Determine if I triangle can be constructed with the following sides. Explain
2/3 , 4/5 , 1/2


what value of x would allow a triangle to be constructed with the following measures?

a. 21,8,x
b. 13,7,x

The factors of n are 4y³, xy, and 8. So the correct options are:

Finding a number's prime factors in a way that the original number may be divided equally by them is known as prime factorization.

To find the factors of n, we need to consider all possible combinations of the prime factors 2, x, and y.

The factors of n can be found by taking all possible combinations of the exponents of the prime factors 2, x, and y, as long as the exponents are less than or equal to their respective powers in the prime factorization of n.

From the given prime factorization of n, we know that the powers of 2, x, and y are 5, 1, and 4, respectively.

Therefore, the possible factors of n are:

2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32

x⁰ = 1, x¹ = x

y⁰ = 1, y¹ = y, y², y³, y⁴

Now we can check which of the given numbers are factors of n:

Therefore, the factors of n are 4y³, xy, and 8. So the correct options are:

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Based on your question, it sounds like you are asking about random variables that have a joint probability density function (PDF) of 1/50 over a certain range of values.

In probability theory, a random variable is a variable whose value is determined by chance. It can take on a range of possible values, and the probabilities of each possible value occurring can be described using a probability distribution.

A joint probability density function is a function that describes the probabilities of two or more random variables taking on specific values simultaneously. In your case, you have two random variables that have a joint PDF of 1/50.

Without knowing the specific range of values over which the PDF is defined, it's hard to provide a more detailed answer. However, here are a few general observations about random variables and joint PDFs:

- Random variables can be either discrete or continuous. Discrete random variables take on specific, countable values (e.g. the number of heads in a series of coin tosses), while continuous random variables can take on any value within a certain range (e.g. the height of a randomly selected person).
- A joint PDF is typically used to describe the behavior of two or more continuous random variables. It gives the probability density at each point in the two-dimensional space defined by the values of the two variables.
- The total probability over the entire range of values for a joint PDF must sum to 1. This ensures that the probability of all possible outcomes occurring is equal to 1.

I hope this helps! If you have any further questions or clarifications, please let me know.
It seems that you are asking about random variables with a joint probability density function (pdf) of 1/50. Random variables are quantities that can take on different values according to some probability distribution. When two or more random variables are considered together, their relationship can be described using a joint pdf. In this case, the joint pdf is 1/50, indicating that the probability of a specific combination of these random variables is 1/50.

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If Jackson has  [tex]4\frac{1}{2}[/tex]  pounds of salt to fill in containers that hold 1/4 a pound then he fill 18 containers.

Given that Jackson has [tex]4\frac{1}{2}[/tex] pounds of salt

He has to fill in containers that hold 1/4 a pound

We have to find the number of containers to fill  [tex]4\frac{1}{2}[/tex] pounds of salt.

To find containers we have to divide  [tex]4\frac{1}{2}[/tex] pounds of salt by 1/4

[tex]4\frac{1}{2}[/tex]/1/4

(9/2)×4

36/2= 18

Hence, 18 contains can Jackson fill, option D is correct.

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The total number of routes possible is 6227020800, under the given condition that a overnight express company must include thirteen cities on its route, assuming that it does matter in which order the cities are included.

For this given question in order to find the accurate answer we have to perform calculations based on the principles of factorial operation.
The total  number of different routes possible, considering  that it matters in which order the cities are included  is 13!
The factorial of 13 is evaluated
13! = 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 6227020800
The total number of routes possible is 6227020800, under the given condition that a overnight express company must include thirteen cities on its route, assuming that it does matter in which order the cities are included.

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After matching the given angles to their values, the results are:

In the given unit circle we have the angle details and the value associated with that angle. From the given unit circle,

From the above analysis, we can match the given details.

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The transformations that maps triangle A onto triangle B are given as follows:

Examples of transformations are given as follows:

We note that the triangles have different orientations, hence the triangle A was reflected over the line y = 2.

The side lengths on triangle B are half the side lengths on triangle A, hence there was a dilation with a scale factor of 0.5.

Then the x-coordinates of the triangles had it's signal exchanged, meaning that the graph was reflected over the y-axis.

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It is recommended to consume a pre-competition meal consisting of an egg white sandwich with 2 egg whites and 2 pieces of white bread about 3-4 hours before the competition. This allows enough time for digestion and absorption of nutrients, while also preventing any discomfort or bloating during the event.

An explanation for this timing is that it takes around 3-4 hours for a meal to pass through the stomach and into the small intestine, where most of the nutrient absorption occurs.

Consuming a meal too close to the competition may cause digestive issues or an energy crash, while consuming it too far in advance may result in hunger or a drop in blood sugar levels.

In summary, timing is important when it comes to consuming a pre-competition meal. It is recommended to consume an egg white sandwich with 2 egg whites and 2 pieces of white bread about 3-4 hours before the competition to allow for proper digestion and absorption of nutrients, while also preventing discomfort or energy crashes during the event.

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Olivia plans to spend $44 on each nephew and $54 on each sister, for a total of $250 on presents.

What is variables?

In mathematics, a variable is a symbol or letter that represents a value that can change or vary. Variables are commonly used in algebraic expressions and equations to denote unknown values that need to be determined, or to represent values that can change in a given situation.

For example, in the equation y = 2x + 3, x is a variable that can represent any number, and y is the value that results from multiplying x by 2, adding 3, and solving for y. In this case, x can be any number, so it is a variable.

Let's start by assigning some variables to represent the amounts Olivia spends on each present. Let's call the amount she spends on each nephew "n" and the amount she spends on each sister "s". We know that Olivia has 2 nephews and 3 sisters, so we can write:

2n + 3s = 250

We also know that Olivia wants to spend $10 more on each sister than she spends on her nephew. In other words, the amount she spends on a sister is $10 more than the amount she spends on a nephew:

s = n + 10

Now we can substitute this expression for "s" into the first equation to get:

2n + 3(n + 10) = 250

Simplifying this equation, we get:

5n + 30 = 250

Subtracting 30 from both sides, we get:

5n = 220

Dividing both sides by 5, we get:

n = 44

So Olivia plans to spend $44 on each nephew. Using the equation s = n + 10, we can see that she plans to spend $54 on each sister.

To check that this solution works, we can verify that the total amount Olivia plans to spend on presents is equal to $250:

2(44) + 3(54) = 88 + 162 = 250

Therefore, Olivia plans to spend $44 on each nephew and $54 on each sister, for a total of $250 on presents.

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Check the picture below.

The expected number of assignments for Ms. Clea's advisory class in a day is 1.4.

The probability distribution can be written in a table as follows:

When Number of assignments 0,1,2,3, probability will be 0.3, 0.2, 0.3, 0.2 respectively.

To find the expected value, we can use the formula:

Expected value = Σ (number of assignments × probability)

where the sum is taken over all possible values of the number of assignments.

So, the expected value is:

Expected value

[tex] = (0 \times 0.3) + (1 \times 0.2) + (2 \times 0.3) + (3 \times 0.2) \\ = 0 + 0.2 + 0.6 + 0.6 \\ = 1.4[/tex]

Therefore, the expected number of assignments for Ms. Clea's advisory class in a day is 1.4.

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Answer:

10feet

Step-by-step explanation:

Calculate the length from the base of the stair to the walls of the house.

We have the ladder extend 2 feet beyond the edge of the roof so 28-2=26feet

Let x is the length from the base of the stair to the wall of the house

(26)²=(24)²+x²

x²=(26)²-(24)²=676-576=100

x=√100=10feet

So the length from the base of the stair to the wall of the house is 10 feet.

The margin of error for the proportion of all U.S. adults who think things are on the wrong track for 90% confidence is approximately 2.2%.

To calculate the margin of error, we first need to find the standard error, which can be calculated using the formula:
Standard Error = Square Root [ (p * q) / n ]
where p is the proportion of the sample who said things are on the wrong track (0.747), q is the complement of p (1 - p, which is 0.253), and n is the sample size (1997).
Plugging in the values, we get:
Standard Error = Square Root [ (0.747 * 0.253) / 1997 ] = 0.014
To find the margin of error at 90% confidence, we need to multiply the standard error by the z-score corresponding to 90% confidence, which is 1.645.
Margin of Error = 1.645 * 0.014 = 0.022 or approximately 2.2%

Hence, we can say with 90% confidence that the true proportion of all U.S. adults who think things are on the wrong track is between 72.5% and 77.0% (74.7% ± 2.2%).

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A model that could model the probability of a student participating is a model in which 3 out of 4 outcomes represent a success.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The participation rate in this problem is of 75%, which represents the probability of a success, hence we want to model an experiment in which 3 out of 4 outcomes represent a success.

One possible example is using numbers from 1 to 4, in which:

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Answer: x < 4

Step-by-step explanation:

    The graph uses an open circle, this means we will use the < or > symbol because it is not equal to.

    The open circle is on the 4.

    The arrow goes to the left of 4, meaning it is equal to values less than 4.

    Our inequality:

              x < 4

Answer: 40% of her budget

Step-by-step explanation:

Step-by-step explanation:

tan (40) = 1250 / x

x = 1250 / tan 40 = 1490 ft

The following are the values for the segments of the triangles:

4). a = 6.5

5). x = 2.7

6). x = 7.8 and y = 7.2

Using the proportionality theorem for calculating for the triangle segments as follows:

4). YZ/ZW = XY/XW

a/12 = 12/22

a = (12 × 12)/22 {cross multiplication}

a = 6.2

5). BC/CD = AB/AD

x/(7 - x) = 5/8

8x = 5(7 - x) {cross multiplication}

8x = 35 - 5x

8x + 5x = 35

13x = 35

x = 2.7

6). KL/LM = NK/NM

y/(15 - y) = 23/25

25y = 23(15 - y)

25y + 23y = 345

48y = 345

y = 7.2

x = LM so;

x = 15 - y

x = 15 - 7.2 = 7.8.

Therefore, the values for the segments of the triangles are:

4). a = 6.5

5). x = 2.7

6). x = 7.8 and y = 7.2

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A linear equation of the trend line (line of best fit) that models the data point contained in the table is y = 1.875x - 12.25.

In order to determine a linear equation of the trend line (line of best fit) that models the data point contained in the table (see attachment), we would have to first calculate the slope as shown below.

In Mathematics and Geometry, the slope of any linear equation can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided about the servers' collected tips (in dollars) with respect to customers, we have the following parameters:

Substituting the given points into the formula, we have;

Slope, m = (91 - 76)/(42 - 34)

Slope, m = 15/8

Slope, m = 1.875

At point (34, 76), the equation of this line is given by:

y - y₁ = m(x - x₁)

Where:

By substituting the data points, we have;

y - 76 = 1.875(x - 34)

y - 76 = 1.875x - 63.75

y = 1.875x - 63.75 + 76

y = 1.875x - 12.25

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Answer: 3%

Step-by-step explanation:

We can use this equation to solve for the simple interest:

        A = P(1 + rt)

We will substitute our known values and solve:

➜ A = final amount ($5,000 + $600 = $5,600)

➜  P = initial balance ($5,000)

➜  r = interest rate (solving for r)

➜  t = time (4 years)

        A = P(1 + rt)

        5,600 = 5,000(1 + (r)(4))

        [tex]\frac{5,600}{5000}[/tex] = 1 + (r)(4)

        1.12 = 1 + 4r

        0.12 = 4r

        4r = 0.12

        r = 0.03

        r = 3%

Therefore, the image of the point (0, -7) after a dilation by a scale factor of 4 centered at the origin is (0, -28).

In mathematics, a scale factor is a numerical value that describes how much an object has been scaled or resized. It is the ratio of the size of the image to the size of the original object. Scale factors can be applied to two-dimensional or three-dimensional objects, and can be used to describe enlargements (scaling up) or reductions (scaling down) of the object.

Here,

To find the image of the point (0, -7) after a dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) is the original point, (x', y') is the image of the point after dilation, k is the scale factor, and the dilation is centered at the origin.

In this case, the original point is (0, -7), the scale factor is 4, and the origin is (0, 0). Plugging these values into the formula, we get:

(x', y') = (4 * 0, 4 * (-7))

Simplifying, we get:

(x', y') = (0, -28)

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The angle in degrees at the center of Aron's slice of cake is (A / (A + K + G)) × 360 degrees.

Assuming that the cake is divided into three slices, with each slice having a size proportional to the age of each person, let A, K, and G represent the ages of Aron, Kai, and Grace, respectively. Then, the total size of the cake can be represented as A + K + G.

Let x be the size of Aron's slice of cake. Then, Kai's slice of cake is (K / (A + K + G)) × 360 degrees, and Grace's slice of cake is (G / (A + K + G)) × 360 degrees.

Since the total angle at the center of the cake is 360 degrees, we can write

x + (K / (A + K + G)) × 360 degrees + (G / (A + K + G)) × 360 degrees = 360 degrees

Simplifying this equation, we get

x = (A / (A + K + G)) × 360 degrees

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The equation of the line with slope -1.5 and passing through origin in slope intercept form is given by y = -1.5x + 0

Slope of the line = -1.5

and one of the coordinates is at the origin.

let us consider the coordinate of the origin as ( x₁ , y₁ ).

Use the point-slope form of a linear equation to write the equation of the line as,

y - y₁= m(x - x₁)

where m is the slope

and (x₁, y₁) is the point on the line.

(x₁, y₁) =  (0, 0)

Since the line passes through the origin.

Substituting the values, we get,

⇒ y - 0 = -1.5(x - 0)

Simplifying, we get,

⇒ y = -1.5x

Here,

y = -1.5x + 0

y-intercept is 0

Therefore , the equation of the line in slope intercept form is equal to y = -1.5x + 0.

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The given question is incomplete, I answer the question in general according to my knowledge:

Given the line:

The slope of the line is -1. 5 and one of the coordinate is at the origin .Write the equation of the line in slope intercept form.

