Let

A = {1, 3, 5, 7, 9},
B = {3, 6, 9},
and
C = {2, 4, 6, 8}.

Find each of the following. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.)

(a). A ∪ B
(b). A ∩ B
(c). A ∪ C
(d). A ∩ C
(e). A − B
(f). B − A
(g). B ∪ C
(h). B ∩ C

Given three side lengths form an acute obtuse or a right triangle 17, 21, & 28

Check Right triangle

Not a Right triangle

An obtuse triangle is a triangle with one obtuse angle and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry.

Not an Obtuse triangle

Hence it is acute angle because all angles are less than 90°

The values of d that make the inequality 9d > 9 true are given as follows:

2, 4, 11.

Hence the equivalent inequality is given as follows:

d > 1.

The inequality in the context of this problem is defined as follows:

9d > 9.

To solve the inequality, we solve it similarly to an equality, isolating the desired variable d, hence the solution is given as follows:

d > 9/9

d > 1.

The > symbol means that the solution is composed by values that are greater than 1, hence the options are 2, 4, 6 and 11.

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Answer:

please what did you put as the first option

Step-by-step explanation:

I think the answer is 29

(a) Parameter being estimated in the given information is the difference between two proportions (p_1 - p_2).

(b) A 95% confidence interval is given by  (0.075, 0.225)

(a) The parameter being estimated is the difference between two population proportions, which is denoted by (p_1 - p_2).

(b) The margin of error for a 95% confidence interval is 5%, which means that the critical value of z is 1.96 (obtained from a standard normal distribution table). Using the formula for the margin of error, we can write:

1.96 * √(p_1_hat*(1-p_1_hat)/n_1 + p_2_hat*(1-p_2_hat)/n_2) = 0.05

where p_1_hat and p_2_hat are the sample proportions from the two samples, and n1 and n2 are the sample sizes.

Solving for p_1_hat - p_2_hat, we get:

p1_hat - p2_hat = ±0.075

Since we are interested in a 95% confidence interval, we can subtract and add this value from P1 - P2 to obtain the interval:

P_1 - P_2 ± 0.075

Substituting the given value of P_1 - P_2 = 0.15, we get:

95% Confidence Interval: (0.075, 0.225)

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Answer:

The answer is C ≈ 86.7 cm

Answer:

The answer is 86. 7

Step-by-step explanation:

\(c = 2\pi \times r \\ c = 2 \times 3.14 \times 13.8 \\ c = 86.742857 \ \\ \)

Then C to the nearest tenth is

\(c = 86.7\)

The total number of ways students and teachers line up according to given condition is equal to 840.

Total number of students in a school = 8

Total number of teachers in a school = 3

Since the line must start with a teacher and end with a student,

Consider them as fixed positions in the line.

Arrange the remaining 7 people in the middle of the line.

First, choose one of the three teachers to be at the front of the line in 3 ways.

Then, choose one of the 8 students to be at the end of the line in 8 ways.

Next, arrange the remaining 4 teachers and 3 students in the middle of the line.

This can be done in 7!/(4!3!) = 35 ways,

Using the formula for combinations with repetition.

The total number of ways to form the line is equal to

= 3 x 35 x 8

= 840

Therefore, there are 840 ways they can line up.

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The solution is (3, 1). Hence, the system has a unique solution.

The augmented matrix of the linear system is given below:100-30001The augmented matrix is already in row echelon form. Row echelon form is a form in which the elements below the leading coefficients are all zero. In this matrix, the first non-zero element of the first row is 1, which is called a leading coefficient.

Therefore, the first row is a pivot row. The pivot column is the column in which the pivot row's leading coefficient appears.In this case, the first column is the pivot column. The second row has only one non-zero element, which is also a leading coefficient. Thus, the second row is also a pivot row.

The pivot column for the second row is the third column. Since there are two pivot rows, there will be two variables in the system. Assign x1 and x2 to the first and second columns, respectively. The linear system is: x1 - 3x2 = 0, x3 = 1x1 = 3x2 x2 = x2 x3 = 1.

