11.the admission fee at a small fair is $2 for children and $4 for adults. on a certain day, 50 people enter the fair and $140 is collected. how many children and how many adults attended?

Yes, the equation y = 5x represents a proportional relationship

Two or more expressions with an Equal sign is called as Equation.

The given equation is y=5x.

In a proportional relationship, the ratio of y to x is constant.

In the given equation the variable x and y has a proportional relationship.

The equation is in the form of y=mx+b

the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.

Hence,  Yes, the equation y = 5x represents a proportional relationship

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Answer:

2 6/13

Step-by-step explanation:

The linear function rule for the given data is y = 6x + 6.

A linear function is defined as an equation in which the highest exponent of the variable is always one.

The rule for the data in the given table:

x:  1   2   3   4

y: 12 18 24 30

The linear function rule for the given data can be found using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Let's use the first and second points: (1,12) and (2,18).

The slope can be found using the formula:

m = (18 - 12) / (2 - 1) = 6

Next, we can use the slope and one point from the table to find the y-intercept:

b = y - mx = 12 - m × 1 = 12 - 6 × 1 = 6

So the linear function rule for the given data is:

y = 6x + 6

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Answer:

i think its answer 2

Reduced form of given fraction is (2 + n)/7

An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

Given expression

(2x + nx - 2y - ny)/(7x - 7y)

It can be written as

[(2x - 2y) + (nx - ny)]/(7x - 7y)

Factoring out common factors

[2(x - y) + n(x - y)]/7(x - y)

Again factoring out common factor

(x - y)(2 + n)/7(x - y)

(2 + n)/7

Hence (2 + n)/7 is reduced form of the given expression.

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If a trapezoid has an area of 100 square units, the scale factor that would be required to dilate the trapezoid to have each area is:

sqrt(A / 100)

To find the scale factor required to dilate a shape, you need to determine what ratio of the new area to the original area you want to achieve.

Let's call the scale factor "k". If the original area of the trapezoid is 100 square units, and the new area is "A", the relationship between the two areas can be expressed as:

So to find the scale factor required to achieve a specific new area, you can solve for k by dividing the new area by 100 and taking the square root:

Note that: This equation assumes that the dilation is proportional, meaning that all dimensions of the trapezoid are scaled by the same factor.

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You can form 56,800 possible teams from a pool of 16 eligible engineers by selecting a total of 3 team members.

The total number of teams can be calculated using combination formula. The combination formula is nCr where n is the total number of items and r is the number of items you want to choose.

In this case, n = 16 and r = 3. Hence, the number of possible teams:

This means you can form 56,800 unique teams by choosing 3 engineers out of 16 eligible engineers. The combination formula helps in finding the number of possible combinations when the order does not matter, which is the case here as the order of engineers in a team does not matter.

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The inequality is x<10, which is true when `x=4`.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a< b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

here, we have,

Given Data,

`x=4

so, from the given inequality, we get,

The inequality is x<10, which is true when `x=4`.

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The equivalent interest rate will be 0.5 % and it will be compounded 24 times

Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

Compound interest is calculated by calculating the Amount

A = P( 1+r/n)^ ntp

A = amount

P is the principal

t is the time elapsed

since the interest rate is 6 % , the. monthly compounded interest will be 6/12, since there is 12 months in a year.

= 0.5 %

the number of times it will be compounded will be 12 × 2 = 24 times

therefore the equivalent interest rate is 0.5% per month and it will be compounded 24 times in the space of 2 years.

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Answer:

$6.50

Step-by-step explanation:

25 - 6.25 = 18.75

18.75 - 3.75 = 15

15 - 8.50 = 6.50

The solution is, the table is, for, x= 0, 1, 2, we get, y= 0, 6, 16.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

y = 2x² + 4x

now, for, x= 0 , y = 0

for, x= 1, y = 6

for, x= 2, y = 16

Hence, The solution is, the table is, for, x= 0, 1, 2, we get, y= 0, 6, 16.

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Hence, the standard deviation is more affected by skewness compared to the IQR.

Skewness is a metric for a distribution's asymmetry. When the left and right sides of a distribution are not mirror reflections, it is asymmetrical. Right (or positive), left (or negative), or zero skewness can all apply to a distribution.

Skewness refers to the degree of asymmetry in a distribution and a skewed distribution has more observations on one side than the other. In a skewed distribution, the standard deviation is a better measure of spread as it takes into account the deviation of each data point from the mean. On the other hand, the interquartile range (IQR),

which is the difference between the 75th and 25th percentile, is less affected by skewness as it only considers the middle 50% of the data. Hence, the standard deviation is more affected by skewness compared to the IQR.

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the surface area of the rectangular prism is 348 inches²

The surface area of a rectangular prism is given by: SA = 2 (lh +wh + lw ) Square units.

Given here: A rectangular prism with dimensions are 6 in.

We know the surface area of a prism is given by

2(wl+hl+hw)

where l is the length , w is width and h is the height.

Thus Surface area A=2(wl+hl+hw)

2·(8·6+9·6+9·8)=348

Thus the surface area of the rectangular prism is 348 inches²

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The amplitude, period, and zero value of the function y = 3cos(x+5) are (A) 3, 2π, later.

Option D is correct.

The amplitude of a cosine function is described  as half the difference between the maximum and minimum values of the function.

In the question given, the maximum value of the function y = 3cos(x+5) is 3 and the minimum value is -3, hence amplitude is:

A = (3 - (-3)) / 2 = 3

For a cosine function with a period of 2π, the maximum or minimum values repeat every 2π units along the x-axis.

In the question above, the period of the function y = 3cos(x+5) is:

P = 2π

in conclusion, the phase shift of a cosine function is the horizontal shift of the graph of the function along the x-axis, which is represented by the constant term (x+5) in this case.

Phase shift = later

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If we change the 0's to negative numbers then the average, median and SD. The average would b) decrease.

The average value calculated within a specific data set is referred to as the "mean.". This calculation can be used in any situation where knowing a data set's average value, such as its cost or income, may be deemed as useful.

By being aware of the average cost or income within a given data set, you can better position yourself to increase your profits or savings.

A normal distribution can have a mean that is negative in nature. When only some of the data points have negative values, this is both a possibility and a foregone conclusion;

however, if all of the data points have negative values as nature it should be noted that if a normal distribution has a negative mean, at least half of the data points in the distribution must also have a negative mean.

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Note that the full question is:

some of the girls with 0 weight gain actually lost weight. if we changed their 0's to negative numbers how would the average, median and sd change? the average would

a) increase

b) decrease

c) stay the same

Answer:

89.28

Step-by-step explanation:

First lets find 7% of 96

96 x 0.07 = 6.72

then subtract 6.72 from 96

96-6.72=89.28

The requried, a number that is 7% smaller than 96 is approximately 89.28.

To find a number that is 7% smaller than 96, we need to calculate 7% of 96 and then subtract that value from 96.

Calculate 7% of 96.

7% of 96 = (7/100) * 96 = 0.07 * 96 = 6.72

To get a number that is 7% smaller than 96, we need to subtract the value we found in Step 1 from 96. subtract the calculated value from 96.

Number = 96 - 6.72 = 89.28

Therefore, a number that is 7% smaller than 96 is approximately 89.28.

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The system of inequalities is y >= 3x and y > 3 - x

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

The graph

The inequalities on the graph are linear inequalites

So, we first write out their equations as follows:

y = 3x --- red line

y = 3 - x -- blue line

For the red line, we have

Thick line and the upper region is shaded

This is represented as y >= 3x

For the red line, we have

Dotted line and upper region is shaded

This is represented as y > 3 - x

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Answer:

length = 10 inches

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2l + 2w ( l is the length and w the width )

here w = 14 and P = 48 , then

48 = 2l + 2(14)

48 = 2l + 28 ( subtract 28 from both sides )

20 = 2l ( divide both sides by 2 )

10 = l

then length is 10 inches

The distance of the parking lot from the first campsite is 3.14 miles.