The statement that is true if the measures of the sides of the original square is that each side of the original square is 4 times the length of each side of the scale model. That is option B.

To determine the dimensions of the original square is through the formula of the scale factor. That is;

Scale factor = original scale/scale model

The given scale factor = 4

the dimensions of square model = 8

Therefore the original dimensions of the square = 4×8 = 32ft

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1) The Combination, Probability is (5C2 x 12C3) / 30C5

2) The Combination, Probability is (C(4,7) x C(2,5)) / C(6,12)

3) The Combination, Probability is (C(3,5) x C(3,5)) / C(6,10)

4) The Permutation, Probability is 1 / P(50,3)

1) This situation is describing a combination because the order in which the students are chosen does not matter. The probability of randomly choosing 2 blonde girls and 3 dark-haired boys can be found as follows:

Number of ways to choose 2 blonde girls out of 5 = C(5, 2) = 10

Number of ways to choose 3 dark-haired boys out of 12 = C(12, 3) = 220

Total number of ways to choose 5 students out of 30 = C(30, 5) = 142,506

Probability = (10 x 220) / 142,506 = 0.0154

Therefore, the probability of randomly choosing 2 blonde girls and 3 dark-haired boys if 5 students are randomly chosen to be class representatives is 0.0154.

2) This situation is describing a permutation because the order in which the smartphones are sold matters. The probability that exactly four of the first six sold have cracked screens can be found as follows:

Number of ways to choose 4 cracked screens out of 7 = C(7, 4) = 35

Number of ways to choose 2 intact screens out of 5 = C(5, 2) = 10

Number of ways to arrange the 6 chosen smartphones = P(6, 6) = 720

Probability = (35 x 10 x P(6, 6-4)) / P(12, 6) = 0.078

Therefore, the probability that exactly four of the first six sold have cracked screens is 0.078.

3) This situation is describing a combination because the order in which the songs are listened to does not matter. The probability that exactly three country songs are listened to can be found as follows:

Number of ways to choose 3 country songs out of 5 = C(5, 3) = 10

Number of ways to choose 3 pop songs out of 5 = C(5, 3) = 10

Total number of ways to choose 6 songs out of 10 = C(10, 6) = 210

Probability = (10 x 10) / 210 = 0.476

Therefore, the probability that exactly three country songs are listened to is 0.476.

4) This situation is describing a permutation because the order in which the hurdlers finish matters. The probability of randomly choosing the correct finishing order of the first, second, and third place for the hurdlers out of 50 contestants can be found as:

Probability = 1 / P(50, 3) = 1 / 117,600

Therefore, the probability of randomly choosing the correct finishing order of the first, second, and third place for the hurdlers out of 50 contestants is approximately 0.0000085.

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Answer: First one

Step-by-step explanation:

The length of the third wire piece is [tex]7 / 20 m[/tex].

A length means the measurement or extent of something from end to end. It is the measure of distance from Point A to Point B.

Given:

First piece length = 3/20 m

The second piece length is:

= (5/3) x (3/20) m

= 1/4 m

The total length of the first two pieces is:

= 3/20 m + 1/4 m

= 2/5 m

The length of the third piece will be:

= Total length - Length of first two pieces

= 3/4 m - 2/5 m

= (15 - 8) /20

= 7/20 m.

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Answer:

An angle that has a measure between 90 and 180 degrees is called an obtuse angle. An obtuse angle is characterized by having a measure greater than 90 degrees but less than 180 degrees. In other words, the angle "opens up" more than a right angle (which has a measure of 90 degrees) but less than a straight angle (which has a measure of 180 degrees).                                                                             Obtuse

Step-by-step explanation:

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Answer: 4cm² 

Step-by-step explanation:

To find the area of a triangle, we can use the formula:

Area: (base x height) ÷ 2

In this case, the base of the triangle is 4cm and the height of the triangle is 2cm. We simply replace the values with the variables in the formula. So, we get:

Area: (4cm x 2cm) ÷ 2

Area: 8cm² ÷ 2

Area: 4cm² 

Therefore, the area of the triangle is 4cm².

The area of the circle Z is 72.1 square cm and the length of the segment XV is 9 cm

Given that

Arc XY = 40 degrees

This means that

∠V = 1/2 * 40 degrees

∠V = 20 degrees

The angle in a semicircle is a right-angle

So, we have

∠X = 90 degrees

So, we calculate the length VZ using

cos(V) = XV/2VZ

This gives

cos(20) = 9/2VZ

So, we have

VZ = 9/[2 cos(20)]

Evaluate

VZ = 4.79

The area is calculated  using

Area = πVZ²

So, we have

Area = π * 4.79²

Evaluate

Area = 72.1

Hence, the area is 72.1 square cm and the length XV is 9 cm (given)

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