(07.02 mc) which ordered pair is included in the solution set to the following system? y < x2 3 y > x2 – 2x 8

Answer:

The width of the frame must be 12 inches (15in by 12in)

Step-by-step explanation:

Given

See attachment for painting and frame

Required

Determine the dimension of the frame

To do this, we make use of the following scale ratio.

\(Scale = Length : Width\)

For the painting,

\(Scale = 20: 16\)

For the frame,

\(Scale = 15: w\)

Since she wants to maintain the same ratio; both scale must be the same.

i.e.

\(15 : w = 20 : 16\)

Express as fraction

\(\frac{w}{15} = \frac{16}{20}\)

\(\frac{w}{15} = 0.8\)

Make w the subject

\(w = 15 * 0.8\)

\(w = 12\)

The width of the frame must be 12 inches i.e. 15in by 12in frame

The values that represent the possible distance, d, in miles, between Lincoln, NE, and the third city are given as follows:

300 < d < 699.

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements for this problem are given as follows:

Then if 500 miles is the largest distance, we have that:

x can be between 300 and 500.

If x is the largest distance, we have that:

x can be between 501 and 699.

Then the range of possible distances is given as follows:

300 < d < 699.

(which are the distances for each case).

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Answer:

see picture

Step-by-step explanation:

2DuT = 2u·∇T = 2( (√3/2) * sin(2*(√3/2)) + (-1/2) * cos(2*(√3/2)) )

The result is the rate of change of temperature experienced by the insect at point P in degrees Celsius per second.

To find the rate of change of temperature experienced by the insect at point P(1/2, √3/2), we will use the gradient of the temperature function T(x,y) = xsin(2y) and the given unit velocity vector u = (√3/2, -1/2).

First, let's compute the partial derivatives of T(x,y) with respect to x and y:

∂T/∂x = sin(2y)
∂T/∂y = 2x*cos(2y)

Now, let's evaluate the partial derivatives at point P(1/2, √3/2):

∂T/∂x (1/2, √3/2) = sin(2*(√3/2))
∂T/∂y (1/2, √3/2) = 2*(1/2)*cos(2*(√3/2))

Next, we form the gradient vector ∇T = (∂T/∂x, ∂T/∂y) at P:

∇T = (sin(2*(√3/2)), cos(2*(√3/2)))

Finally, we calculate 2DuT at P by taking the dot product of the unit velocity vector u and the gradient vector ∇T:

2DuT = 2u·∇T = 2( (√3/2) * sin(2*(√3/2)) + (-1/2) * cos(2*(√3/2)) )

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Answer:

-4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

i jus took the quiz on edge

Answer: (2x+6y)^2 = (2x+6y)(2x+6y) = 4x^2 +12xy + 12yx + 36y^2 = 4x^2 + 24xy + 36y^2

So the result of (2x+6y)^2 is 4x^2 + 24xy + 36y^2

Answer:

1 litro de leche cuesta 2.5

1 kg de jamón serrano cuesta 35

1 litro de aceite de oliva cuesta 7,5

Step-by-step explanation:

Pregunta correcta completa

Un cliente de un supermercado ha pagado un total de 240 por 16 litros de leche,4kg de hamon serrano y 8 litros de aceite de oliva. Sabiendo que 1 litro de aceite cuesta el tripe de 1 litro de leche; que 1kg de jamon cuesta igual que el cliente tendria que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva. Calcule el precio de cada artículo.

Solución

Deje que el precio de un litro de leche, un kilogramo de jamón serrano y un litro de aceite de oliva sea x, y y z respectivamente.

16 litros de leche, 4 kg de hamon serrano y 8 litros de aceite de oliva cuestan 240

16x + 4y + 8z = 240 (ecuación 1)

1 litro de aceite cuesta el triple de 1 litro de leche

z = 3x (ecuación 2)

Y ese 1 kg de jamón cuesta lo mismo que el cliente tendría que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva.

y = 5x + 3z (ecuación 3)

Sustituyendo las ecuaciones 2 y 3 en la ecuación 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recordemos que z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

English Translation

A supermarket customer has paid a total of 240 for 16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil. Knowing that 1 liter of oil costs the tripe of 1 liter of milk; t that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil. Calculate the price of each item.

Solution

Let the price of a liter of milk, a kilogram of Serrano ham and a liter of olive oil be x, y and z respectively.

16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil cost 240

16x + 4y + 8z = 240 (eqn 1)

1 liter of oil costs the triple of 1 liter of milk

z = 3x (eqn 2)

And that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil

y = 5x + 3z (eqn 3)

Substituting eqn 2 and 3 into eqn 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recall that z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

1 liter of milk costs 2.5

1 kg of Serrano ham costs 35

1 liter of olive oil costs 7.5

Hope this Helps!!!