The scale of the map is 1/24,000, which means that for every 1 inch on the map, it is equal to 24,000 inches in reality. To calculate the distance of the parking lot from the first campsite, we need to first convert the 8.3 inches on the map into inches in reality. To do this, we use the formula:

Actual distance = Map distance x (Map scale)

Actual distance = 8.3 inches x 24,000 inches

Actual distance = 199,200 inches

Now, to convert inches to miles, we can use the formula:

Miles = Inches / 63360

Miles = 199,200 inches / 63360

Miles = 3.14 miles

Therefore, the distance of the parking lot from the first campsite is 3.14 miles.

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A reduced row echelon form of a matrix is a way to solve a system of linear equations. A reduced row echelon matrix has the following properties:

For a system of three equations and three variables with no solution, the reduced row echelon form of the augmented matrix would be in the form:

\begin{bmatrix}

1 & a & b & c \

0 & 0 & 0 & d \

0 & 0 & 0 & e

\end{bmatrix}

where a, b, c, d and e are constants and d and e are non-zero.

This form indicates that the system has no solution because the bottom row represents an equation that is false (0 = non-zero).

The reduced row echelon form of a matrix is a way to determine whether a system of linear equations has a solution. A system of linear equations has no solution if and only if the reduced row echelon form of the augmented matrix contains a row in the form of 0 = k, where k is non-zero.

In this case, the reduced row echelon form of the augmented matrix has the bottom row with the form 0 = d, and d is non-zero. This means that the equation is false, indicating that the system has no solution.

So, the fact that the bottom row of the reduced row echelon form has the form 0 = k, where k is non-zero, allows us to determine that the system of linear equations has no solution.

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The sine function with the values in the table is defined as follows:

y = 5sin(πx/2) - 1.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a maximum value of 4 and a minimum value of -6, for a difference of 10 units, hence the amplitude is obtained as follows:

A = [4 - (-6)]/2

A = 10/2

A = 5.

Without vertical shift, a function with amplitude of 2 would oscillate between -5 and 5, while this one oscillates between -6 and 4, hence the vertical shift is given as follows:

D = -1.

The shortest distance between repetitions can be given by 4 - 0, hence the period is of 4 units and the coefficient B is given as follows:

2π/B = 4

B = 2π/4.

B = π/2.

The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:

y = 5sin(πx/2) - 1.

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The solution of the system of equation is , x= -4 & y= -8.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

from the given graph we get,

one line is passing through the points (0,10) , ( 4,28)

so, the equation of the line can be,

4y= 18x + 40

and, second line is passing through the points (0,8) , (1,12)

so, the equation of the line can be,

y= 4x+8

solving the equations we get,

x= -4

y= -8

Hence, The solution of the system of equation is , x= -4 & y= -8.

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The set describes the zeroes of the function f(x)=6pi sin(4x) is C. {x|x = k/4π} for every integer k

The function has zeroes at the x-intercepts in the graph.

If you look at the graph from 0 to π, you will see that the graph cuts the x-axis at 4 points.

They are at half of π/2, which is π/4, at π/2, at half point between π/2 and π, which is at 3π/4, and at π.

They are basically all multiples of π/4

Looking at the answer choices, option C is correct.

Plugging in k=1, k=2, k=3, and k=4 into the equation, we see that the zeroes are exactly what we saw.

Also, the negative side of the function holds true as well.

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Answer:

Below

Step-by-step explanation:

This is a two-stage problem

  for the first 12 years use cont compounding formula

        FV = PV e^(rt)     Future value  Presnt value   r = decimal int   t = years

         = 2000 e^(.05 * 12) = 3644.24    use this amount for the second stage

     Fv = pv e^(rt)  = 3644.24 ( e^(.08*8) ) = $ 6911.23