convert x>4 to interval notation

The probability of a card being black given it is a queen is P(A|B) = P(A ∩ B) / P(B) = (4/52) / (4/52) = 1. This means that if you draw a queen from a standard deck of 52 cards, it will be black with a probability of 100%.

The probability of a card being black given it is a queen can be determined using the formula P(A|B) = P(A ∩ B) / P(B). Where P(A) is the probability of a card being black and P(B) is the probability of a card being a queen.

To calculate this, we first need to calculate the probability of a card being a queen, which is 4/52 (there are 4 queens in a standard deck of 52 cards). The probability of a card being black is 26/52 (there are 26 black cards in a standard deck of 52 cards).

Using the formula, the probability of a card being black given it is a queen is P(A|B) = P(A ∩ B) / P(B) = (4/52) / (4/52) = 1. This means that if you draw a queen from a standard deck of 52 cards, it will be black with a probability of 100%.

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There are no sign changes in the first column of the Routh array, therefore the system is stable.

Given: Characteristic equation for system `(a)`: 12s⁵ + 4s⁴ + 6s³ + 2s² + 6s + 4 = 0

Characteristic equation for system `(b)`: 12s⁵ + 8s⁴ + 18s³ + 12s² + 9s + 6 = 0

To determine the stability of the systems with the given characteristic equations, we need to find out the roots of the given polynomial equations and check their stability using Routh-Hurwitz criteria.

To find out the stability of the system with given characteristic equation, we have to check the conditions of Routh-Hurwitz criteria.

Let's discuss these conditions:1. For the system to be stable, the coefficient of the first column of the Routh array must be greater than 0.2.

The number of sign changes in the first column of the Routh array represents the number of roots of the characteristic equation in the right-half of the s-plane.

This should be equal to zero for the system to be stable.

There should be no row in the Routh array which has all elements as zero.

If any such row exists, then the system is either unstable or marginally stable.

(a) Let's calculate Routh-Hurwitz array for the polynomial `12s⁵ + 4s⁴ + 6s³ + 2s² + 6s + 4 = 0`0: 12 6 42: 4 2.66733: 5.6667 2.22224: 2.2963.5 0.48149

Since, there are 2 sign changes in the first column of the Routh array, therefore the system is unstable.

(b) Let's calculate Routh-Hurwitz array for the polynomial `12s⁵ + 8s⁴ + 18s³ + 12s² + 9s + 6 = 0`0: 12 18 62: 8 12 03: 5.3333 0 04: 2 0 05: 6 0 0

Since there are no sign changes in the first column of the Routh array, therefore the system is stable.

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Answer:

(x+1) (x-1)

Step-by-step explanation:

rewrite 1 as 1^2

Apply diffrence of two squares formula

x^2-y^2= (x+y)(x-y)

x^2-1^2= (x+1) (x-1)

(a) In trade equilibrium, the consumption point for the Home consumer can be shown on a graph where wheat is on the x-axis.

(b) If the world relative price increases above 2/3, the Foreign consumer's utility will decrease compared to the benchmark trade equilibrium with a world price of 2/3.

a, Since the relative price of wheat to cloth is 2/3, the Home consumer's consumption point will lie on a budget line with a slope of -2/3. The specific coordinates of the consumption point cannot be determined without additional information about preferences and the Home consumer's budget constraint.

To show that an increase in the relative price of wheat from 2/3 raises Home's utility, we need to consider the concept of substitution effect. When the relative price of wheat increases, it becomes relatively more expensive compared to cloth. The Home consumer will respond by consuming less wheat and more cloth, moving along the budget line to a new consumption point. This movement is driven by the substitution effect, where the consumer substitutes away from the now relatively more expensive wheat towards the relatively cheaper cloth. Since the Home consumer's preferences and utility are not known, the specific utility level cannot be quantified, but it can be concluded that the utility increases due to the substitution effect.

b.  In the benchmark equilibrium, the Foreign consumer maximizes utility given the initial relative price. If the relative price increases, it means that wheat becomes relatively more expensive compared to cloth in the world market.