Ratio compares two things. The length of the trail, in reality, is 6.75 km.

A scaling ratio helps us to compare two things.

Given to us

The scale on the map states that 2 centimeters represent 3 kilometers.

Length of the trail on the map, L = 4.5 cm = 0.045 m

As we know that 2 centimeters represent 3 kilometers. therefore,

\(\rm \dfrac{Map}{Real} = \dfrac{0.02\ m}{3000\ m}\)

We know that the Length of the trail on the map is 0.045 m,

\(\rm \dfrac{L}{L'} = \dfrac{0.02\ m}{3000\ m}\)

Substitute the value,

\(\rm \dfrac{0.045}{L'} = \dfrac{0.02\ m}{3000\ m}\\\\L' = 6750\ m\\\\L' = 6.750\ km\)

Hence, the length of the trail, in reality, is 6.75 km.

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The total distance traveled by the particle over the time interval [1, 5] is 12 units.

To find the total distance traveled, we need to consider both the magnitude and direction of the velocity function. Since the velocity function given is in meters per second (m/sec), the total distance traveled will be measured in meters.

To calculate the total distance, we need to consider the intervals where the velocity function changes its sign. In this case, the velocity function is linear and increasing, starting at t = 1 with a velocity of 3 m/sec. From t = 1 to t = 3, the particle moves in the positive direction, covering a distance of (3t - 9) × (t - 1) = 12 units. From t = 3 to t = 5, the particle moves in the negative direction with the same magnitude, covering a distance of (-1) × (3t - 9) × (t - 3) = 12 unit

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The number of students should be invited to a party to make sure that ap least two of them have the same initials are equals to the 677 (students).

The solution of this problem is obtained by using the pigeonhole principle, which states if there are N boxes and N+1 pigeons, at least two pigeons must be in the same box. We have to determine the number of students invited in party to make make sure that at least two of them have the same initials. Now, first we figure out what N is to solve the problem. Here, box for this problem is labelled by first and last initials. If we are using the A-Z alphabet, then there are 26×26 = 676 possible sets of initials.

As soon as there are N+ 1 or 677 people, at least two must have the same first and last initials. Hence, required value is 677.

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It will take 5 years to recoup the extra cost of buying the Prius.

The number of years it will take to recoup the extra cost of buying the Prius will depend on several factors such as the price of the car, the cost of gas, and the average number of miles driven per year. However, according to a study by Consumer Reports, the Prius has an average payback period of about 4 years compared to a similar gas-powered vehicle. This means that if the extra cost of buying the Prius is $4,000, for example, it would take about 4 years to recoup that cost through fuel savings. Keep in mind that this is just an estimate and individual results may vary.
To determine the number of years it will take to recoup the extra cost of buying the Prius, follow these steps:

1. Identify the extra cost of buying the Prius compared to a similar non-hybrid vehicle.
2. Determine the annual fuel cost savings of the Prius compared to the non-hybrid vehicle.
3. Divide the extra cost by the annual fuel cost savings.

For example, let's say the extra cost of buying the Prius is $5,000 and the annual fuel cost savings is $1,000.

Number of years to recoup extra cost = Extra cost / Annual fuel cost savings
Number of years = $5,000 / $1,000
Number of years = 5.00

So, it will take 5.00 years to recoup the extra cost of buying the Prius.

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To determine if a(n) (not an event) of flipping a coin is heads is valid, we need to ensure that all probabilities are between 0% and 100% and the sum of all probabilities is 100%.

In probability theory, it is important to ensure that the probabilities associated with an event or outcome are valid. When flipping a coin, if we define the event "a" as getting heads, we need to check that the probability of heads is between 0% and 100% and that the sum of the probabilities of all possible outcomes (heads and tails) is 100%. This ensures that the probabilities are within a valid range and account for all possibilities.

The ratio of the ways to succeed (the favorable outcomes) to all possible ways that something can occur (the total outcomes) is known as the probability. It represents the likelihood of a specific outcome occurring relative to all possible outcomes. By calculating this ratio, we can quantify the probability of an event happening.

When dealing with a multi-step process, the multiplication principle is used to determine the total number of ways the process can be completed. It states that if there are "n" independent steps, and each step has "m" possible outcomes, then the total number of ways the process can be completed is the product of the number of outcomes at each step. This principle is based on the concept that each step's outcomes are independent of the others, allowing us to multiply the possibilities together to determine the overall number of ways the process can unfold.

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The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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Answer:

7

Step-by-step explanation:

Answer:  E, A, D, C, B

Step-by-step explanation:

First, we need to get y alone. So we will add 7 to the side of the equation that has the 4y in it.

So the first one will be.

Add 7 to both sides of the equation.

