The start of a quadratic sequence is shown
below.
What is the nth term rule for the sequence?
-5, -2, 3, 10, 19,

Answer:

1.66

Step-by-step explanation:

hope this helps

Answer:

3/5 or 0.8

Step-by-step explanation:

3 Cartons, divided by 5 people =

3/5 or 0.8

The correct statements are Two data sets could have different means but the same standard deviation, and could have the same mean but different standard deviations. If two data sets have different means they must have different standard deviations. Correct options are A, C , D.

The mean and standard deviation are both measures of the central tendency of a data set, but they capture different aspects of the distribution. The mean represents the average value of the data, while the standard deviation measures how spread out the data is around the mean.

It is possible for two data sets to have different means but the same standard deviation if one data set is more spread out than the other, but the values are symmetrically distributed around the mean. For example, the data sets {1, 2, 3, 7, 8, 9} and {0, 4, 5, 5, 5, 9} have different means (5 and 4.67, respectively) but the same standard deviation (3.16).

Similarly, two data sets could have the same mean but different standard deviations if one data set is more spread out than the other. For example, the data sets {1, 2, 3, 4, 5} and {1, 3, 3, 3, 5} have the same mean (3) but different standard deviations (1.41 and 1.26, respectively).

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Complete question is:

Which of the following statements is true?

multiple select question.

A. two data sets could have different means but the same standard deviation.

B. if two data sets have the same mean they must have the same standard deviation.

C.  two data sets could have the same mean but different standard deviations.

D. if two data sets have different means they must have different standard deviations.

The percentage increase in her taxes from 2010 to 2011 is 44.30%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Sophia paid $3,360,00 in taxes in 2010 and her taxes rose to $4,848,60 in 2011.

So, The amount of tax increase is $(484860 - 336000) = $148860.

Therefore, The percentage increase is,

= (148860/336000)×100%.

= 44.30%.

The net amount change will now be divided by the starting total, and the result will be multiplied by 100% to determine the percentage change.

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Answer:

Step-by-step explanation: The answer is that because if you think about it and do the problem you would be able to get that answer.

Answer:

Mary would have 18 more candies than Gary

Step-by-step explanation:

The value of the expression is 5193.

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

From the notation, we have the following values:

The first term, a = 400

The common ratio, r = 0.93

The number of terms, n = 34 - 1 = 33

The sum of the geometric progression is represented as:

Sum = a(1-rⁿ)/(1-r)

Sum = 400(1-0.93³³)/(1-0.93)

Sum = 5193

Therefore, the value of the expression is 5193

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The equation which is used to find the number of chocolates candy in the jar is given by 18 + 24 + 19 + n = 82 , the number of chocolate candy in the jar is equal to 21.

Number of strawberry candy in the jar = 18

Number of cherry candy in the jar = 24

Number of lime flavored candies = 19

Let 'n' be the number of chocolate candy in the jar

Total number of candy in the jar = 82

Equation used to represent the given condition is :

18 + 24 + 19 + n = 82

⇒ 61 + n = 82

⇒ n = 82 - 61

⇒ n = 21

Therefore, the equation required to represent the number of chocolate candy is 18 + 24 + 19 + n = 82 and the value of n is equal to 21.

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The number of patients that waited for more than 20 minutes is 74

The median waiting time is 17

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

The graph

Where

x = Waiting time

y = Cumulative frequency

This means that

y = Number of patients that waited x or more time

From the graph, we have

(x, y = (20, 74)

So, the number of patients is 74

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

Maximum CF = 100

Divide by 2 to calculate the median

Median = 100/2

Evaluate

Median = 50

From the graph, we have

(x, y = (50, 17)

So, the median is 17

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Answer:

sin(35)

Step-by-step explanation:

Because of the co-function identity [tex]\cos(\theta)=\sin(90^\circ-\theta)[/tex], then [tex]\cos(55^\circ)=\sin(90^\circ-55^\circ)=\sin(35^\circ)[/tex].

Option 3) Sometimes is the correct answer, Sometimes an equilateral triangle is similar to a scalene triangle.