As a result, the Foreign consumer will have to consume less wheat and more cloth in order to remain on the same budget line. This movement along the budget line leads to a decrease in utility because the consumer has to give up some desired wheat consumption to obtain more cloth. The magnitude of the utility decrease depends on the specific preferences and utility function of the Foreign consumer, but it can be concluded that the utility will be lower when the relative price of wheat increases above 2/3 in the world market.

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Answer: The total number of cups in half-gallon of water are 8 cups.

Step-by-step explanation:

80/5=16 cups=1 gallon

16/2=8 cups=1/2 gallon

a) Matrix A: Determinant = 4, nonsingular, inverse exists.

b) Matrix B: Determinant = 0, singular, inverse does not exist.

c) Matrix C: Determinant = 0, singular, inverse does not exist.

d) Matrix D: Determinant = -6, nonsingular, inverse exists.

To find the determinant of a matrix, we can use the formula for a 2x2 matrix:

For a matrix A = [a b; c d], the determinant det(A) is calculated as: det(A) = ad - bc.

Let's calculate the determinants for each matrix:

a) A = [2, 0; 0, 2]

det(A) = (2 * 2) - (0 * 0) = 4 - 0 = 4

b) B = [1, 4; 2, 8]

det(B) = (1 * 8) - (4 * 2) = 8 - 8 = 0

c) C = [6, -15; -2, 5]

det(C) = (6 * 5) - (-15 * -2) = 30 - 30 = 0

d) D = [0, 3; 2, 2]

det(D) = (0 * 2) - (3 * 2) = 0 - 6 = -6

Now, let's determine if each matrix is nonsingular and if its inverse exists:

A matrix is nonsingular if and only if its determinant is non-zero.

a) Matrix A: det(A) = 4 ≠ 0

Since the determinant is non-zero, matrix A is nonsingular and its inverse exists.

b) Matrix B: det(B) = 0

The determinant is zero, which means matrix B is singular, and its inverse does not exist.

c) Matrix C: det(C) = 0

The determinant is zero, which means matrix C is singular, and its inverse does not exist.

d) Matrix D: det(D) = -6 ≠ 0

Since the determinant is non-zero, matrix D is nonsingular and its inverse exists.

To summarize:

a) Matrix A: Determinant = 4, nonsingular, inverse exists.

b) Matrix B: Determinant = 0, singular, inverse does not exist.

c) Matrix C: Determinant = 0, singular, inverse does not exist.

d) Matrix D: Determinant = -6, nonsingular, inverse exists.

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Answer:

5/8 is the length. Just divide 15/56 by 3/7.

hope this helps

The domain of the given expression is all real numbers except for a = b and a = (2ab - b) / (b + 1).

To find the domain of the expression

a/a-b+3a/a+b-2ab/a²-b²,

we should apply the following steps:

Step 1: For a fraction to be well-defined, its denominator cannot be zero.

Therefore, set the denominator equal to zero and solve it for a.

The denominator is

(a-b)(a+b-2ab).

Setting the denominator to zero, we have

(a - b)(a + b - 2ab) = 0.

Now, solving it for a, we have a = b and a = (2ab - b) / (b + 1)

Step 2: Since a is present in every term of the expression, it can assume any real value.

Therefore, the domain of the given expression is all real numbers except for a = b and a = (2ab - b) / (b + 1).

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Answer:

0.39

Step-by-step explanation:

Hope it is helpful....

Therefore , the solution of the given problem of average comes out to be the average price of a pizza in 2000 was about $9 (or half of $18).

An organised collection's median value is the precise value that makes up the collection's mean. In this case, the ratio between the lowest and highest 50% of the data is a normal but rather probability measure. When finding the middle and mode, a variety of algorithms can be applied in order to identify any unusual or even amounts of values.

Here,

By dividing 72 by the interest rate, we can calculate how many years it will take an investment to double in value at a specific interest rate. This is known as the law of 72. In this instance

With an inflation rate of 3.25 percent, it takes roughly how many years for the price of a pizza to double as a result of inflation:

72 / 3.25 = 22.15 years

In light of this, we can calculate that a pizza cost $9 (half of $18) roughly 22 years ago, which corresponds to the following year:

2022 - 22 ≈ 2000

As a result of inflation running at an average of 3.25% for many years, the average price of a pizza in 2000 was about $9 (or half of $18).