Now the second one is

4y = 25 + 7  Because what you do to one side of the equation, you do to the other. So we add 7 to 25.

Then the 3rd one will be 4y = 32  because 25+7 is equal to 32. But we still have that 4y on the other side of the equation. So the next equation is 4y = 32.

The second to last step is Divide both sides by 4  because thats

how you isolate y. So once you divide both sides by 4. You will get 8. Leading you into the next and final step.

Y = 8

And thats how you do it!

Answer:

Substitute the given value for the  

✔ variable

.

Use the  

✔ order of operations

to simplify.

First, complete the  

✔ multiplication

inside the parentheses.

Next, complete the  

✔ addition

inside the parentheses.

Last, complete the subtraction.

The value is  

✔ 1

.

Step-by-step explanation:

Answer:Evaluate (3n + 2) – 10 when n = 3.

First, evaluate within the parentheses. Then evaluate exponents. Next multiply and divide from left to right. Then, add and subtract from left to right.

Evaluate the expression for the given value of the variable and use the drop-down menus to complete the statements.

Substitute the given value for the

✔ variable

.

Use the

✔ order of operations

to simplify.

First, complete the

✔ multiplication

inside the parentheses.

Next, complete the

✔ addition

inside the parentheses.

Last, complete the subtraction.

The value is

✔ 1

.

Step-by-step explanation:

The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.

The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).

In other words, it tells us how much the information values are scattered around the mean.

When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.

This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.

This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.

For case, let's consider two sets of information:

Set A and Set B.

Set A:

2, 3, 4, 5, 6

Set B:

1, 3, 5, 7, 9

Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).

This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.

Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.

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Categorical are assigned to discrete categories; continuous can take any value in a range.

Categorical Data Variable:

Categorical data is a statistical data type that consists of categorical variables or data transformed into that form, such as clustered data. More specifically, categorical data can be derived from observations made from qualitative data grouped as counts or crosstabs, or from quantitative data observations grouped within specified intervals . Purely categorical data are often summarized in the form of contingency tables. However, when specifically considering data analysis, it is common to use the term "categorical data" for data sets that contain some categorical variables and may also contain non-categorical variables.

Continuous Data Variable:

A continuous variable is defined as a variable that can take an uncountable set of values ​​or an infinite set of values. For example, if a variable is a continuous non-empty range of real numbers, it can take on any value within that range. Thus the range of real numbers between x and y is x, y ∈ R and x ≠ y. It must be uncountable and infinite.

Categorical is independent (explanatory); continuous is dependent (response) is wrong since categorical variable can also be dependent.

Categorical are subjective (based on researcher’s judgment); continuous are measured is wrong since categorical variable may not be subjective.

Categorical can be measured accurately; continuous have to be estimated is wrong since continuous variable can also be measured.

Categorical are assigned to discrete categories; continuous can take any value in a range. This is true

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Answer:

\(x=7\)

Step-by-step explanation:

\(-3x--3+8x-24=6x+7-5x\)

Two negative signs equate to a positive sign, so we can write \(--3\) as just \(3\):

\(-3x+3+8x-24=6x+7-5x\)

Add up similar terms:

\(5x-21=x+7\)

Add 21 to both sides:

\(5x-21+21=x+7+21\)

\(5x=x+28\)

Subtract x from both sides:

\(5x-x=x+28-x\)

\(4x=28\)

Divide both sides by 4:

\(\frac{4x}{x} =\frac{28}{4}\)

\(x=7\)

a) The center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

b) We have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

(a) Deriving the class equation of a finite group G involves partitioning the group into conjugacy classes. Conjugacy classes are sets of elements in the group that are related by conjugation, where two elements a and b are conjugate if there exists an element g in G such that b = gag^(-1).

To derive the class equation, we start by considering the group G and its conjugacy classes. Let [a] denote the conjugacy class containing the element a. The class equation is given by:

|G| = |Z(G)| + ∑ |[a]|

where |G| is the order of the group G, |Z(G)| is the order of the center of G (the set of elements that commute with all other elements in G), and the summation is taken over all distinct conjugacy classes [a].

The center of a group, Z(G), is the set of elements that commute with all other elements in G. It can be written as:

Z(G) = {z in G | gz = zg for all g in G}

The order of Z(G), denoted |Z(G)|, is the number of elements in the center of G.

The conjugacy classes [a] can be determined by finding representatives from each class. A representative of a conjugacy class is an element that cannot be written as a conjugate of any other element in the class. The number of distinct conjugacy classes is equal to the number of distinct representatives.

By finding the center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

(b) To prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique, we need to show two implications: if it is normal, then it is unique, and if it is unique, then it is normal.