If the respective sides are proportional and the corresponding angles are congruent, two triangles are comparable. An equilateral triangle has three congruent sides and three congruent angles, so any triangle that is similar to an equilateral triangle must also have three congruent angles. However, a scalene triangle has no congruent sides and no congruent angles, so it is possible for a scalene triangle to be similar to an equilateral triangle only if it has the same angle measurements as an equilateral triangle, but with different side lengths. Therefore, a scalene triangle can be similar to an equilateral triangle, but it is not always the case.

In general, if two triangles are similar, it means that they have the same shape but possibly different sizes. In the case of an equilateral triangle and a scalene triangle, if they are similar, then it means that the scalene triangle has the same angles as the equilateral triangle, but its sides are of different lengths. So it is possible for a scalene triangle to be similar to an equilateral triangle, but not in all cases.

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The word that best describes the degree of overlap between the two data sets is C. low

In statistics, data overlap refers to the situation where two or more groups being compared have some individuals or data points that have similar or identical values. When this happens, it can make it more difficult to accurately distinguish between the groups and to draw meaningful conclusions from the data.

From the given data, we can see that one data set is positively skewed while the other is negative. This shows that the data overlap is quite low.

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The percent error of Brandi’s estimate to the nearest tenth is equal to 2.9%.

In Mathematics, percentage error is also referred to as percent error and it can be defined as a measure of the extent to which an experimental value (numerical) differs from the actual (theoretical) numerical value.

Mathematically, percentage error can be calculated by using this expression;

Percent error = {experimental value - actual value}/{actual value} × 100

By substituting the given parameters into the percentage error formula, we have;

Percent error = {107 - 104}/{104} × 100

Percent error = 3/104 × 100

Percent error = 0.029 × 100

Percent error = 2.9%.

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The options that represent an amount and price of gas that Pedro purchased are 19 gallons of gas for $52.25, 16 gallons of gas for $44. So options C and D are correct.

To calculate the amount of gas and the total price that Pedro purchased, we need to use the formula:

Price = Cost per gallon * Number of gallons

Dividing the total price by the cost per gallon will give us the number of gallons purchased. We can then compare this with the given options to see which one(s) match.

Using the given cost per gallon of $2.75, we can check each option:

a) 13.75 gallons of gas for $41.25

Price = $2.75/gallon * 13.75 gallons = $37.81

This option does not match the total price of $41.25, so it is not correct.

b) 22 gallons of gas for $71.5

Price = $2.75/gallon * 22 gallons = $60.50

This option does not match the total price of $71.5, so it is not correct.

c) 19 gallons of gas for $52.25

Price = $2.75/gallon * 19 gallons = $52.25

This option matches the total price of $52.25, so it is correct.

d) 16 gallons of gas for $44

Price = $2.75/gallon * 16 gallons = $44

This option matches the total price of $44, so it is correct.

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Complete question is:

Pedro fills up his truck with gas he paid $2.75 a gallon which of these represents an amount and price of gas that Pedro purchased select all that apply.

a) 13.75 gallons of gas for $41.25

b) 22 gallons of gas for $71.5

c) 19 gallons of gas for $52.25

d) 16 gallons of gas for $44

Answer:  [tex]5\sqrt{5} \ \text{ feet}[/tex]

Work Shown:

[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+10^2}\\\\c = \sqrt{125}\\\\c = \sqrt{25*5}\\\\c = \sqrt{25}*\sqrt{5}\\\\c = 5\sqrt{5}\\\\[/tex]

For more information, search out "pythagorean theorem".

A minimum score of 182 is required to stay out of the bottom 1.5% of students and avoid going to summer school.

To find the minimum score required to avoid going to summer school, we need to determine the score that separates the bottom 1.5% of students from the rest of the distribution. This score is also known as the cutoff or the critical value.

We know that the test scores have a normal distribution with a mean of 400 and a standard deviation of 100. To find the critical value, we can use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can standardize the test scores using the z-score formula:

z = (x - mu) / sigma

where x is the test score, mu is the mean, and sigma is the standard deviation.