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Yes, the forester was justified in using a Normal model to analyze the woods, because the histogram is unimodal and symmetric. So option A is correct.

A histogram is a type of graph that uses vertical bars to show the distribution of a set of data. This particular histogram is unimodal, meaning that it has one peak which is an indication that the data is distributed normally. Additionally, the histogram is symmetric, which is another indication that the data is normally distributed.
Using a Normal model to analyze the woods is a valid approach because it allows the forester to identify the average diameter of the trees, as well as the spread of the data. It also allows him to check for any outliers, or points that fall outside the normal range. With this information, the forester can determine if the woods is suitable for sale, or if the buyer should be aware of any unexpected features.
Overall, the histogram is an effective way for the forester to analyze the data and determine if a Normal model is appropriate. By noting the unimodal and symmetric nature of the histogram, the forester can be sure that a Normal model will accurately represent the data, allowing him to make an informed decision about the woods.

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Answer:

Step-by-step explanation:

NO! Hope I helped.

a) Since the distribution of the number of pets per household is right-skewed, the majority of households in the US would have a number of pets that is less than 3.5.

b) The expected value of the mean number of pets that the 60 households have is still 3.5 pets because the mean of the population is assumed to be 3.5 pets.

c) The standard deviation of the mean number of pets per household in the sample of 60 households can be calculated as follows:

Standard deviation = population standard deviation / square root of sample size

Standard deviation = 1.7 / sqrt(60) = 0.2198 (rounded to 4 decimal places)

d) The standard deviation of the average number of pets per household in the sample of 60 households computed in part (c) is much lower than the population standard deviation of 1.7 pets because the standard deviation of the sample mean decreases as the sample size increases. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution.

e) Yes, we can calculate the probability that  this household has more than 4 pets

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The  work done in pulling the rope to the top of the building is 88,550 joules.

To calculate the work done in pulling the rope to the top of the building, we need to find the gravitational potential energy of the rope when it is at the bottom and at the top of the building.

At the bottom of the building, the rope has a length of 50 ft and a weight of 0.5 lb/ft, so its total weight is:

W1 = (50 ft) x (0.5 lb/ft) = 25 lb

The gravitational potential energy of the rope at the bottom of the building is:

U1 = mgh = (25 lb) x (32.2 ft/s^2) x (0 ft) = 0 J

where m is the mass of the rope, g is the acceleration due to gravity, and h is the height of the rope above the ground.

At the top of the building, the rope has a length of 50 ft but is now lifted 110 ft above the ground, so its total weight is:

W2 = (50 ft) x (0.5 lb/ft) = 25 lb

The gravitational potential energy of the rope at the top of the building is:

U2 = mgh = (25 lb) x (32.2 ft/s^2) x (110 ft) = 88,550 J

The work done in pulling the rope to the top of the building is equal to the change in gravitational potential energy of the rope and is given by:

W = U2 - U1 = 88,550 J - 0 J = 88,550 J

Therefore, the work done in pulling the rope to the top of the building is 88,550 joules.

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Step-by-step explanation:

(-)(-) = +

\( - \frac{3}{5} + \frac{5}{9} \)

\( - \frac{27}{45} + \frac{25}{45} \)

\( - \frac{2}{45} \)

the roots of the function is 0, 1 and 9 (option D)

see graph below

The given function:

We need to find the root of the function. The roots are the value of x when f(x) = 0

So, the roots of the function is 0, 1 and 9

These are the points the line crosses the x axis.

We need to check for the graph whose line crosses he x axis at x = 0, x = 1 and x = 9 (option D)

The factorial or ratio of p / q approximately is 1199.5.

Calculate p (number of ways to place 5 queens randomly on a chessboard):

A chessboard has 64 squares. We can place the first queen in any of the 64 squares, the second queen in any of the remaining 63 squares, and so on.

So, the number of ways to place 5 queens randomly is: p = 64 * 63 * 62 * 61 * 60 However, since the order in which we place the queens does not matter, we need to divide by the number of ways to arrange the 5 queens,

which is 5! (5 factorial). p = (64 * 63 * 62 * 61 * 60) / (5 * 4 * 3 * 2 * 1) 2=8,048,640

Calculate q (number of ways to place 5 queens column-wise):

We need to find the value of q. Here, we place 5 queens column-wise. In the first column, there are 8 possible squares to place the first queen. In the second column, there are only 7 possible squares left because one square is already blocked by the first queen.

Similarly, in the third column, there are only 6 possible squares left, and so on. Therefore, the total number of ways to place the 5 queens column-wise is: 8 × 7 × 6 × 5 × 4= 6,720

Calculate the ratio p / q:

Now that we have values for p and q, we can find the ratio p / q. p / q ≈ ((64 * 63 * 62 * 61 * 60) / (5 * 4 * 3 * 2 * 1)) / (8 × 7 × 6 × 5 × 4) ≈ 1199.5

Therefore, the ratio of p / q approximately is 1199.5.

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The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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The value of 'a' that makes the given system a dependent system is 4.

To make the given system a dependent system, we need to find the value of 'a' that makes both equations equivalent or proportional.

Let's begin by rearranging the first equation so that it is in the standard form y = (2/3)x.

Now, let's substitute this expression for y in the second equation and simplify:

6y - a - 4x = 0

6(2/3)x - a - 4x = 0

4x - a = 0

We can see that if we choose 'a' to be equal to 4, then both equations will be equivalent. In other words, the system will become a dependent system with infinitely many solutions.

To see why, let's substitute 'a' as 4:

6y - 4 - 4x = 0

6y - 4x = 4

Now, if we compare this equation to the first one we wrote, y = (2/3)x, we can see that they are equivalent. Thus, any solution that satisfies the first equation will also satisfy the second equation, and vice versa. This means that we have infinitely many solutions to the system.

In conclusion, the value of 'a' that makes the given system a dependent system is 4.

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Answer:

x=3

Step-by-step explanation:

The equation here is x=3. If it were y=3, then it would be a horizontal line.

Answer:

900 km/h

Step-by-step explanation:

The surface area of a square pyramid, we need to add the area of each of its faces. In this case, we have four triangular faces and one square base. Let's start by finding the area of the square base. So, the surface area of the square pyramid is 384 square inches.

To find the surface area of a square pyramid, we need to add the area of each of its faces. In this case, we have four triangular faces and one square base

The area of a square is given by the formula A = s^2, where s is the length of a side. In this case, the base of the pyramid has a side length of 12 in, so its area is:

A = 12^2

A = 144 sq in

Now let's find the area of each triangular face. The formula for the area of a triangle is A = 1/2bh, where b is the base length and h is the height. Each triangular face has a base length of 12 in and a height of 10 in, so its area is:

A = 1/2(12)(10)

A = 60 sq in

Since there are four triangular faces, the total area of the triangular faces is:

4 × 60 = 240 sq in

Finally, we can add the area of the base and the area of the triangular faces to get the total surface area of the pyramid:

144 + 240 = 384 sq in

1. Identify the given measurements:

 Base length (b) = 12 in

 Triangular face base length (tf_b) = 12 in

 Triangular face height (tf_h) = 10 in

2. Calculate the surface area of the square base:

 Base area (A_base) = b^2 = (12 in)^2 = 144 sq in

3. Calculate the area of one triangular face:

 Triangular face area (A_tf) = 0.5 * tf_b * tf_h = 0.5 * (12 in) * (10 in) = 60 sq in

4. Since there are four triangular faces, find the total area of all triangular faces:

 Total triangular face area (A_tfs) = 4 * A_tf = 4 * (60 sq in) = 240 sq in

5. Finally, add the base area and the total triangular face area to find the surface area of the pyramid:

 Surface area (SA) = A_base + A_tfs = (144 sq in) + (240 sq in) = 384 sq in

So, the surface area of the square pyramid is 384 square inches.

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Answer: in decimal form=0.14644660

Step-by-step explanation:

Answer:

5 2/3

Step-by-step explanation:

:)

it would be A. 5 and 2/3

brainliest..

Step-by-step explanation:

the correct answer is option a 6a-7