The solution to this system is (3t, t, 1), where t is a free variable. The solution is a line since there is one free variable, t. The solution can be represented parametrically as a line in three dimensions. The solution can be represented as a point in two dimensions since there are two variables in the system. The solution is (3, 1). Hence, the system has a unique solution.

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\(\text{Given that,}~ f(x) = 2x^2 -5 ~ \text{and}~ g(x) = 3x^3\\\\\text{Now,}\\\\ ~~(f-g)(x)\\\\=f(x) - g(x)\\\\=2x^2 -5 - 3x^3\\\\=-3x^3 +2x^2 -5\)

The conditional probability that a repair takes at least 10 hours, given that its duration exceeds 9 hours, is approximately 0.0067 / 0.0037 ≈ 1.81.

(a) To find the probability that a repair time exceeds 1/2 hours, we need to calculate the complementary probability of the repair time being less than or equal to 1/2 hours. The exponential distribution has a cumulative distribution function (CDF) given by F(x) = 1 - e^(-λx), where λ is the parameter. Using this formula, we can calculate the probability: P(X > 1/2) = 1 - P(X ≤ 1/2) = 1 - (1 - e^(-λ(1/2))) = 1 - (1 - e^(-1/4)) = e^(-1/4) ≈ 0.7788. Therefore, the probability that a repair time exceeds 1/2 hours is approximately 0.7788. (b) To find the conditional probability that a repair takes at least 10 hours, given that its duration exceeds 9 hours, we need to calculate the ratio of the probability of the repair taking at least 10 hours and the probability of the repair time exceeding 9 hours. P(X ≥ 10 | X > 9) = P(X ≥ 10 and X > 9) / P(X > 9). The probability that the repair time exceeds 9 hours is the same as the probability that the repair time exceeds 9 hours or 10 hours. P(X > 9) = 1 - P(X ≤ 9) = 1 - (1 - e^(-λ(9))) = 1 - (1 - e^(-9/2)) = e^(-9/2) ≈ 0.0037.

The probability that the repair time exceeds both 9 and 10 hours is the same as the probability that the repair time exceeds 10 hours. P(X ≥ 10 and X > 9) = P(X ≥ 10) = 1 - P(X ≤ 10) = 1 - (1 - e^(-λ(10))) = 1 - (1 - e^(-5)) = e^(-5) ≈ 0.0067. Therefore, the conditional probability that a repair takes at least 10 hours, given that its duration exceeds 9 hours, is approximately 0.0067 / 0.0037 ≈ 1.81.

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Answer:

1 5/8

Step-by-step explanation:

2 7/8 - 1 1/4 = 1 5/8.

hope this helps :)

Answer:

The multiplicative rate of change is 3/4

Step-by-step explanation:

Here, we want to get the multiplicative rate of change

In this case, by dividing the succeeding term by the preceding term, we will get the multiplicative rate of change

mathematically, we have this as;

81/128 divided 27/32

= 81/128 * 32/27

= 3/4

The requried, to find the angle by which AB turns clockwise about point B to coincide with BC, we need to first identify points A, B, and C on a diagram.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
To find the angle by which AB turns clockwise about point B to coincide with BC, we need to first identify points A, B, and C on a diagram. Once we have done that, we can draw a line from B to C, and then compare the direction of AB to the direction of BC. The angle between these two lines will be the angle by which AB turns clockwise to coincide with BC.

Similarly, to find the angle by which AB turns counterclockwise to coincide with BE, we need to identify points A, B, C, and E on a diagram. Once we have done that, we can draw a line from B to E, and then compare the direction of AB to the direction of BE. The angle between these two lines will be the angle by which AB turns counterclockwise to coincide with BE.

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\(4a^4-8a^2+4=0\implies 4(a^4-2a^2+1)=0\implies a^4-2a^2+1=0 \\\\\\ (a^2)^2-2a^2+1=0\implies (a^2-1)(a^2-1)=0\implies a^2=1 \\\\\\ a=\pm\sqrt{1}\implies a=\pm 1\)

Answer:

she cant

Step-by-step explanation:

Sarkis cannot draw a triangle with these side lengths. Therefore, option A is correct.

Given that, a triangle with sides measuring 4 ft, 10 ft, and 16 ft.

What are the conditions to construct a triangle?

In the triangle, the sum of any two sides is always greater than the third side. The difference between any two sides of the triangle is always less than the third side.

Sarkis cannot draw a triangle with these side lengths. Therefore, option A is correct.

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The limit lim(x→∞) x/√(x^2 + 3) is 1, and there is no need to apply L'Hospital's Rule in this case.

When trying to use L'Hospital's Rule to find the limit lim(x→∞) x/√(x^2 + 3), it is important to note that L'Hospital's Rule can only be applied if the function is continuous and differentiable. In this case, the function is continuous and differentiable, but applying L'Hospital's Rule is not necessary as the limit can be evaluated using another method.
First, let's rewrite the given function by dividing both the numerator and the denominator by x:
lim(x→∞) (x/x) / (√(x^2 + 3)/x) = lim(x→∞) 1 / √(1 + 3/x^2)
As x approaches infinity, the term 3/x^2 approaches 0, so the limit becomes:
lim(x→∞) 1 / √(1 + 0) = 1 / √(1) = 1
Therefore, the limit lim(x→∞) x/√(x^2 + 3) is 1, and there is no need to apply L'Hospital's Rule in this case.

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Answer:

I believe that the answer would be 1 because after doing tan^-1 (5) i got 1.3734=1 degree

The ordered pair (s,t) that satisfies the system are (1/2,4) and (1,5).

We can use the second equation to solve for one of the variables in terms of the other. Let's solve for t:

3t - 6s = 9

3t = 6s + 9

t = (2s + 3)

Now we can substitute this expression for t into the first equation and solve for s:

s/2 + 5/t = 3

s/2 + 5/(2s + 3) = 3

Multiplying both sides by the denominator (2s + 3) gives:

s(2s + 3)/2 + 5 = 3(2s + 3)

Simplifying and collecting like terms yields:

2s^2 + 3s + 10 = 6s + 9

2s^2 - 3s + 1 = 0

This quadratic equation can be factored as:

(2s - 1)(s - 1) = 0

So s = 1/2 or s = 1.

Now we can substitute these values for s into the equation we derived for t:

If s=1/2 then t=2(1/2)+3=4

If s=1 then t=2(1)+3=5

Therefore, the ordered pairs that satisfy the system are (1/2,4) and (1,5).

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Answer:

7

Step-by-step explanation:

If range is 6 then the difference between highest and lowest is 6 so 1 + 6 = 7 so b is equal to 7.

Step-by-step explanation:

\( {17}^{2} = {8}^{2} + {b}^{2} \\ {b}^{2} = {17}^{2} - {8}^{2} \\ {b }^{2} = 225 \\ b = \sqrt{225} = 15\)

Use Pythagorean theorem

\(\\ \sf\longmapsto b^2=h^2-p^2\)

\(\\ \sf\longmapsto b^2=17^2-8^2\)

\(\\ \sf\longmapsto b^2=289-64\)

\(\\ \sf\longmapsto b^2=225\)

\(\\ \sf\longmapsto b=15ft\)

7.77% of first graders will need developmentally appropriate math and English lessons.

Probability calculations assuming that freshmen entering a private institution have a 61% chance of not needing a math development course or an English development course, compared to 21% and 37%, respectively.

Therefore, the probability is equal to 0.21 x 0.

37, representing 7.77%.

We now know that there is a 7.77% probability that new students will need developmental mathematics and English studies courses.

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The surface whose equation is given by 6r² + z² = 1 is an ellipsoid. The surface whose equation is given by 6r^2 + z^2 = 1 is a three-dimensional shape known as an ellipsoid. An ellipsoid is a type of quadric surface that is defined by three principal axes, with the lengths of these axes determined by the coefficients of the equation.

In this case, the ellipsoid has a major axis in the z-direction with a length of 1, and minor axes in the x and y directions with lengths of √(1/6). The equation can also be rewritten as (r/√(1/6))^2 + (z/1)^2 = 1, which shows that the ellipsoid is centered at the origin and has a radius of √(1/6) in the x and y directions, and a radius of 1 in the z direction.

An ellipsoid is a 3D surface that resembles an elongated sphere, with its general equation given as (x²/a²) + (y²/b²) + (z²/c²) = 1. In this case, the given equation can be rewritten in the standard form as (x²/ (1/6)) + (y²/ (1/6)) + (z²/1) = 1, which shows it's an ellipsoid.This particular ellipsoid has its major axis along the z-axis and two equal minor axes along the x and y-axes, with semi-major axis length of 1 and semi-minor axis lengths of √(1/6).

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Answer:

249.44

Step-by-step explanation:

5 CDs each = 19.55 6 DVDs each =12.97

19.55×5 =97.75 12.97×6=77.82

mp3= 124.99

124.99+97.75+77.82=300.56

550.00-300.56=249.44

If a nonhomogeneous system of linear equations is underdetermined, it can have either infinitely many solutions or no solutions.

A nonhomogeneous system of linear equations is represented by the equation Ax = b, where A is the coefficient matrix, x is the vector of unknowns, and b is the vector of constants. When the system is underdetermined, it means that there are more unknown variables than equations, resulting in an infinite number of possible solutions. In this case, there are infinitely many ways to assign values to the free variables, which leads to different solutions.

To determine if the system has a solution or infinitely many solutions, we can use techniques such as row reduction or matrix methods like the inverse or pseudoinverse. If the coefficient matrix A is full rank (i.e., all its rows are linearly independent), and the augmented matrix [A | b] also has full rank, then the system has a unique solution. However, if the rank of A is less than the rank of [A | b], the system is underdetermined and can have infinitely many solutions. This occurs when there are redundant equations or when the equations are dependent on each other, allowing for multiple valid solutions.

On the other hand, it is also possible for an underdetermined system to have no solutions. This happens when the equations are inconsistent or contradictory, leading to an impossibility of finding a solution that satisfies all the equations simultaneously. Inconsistent equations can arise when there is a contradiction between the constraints imposed by different equations, resulting in an empty solution set.

In summary, when a nonhomogeneous system of linear equations is underdetermined, it can have infinitely many solutions or no solutions at all, depending on the relationship between the equations and the number of unknowns.

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The answer is B

When there is a solid point that means it is included in the graph, so you'd use a greater/less than or equal to symbol (the one with a line under). If it's an unfilled point then it means that it is not included in the graph, so you'd use a greater/less than sign.

The x² equation is less than 2 while the linear equation is greater than or equal to 2.

We know it's the x² equation that is less than two because it has a curve in it.

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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The expression that equals 2B+C in standard form is 4x² + 6

From the question, we have the following parameters that can be used in our computation:

B = x² + 2

C = 2 + 2x²

The expression to calculate is given as

2B + C

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

2B + C = 2x² + 4 + 2 + 2x²

Evaluate the like terms

2B + C = 4x² + 6

Hence, the expression is 4x² + 6

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the standard form of the equation -9x²+25y²-100y = 125 is x²/25 + (y-2)²/9 = 1

Add 125 to both sides of the equation.

-9x²+25y²-100y = 125

Complete the square for 25y²-100y

25(y-2)²-100

Substitute 25(y-2)²-100 for 25y²-100y in the equation

-9x²+25y²-100y = 125

-9x²+25(y-2)²-100 = 125

Move −100 to the right side of the equation by adding 100 to both sides.

-9x²+25(y-2)² = 125 +100 = 225

Divide each term by 225 to make the right side equal to one.

-9x²/225 +25(y-2)²/225 = 225/225

Simplify each term in the equation in order to set the right side equal to 1. The standard form of an ellipse or hyperbola requires the right side of the equation to be 1.

x²/25 + (y-2)²/9 = 1

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Use the Pythagorean theorem to solve for the diagonal distance

Diagonal = sqrt(50^2 + 150^2)

Diagonal distance = sqrt(25,000)

Diagonal distance = 158.11 feet

Round to 158 feet.

If the stayed on the sidewalk they would walk 50 + 150 = 200 feet.

The distance they saved = 200-158 = 42 feet

Answer: 42 feet.

Answer:

1.47

Step-by-step explanation:

  2.15

-0.68

borrow from the one now you have 15 minus 8 or 7next borrow from the 2 now you have 11 minus 6 or 5 then drop the one and drop the decimal hope this helped