Substituting the given values, we get:

z = (x - 400) / 100

To find the z-score corresponding to the bottom 1.5% of the distribution, we can use a standard normal table or a calculator. The area to the left of this z-score is 0.015, which corresponds to a z-score of approximately -2.17.

Now we can solve for x, the minimum score required to stay out of the bottom 1.5%:

-2.17 = (x - 400) / 100

x = -2.17 * 100 + 400

x ≈ 182

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In the given word problem, Ling collected 4/5 bags.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Belle and Ling are collecting clothes for a clothing drive. Ling collected 1/5 as many clothes as Belle did and Belle collected 4 bags of clothes, we need to find how many bags of clothes did Ling collect.

Since, Belle collected 4 bags, and Ling is collected 1/5 of the Belle collection,

So, Ling collected = 4 x 1/5 = 4/5

Hence, Ling collected 4/5 bags.

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X = 11 when y = 4 when X=a+b+4 and a directly proportional to y squared , b is inversely proportional to y.

Given that a is directly proportional to y^2 and b is inversely proportional to y, we can write the following two relationships:

[tex]a = k * y^2[/tex]

[tex]b = m / y[/tex]

where k and m are constants. From the first equation, we can find the value of k when y = 2:

[tex]a = k * 2^2[/tex]

[tex]k = a / 4[/tex]

And from the second equation, we can find the value of m when y = 2:

[tex]b = m / 2[/tex]

[tex]m = 2b[/tex]

Substituting these values into the equation X = a + b + 4, we can find X when y = 2:

[tex]X = (k * 2^2) + (m / 2) + 4[/tex]

[tex]X = (a / 4) * 4 + 2b + 4[/tex]

[tex]X = a + 2b + 4[/tex]

[tex]X = 18[/tex]

We can now use the value of k and m to find X when y = 4:

[tex]X = (k * 4^2) + (m / 4) + 4[/tex]

[tex]X = (a / 4) * 16 + (2b) / 4 + 4[/tex]

[tex]X = 4a + 2b + 4[/tex]

Substituting the value of X = 18 when y = 2, we can solve for a and b:

18 = 4a + 2b + 4

14 = 4a + 2b

7 = 2a + b

Solving the system of equations for a and b, we find:

a = 5

b = 2

Finally, substituting these values into the equation X = a + b + 4, we can find X when y = 4:

X = (5) + (2) + 4

X = 11

Therefore, X = 11 when y = 4.

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The number of sides the polygon have 9.

A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.

Given:

We have a polygon can be divided into 5 triangles when the diagonals are drawn from one of its vertices.

As, we know  the number of triangles in a polygon is  = n−2

where n is the number of sides (or vertices)

So, the number of sides the polygon have

n= 5+ 2

n = 7 sides

Thus, the polygon is Heptagon.

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Composition is sometimes referred to as has-a relationship.

A form of aggregation, a composition association relationship represents a whole-part relationship. The lifetime of the part classifier is a function of the lifetime of the whole classifier, according to a composition association relationship.

Data typically only flows in one direction (from the whole classifier to the part classifier) in a composition association relationship. For instance, if a student is removed from a class that has a composition association relationship with a schedule class, the schedule is also removed.

Any association may be named to describe the type of connection between the two classifiers; however, names are not required if association end names are used.

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The lower quartile is 2, the median is 5 and the upper quartile is 8.

What are quartiles?

The values that divide a list of numerical data into three quarters are known as quartiles.

We are given a data set as 1, 2, 3, 5, 5, 8, 8

From this, we get the median as 5 as median is the middle number of the data set.

We know that lower quartile is the median of the lower half of the data.

So, lower quartile is 2.

Upper quartile is the median of the upper half of the data.

So, upper quartile is 8.

Hence, the lower quartile is 2, the median is 5 and the upper quartile is 8.

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The altitude of the airplane after 30 minutes of descending is 0 feet, which means the airplane has landed.

What is the altitude?

The height of an object or point in relation to sea level or ground level.

Part A:

To create a table for the given equation, we substitute the given values of x in the equation and calculate the corresponding values of y:

x y = -128x + 3,840

0 3,840

5 3,200

8 2,624

10 2,304

30 0

Part B:

To find the altitude after 5 minutes, we substitute x = 5 in the given equation:

y = -128(5) + 3,840

y = 3,200

So the altitude of the airplane after 5 minutes of descending is 3,200 feet.

To find the altitude after 30 minutes, we substitute x = 30 in the given equation:

y = -128(30) + 3,840

y = 0

The altitude of the airplane is decreasing as time (x) increases, as given by the negative slope (-128) of the equation.

At 5 minutes, the airplane has descended to an altitude of 3,200 feet, which is still relatively high.

At 30 minutes, the altitude has decreased to 0, which means the airplane has landed on the ground.

Hence, the altitude of the airplane after 30 minutes of descending is 0 feet, which means the airplane has landed.

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To evaluate the expression x² + 3x for x = 4, we simply substitute 4 for x and simplify and we get 28.

What is expression ?

An expression is a combination of values, variables, and operators that represent a specific computation or operation. Expressions can be used to perform various operations such as arithmetic, logical, relational, and more. The value of an expression is determined by evaluating the expression, which involves simplifying and reducing it to a single value. In programming, expressions are a fundamental building block, and are used to write algorithms and control the flow of execution of a program.

To evaluate the expression x² + 3x for x = 4, we simply substitute 4 for x and simplify:

x² + 3x = 4² + 3 * 4 = 16 + 12 = 28

So, when x = 4, the expression x² + 3x = 28.

Hence, after evalution of the expression we get the result 28.

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Answer:

e would equal a half because it's in the middle

Answer:

a. Let's call the average ticket price for Dallas in 2005 as "d" and the average ticket price for Boston in 2005 as "b". Then the system of equations can be written as:

y_d = d + 0.53x (where y_d represents the price of an average ticket for Dallas after x years)

y_b = b - 1.08x (where y_b represents the price of an average ticket for Boston after x years)

b. To find the number of years in which the average ticket price for Dallas will approximately equal that of Boston, we need to solve the equation y_d = y_b for x. Plugging in the equations for y_d and y_b, we get:

d + 0.53x = b - 1.08x

Rearranging and solving for x, we have:

1.61x = b - d

x = (b - d) / 1.61

Now we just need to plug in the values for d and b from the table:

d = 53.60

b = 55.93

x = (55.93 - 53.60) / 1.61 = 2.33 years

So it will take approximately 2.33 years for the average ticket price for Dallas to approximately equal that of Boston.

Step-by-step explanation:

Answer: a. Let x be the number of years after 2005, and y be the price of an average ticket. Then, we can write the following system of equations to represent the information in the table:

For Dallas:

y = 53.60 + 0.53x

For Boston:

y = 55.93 - 1.08x

This system of equations represents the average ticket price y for Dallas and Boston as a function of the number of years x after 2005, with the change in price from the 2004 season to the 2005 season given in the table.

b. To find the number of years when the average ticket price for Dallas will approximately equal that of Boston, we can set the two equations equal to each other and solve for x:

53.60 + 0.53x = 55.93 - 1.08x

2.33x = 2.33

x = 1

So, the average ticket price for Dallas and Boston will approximately equal each other after 1 year. Therefore, in 2006, the average ticket price for Dallas will approximately equal that of Boston.

Step-by-step explanation:

The  original two-digit number is 11 * 10 + 3 = 113.

Let us correspond to the original two-digit number as "10x + y," with x and y showing the tens and units digits, respectively.

We know from the first piece of information:

x + y = 14

According to the second piece of information:

2(10x + y) + 10y + x = 222

When we simplify this equation, we get:

20x + 22y = 202

We get 10x + 11y = 101 by dividing both sides by 2.

We now have two equations with two variables that can be solved by substitution or elimination. For example, in the first equation, we can solve for x and then substitute into the second equation:

x = 14 - y\s10(14 - y) + 11y = 101

When we simplify this equation, we get: y = 3

Putting y = 3 back into the first equation yields: x = 11.

The  original two-digit number is 11 * 10 + 3 = 113.

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