]R^2[/tex] signifies.

It is not clear what you mean by "b" and "j". However, I can provide a general answer on how to find a holomorphic function.

A holomorphic function is a complex-valued function that is complex differentiable in a neighborhood of each point in its domain. This means that the function must satisfy the Cauchy-Riemann equations, which relate the partial derivatives of the function with respect to the real and imaginary parts of its input.

To find a holomorphic function, one approach is to use the power series representation of complex analytic functions. If a function f(z) is analytic at a point z0, then it has a power series expansion of the form:

f(z) = ∑n=0∞ [tex]c_n (z - z0)^n[/tex]

where [tex]c_n[/tex] are complex coefficients that depend on the function and z0. This power series converges in a neighborhood of z0, and the coefficients can be calculated using complex integration techniques.

Another approach is to use the Cauchy integral formula, which expresses the value of a holomorphic function at a point in terms of an integral over a closed curve that encloses the point. This formula allows one to compute the function at any point in its domain using complex integration techniques.

Without more information about "b" and "j", it is not possible to determine if a holomorphic function exists or what its properties might be. Similarly, without more context, it is not clear what is meant by "j(0,0)" or what the function's codomain being [tex]R^2[/tex] signifies.

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The school newspaper reporter wants to find out how many students will attend Tet festivities. She randomly surveys 13 students and knows that 24% of students typically attend the festivities. We are interested in the probability of the number of students who will attend.

The probability that at most 4 students will attend is 0.4936 and the probability that more than 3 students will attend is 0.5064. Calculating these probabilities can be done using the binomial probability formula. First, calculate the probability of exactly 4 students attending. This probability is [tex]0.24^4 * 0.76^9 = 0.0038[/tex]. Then, calculate the probability of 3 students or fewer attending by adding the probabilities of 0, 1, 2, and 3 students attending, which is 0.0013 + 0.0358 + 0.1045 + 0.2696 = 0.4113. Finally, subtract 0.4113 from 1 to get 0.4936. We are interested in the probability of the number of students who will attend. To calculate the probability of more than 3 students attending, subtract 0.4113 from 1 to get 0.5064.

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The system of equations representing this movie theater scenario is B:

A system of equations involves two or more equations whose solutions are determined concurrently or at the same time.

A system of equations is otherwise called simultaneous equations.

The total sales revenue = $63

The total number of tickets sold = 29

The cost per unit of children tickets = $3

The cost per unit of adult tickets = $2

The cost per unit of senior tickets = $2

Let the number of children tickets sold = 3c

Let the number of adult tickets sold = a

Let the number of senior tickets sold = s

c + a + s =29 Total number of tickets sold

3c+2a+2=63 Total amount realized from the ticket sales

3a=c

Thus, the correct system of equations is Option B.

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The probability that a randomly chosen fitness club member signs up for a free running session is 0.12 or 12%.

What is probability ?
Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. For example, if the probability of an event is 0.5, it means that there is a 50% chance that the event will occur.

Given by the question:

There are a total of 100 members in the fitness club, and 30 members have signed up for the free session. Let's call the number of members who signed up for the weightlifting session "x", so the number of members who signed up for the running session and the swimming session each is "2x".

The total number of members who signed up for the free session is:

x + 2x + 2x = 5x

We know that 30 members signed up for the free session, so we can set up the following equation:

5x = 30

Solving for x, we get:

x = 6

Therefore, 6 members signed up for the weightlifting session, and 12 members signed up for each of the running and swimming sessions.

The probability of a randomly chosen member signing up for a free running session is the number of members who signed up for the running session divided by the total number of members:

P(Running) = 12/100

P(Running) = 0.12

Therefore, the probability that a randomly chosen fitness club member signs up for a free running session is 0.12 or 12%.

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Answer:

Step-by-step explanation:

Answer:

x = 30, -40

Step-by-step explanation:

This a right triangle, so you can use the Pythagorean Theorem.

[tex]a^{2}+ b^{2}=c^{2}[/tex], now in place of the a, b and c use x, x +10 and 50.

so a = x, b =x+10 and c = 50

[tex]x^{2} + (x+10)^{2} =50^{2}[/tex]

[tex]x^{2} +x^{2} +20x +100 = 2500[/tex]

Answer:c

Step-by-step explanation:

because