If a Sylow p-subgroup is normal, then it is unique:

Assume that P is a normal Sylow p-subgroup of G. Let Q be another Sylow p-subgroup of G. Since P is normal, P is a subgroup of the normalizer of P in G, denoted N_G(P). Since Q is also a Sylow p-subgroup, Q is a subgroup of the normalizer of Q in G, denoted N_G(Q). Since the normalizer is a subgroup of G, we have P ⊆ N_G(P) ⊆ G and Q ⊆ N_G(Q) ⊆ G. Since P and Q are both Sylow p-subgroups, they have the same order, which implies |P| = |Q|. However, since P and Q are subgroups of G with the same order and P is normal, P = N_G(P) = Q. Hence, if a Sylow p-subgroup is normal, it is unique.

If a Sylow p-subgroup is unique, then it is normal:

Assume that P is a unique Sylow p-subgroup of G. Let Q be any Sylow p-subgroup of G. Since P is unique, P = Q. Therefore, P is equal to any Sylow p-subgroup of G, including Q. Hence, P is normal.

Therefore, we have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

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Answer:

i am fine and welcome to brainly also thanks for the points

Step-by-step explanation:

have a nice day

Frequency distributions, count the number of times each value or range of values appears in a dataset, while percentage distributions show the proportion or percentage of times each value or range of values appears in the dataset.

Frequency distributions are useful for summarizing and describing the distribution of a variable in a data set, while percentage distributions are useful for comparing different variables or subgroups within the data set.

For example, a frequency distribution could be used to show the number of hours of sleep each participant in a study gets per night, while a percentage distribution could be used to compare the number of hours of sleep between males and females in the study.

Frequency distributions and percentage distributions provide different perspectives on the same data set and can be used together to gain a more complete understanding of the data.

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Answer:

1/2

Step-by-step explanation:

So lets go over what slope is.

The formula for slope is y/x

To find this, we can just count the change in y, and put it over x.

So lets see.

On the graph, we can count that y goes up by one, and that x goes to the right by 2.

So this means our slope is y/x, or 1/2.

This is our answer.

I hope this helps! :)

I included a visual of this as well!

To be greater than a negative number, negative values need to be smaller as they get closer to zero.

The answer would be B) -5, -4.5, -3

Answer:

B

Step-by-step explanation:

This is because you could have a number greater of equal to -5, since b is the only one that has that it makes it true.

The solution is: 3.7%, is the probability that the next customer will be a woman who requests a convertible.

Here, we have,

given that,

At a car rental office, 63% of the customers are men and 37% are women.

If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car

As per given

P(woman)= 37%

P(convertible) = 10%

So combined probability is:

P = 37%*10%

  = 37%*0.1

  = 3.7%

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complete question:

At a car rental office, 63% of the customers are men and 37% are women. If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car, what is the probability that the next customer will be a woman who requests a convertible?

The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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The proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

What is proportion?

A proportion is a statement that two ratios or fractions are equal. It is commonly written in the form of two fractions separated by an equal sign, such as a/b = c/d.

To write a proportion comparing the rise to the run for each of the similar slope triangles, we can use the fact that the ratio of corresponding sides of similar triangles is the same.

Let's say we have two similar triangles with corresponding sides of length a, b, and c, and a', b', and c', respectively. Then we can write the following proportion:

a / a' = b / b' = c / c'

Now, let's apply this to finding the proportion of the rise to the run for each of the similar slope triangles.

In a right triangle, the slope is defined as the ratio of the rise (vertical change) to the run (horizontal change). Let's say we have two similar right triangles with slopes m and m', respectively, and the rise and run of the first triangle are h and b, respectively. The rise and run of the second triangle are then mh and mb', respectively.

We can write the proportion of the rise to the run for each triangle as:

h / b = mh' / mb'

Simplifying this proportion, we can cancel out the common factor of b:

h / b = mh' / mb'

h / 1 = mh' / m'

h = bmh'

Therefore, the proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

The numeric value of this proportion will depend on the specific values of the rise and run for each triangle and the slope of the triangles.

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Refer to the photo taken. Comment any questions you may have.

The domain of g(x) is all real numbers, and the range is (61, ∞) and the range is (61, ∞).

The domain of a function is the set of all possible input values for which the function is defined, while the range is the set of all possible output values.

For the given function g(x) = -1/4 (x−17)² + 61, the domain is all real numbers since there are no restrictions on the input values.

To find the range, we can use the fact that the vertex of the parabola is at (17, 61) and the coefficient of the squared term is negative, indicating a downward opening parabola.

Thus, the maximum value of the function occurs at the vertex and is 61, which is also the minimum possible value. Therefore, the range is (61, ∞).

In summary, the domain of g(x) is all real numbers, and the range is (61, ∞).

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Answer:

C. 2,637 square inches

Step-by-step explanation: