Help me with simplified expressions! Please.

The study comes to the additional conclusion that both interventions—traditional methods of instruction and the use of graphing calculators—improve students' abilities to compute mathematically.

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The Mean for June 2006 and 2005 is  $345,909 and $335,977 respectively. The median for June 2006 and 2005 is $254,000 and $139,000 respectively, there's no mode in this question.

In statistics, the mean, mode, and median are three measures of central tendency that describe a set of numerical data.

The mean is the average of a set of numbers, calculated by adding up all the values and dividing by the number of values. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the mean is (1 + 2 + 3 + 4 + 5) / 5 = 3.

The mode is the value that appears most frequently in a set of data. For example, if a set of data contains the values {1, 2, 2, 3, 4, 4, 4, 5}, the mode is 4, because it appears three times, which is more than any other value.

The median is the middle value in a set of data when it is ordered in ascending or descending order. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the median is 3, because it is the middle value. If there is an even number of values, then the median is the average of the two middle values.

It is important to note that different sets of data may have different measures of central tendency, and sometimes none of these measures may be appropriate.

Measures of central tendency are used to summarize and describe a set of data. The most common measures of central tendency are the mean, median, and mode.

1. Mean:

• Mean for June 2006: (508+435+538+913+367+033+254+240+137+022+160+548+260+458+358+035+222+879+136+371+127+586+201+316)/22 = $345,909

• Mean for June 2005: (422+843+469+588+245+803+199+409+132+054+139+728+254+725+345+065+210+740+134+334+125+455+184+853)/22 = $335,977

2. Median:

• Median for June 2006: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $254,000

• Median for June 2005: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $139,000

3. Mode:

• Mode for June 2006: There is no mode, because no value is repeated.

• Mode for June 2005: There is no mode, because no value is repeated.

Conclusions:

• The mean housing price in June 2006 is higher than the mean housing price in June

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Carl has 2 5/36 yard cable, more than 1 yard, not specified left.

What is yard ?

A yard is a unit of length measurement in the U.S. customary system and the imperial system. It is equal to 3 feet or 36 inches. The symbol for yard is "yd". It is mostly used in the United States and the United Kingdom for measuring small lengths, such as in construction, textiles, and landscaping.

Carl has three lengths of cable, 5/6 yard long, 1/4 yard long and 2/3 yard long. The total length of the cable that Carl has is:

5/6 + 1/4 + 2/3 = (30 + 15 + 40) / 36 = 85 / 36 = 2 5/36 yard

To check whether he has at least one yard of cable or not, we need to compare the total length of the cable he has (2 5/36 yard) with 1 yard. Since 2 5/36 is greater than 1, it means he has more than 1 yard of cable. So, he will have at least 1 yard of cable left after using some of it.

Carl has 2 5/36 yard cable, more than 1 yard, not specified left.

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Carl has three lengths of wire, each measuring 5/6 yards, 1/4 yards, and 2/3 yards. The wire that Carl has measures a total of:

5/6 + 1/4 + 2/3 = (30 + 15 + 40) / 36 = 85 / 36 = 2 5/36 yard

We need to compare the entire length of the cable he has (2 5/36 yard) with 1 yard to see if he has at least one yard of cable or not. He has more than one yard of cable since 2 5/36 is larger than 1, which is greater than 1. After using some of the wire, he will still have at least 1 yard of it.

The equation which is the best model for a line of best fit for the data is y = ½ x – 1. (Option B)

A line of best fit refers to a straight line which minimizes the distance between it and some data. It expresses a relationship in a scatter plot of different data points. It is an educated guess about where a linear equation which may fall in a set of data plotted on a scatter plot. It is an output of regression analysis and is used as a prediction tool.

The equation of the line can be determined using slope intercept form of the line which is y = mx + b where m is the slope and b is the y intercept. From the given graph, two points which lie on the line of best fit can be used to determine the slope. Let consider two points (2, 0) and (0, -1). Hence

m = (-1 – 0)/(0 – 2) = -1/-2 = ½

The value of y intercept is -1 (when x = 0)

Hence, the equation is:

y = ½ x - 1

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Answer: believe it's 49 degrees

Step-by-step explanation:

The equation that shows how the price of a personal pizza y depends on the number of toppings x is y = 7 + x.

The equation of a straight line is an equation that comes in the form of an algebraic equation. It is also referred to as Slope - Intercept form. It can be represented using the equation below:

Equation : y = mx + c

where:

m = Gradient
c = Slope of the line

The equation that shows how the price of a personal pizza y, depends on the number of toppings x  is y = 7 + x

This question can be solved and represented using the equation of a straight line.

Let's represent

y = price of a personal pizza
x = number of toppings
The price for a plain cheese pizza = $7
The price for each of the toppings = $1
Therefore, the equation that shows how the price of a personal pizza y, depends on the number of toppings x  is written as:

y = $7 + $1 × x
y = 7 + x

Therefore, y = 7 + x is the equation represents the relationship between the price of a personal pizza and the amount of toppings.

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Answer:

Step-by-step explanation:

Give them a fixed number of beads, and tell them to divide them equally between a certain number of tins. Start with showing the child how to divide the beads into two tins, using different numbers of beads each time, then gradually move to dividing by different numbers.

Plot the lines and shade in the regions on the same x-y plane to find the solution to the system of inequalities 4x+6y ≤ 24 and x + 5y ≤ 10 fall under the mixed shaded region in the graph.

What is the linear inequalities?

Linear inequalities are mathematical expressions that describe a relationship between two variables that is linear in nature. The most common form of a linear inequality is of the form ax + by < c, where a, b, and c are constants and x and y are variables.

Yes, this system of two linear inequalities can be represented graphically on the x-y plane by plotting the solutions to each inequality. The steps are as follows:

        4x + 6y <= 24

        => -6y <= -4x + 24

        => y >= (4/6)x + 4

        => y = (4/6)x + 4

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The length of a, to the nearest 10th of a centimeter is 18.6 cm.

A triangle is a three-sided polygon that is defined by three points in a plane, called its vertices. The three sides of a triangle are also called edges, and are connected by three angles. The sum of the angles in a triangle is always 180 degrees. There are different types of triangles, including:

Triangles are fundamental in mathematics and are used in many areas such as geometry, trigonometry, and engineering.

In a triangle, the measure of an angle is related to the lengths of the sides opposite and adjacent to it by the formula:

c = a/sin C

Given that c = 75 cm and mm∠C = 13°, we can use this formula to find the length of a:

a = c*sin C

where C is in radians.

a = 75 * sin(13°) = 75 * 0.2225 = 16.7 cm

Also, we know that the sum of the angles in a triangle is always 180°, so we can use that information to find the measure of angle A.

mm∠A = 180 - (mm∠B + mm∠C) = 180 - (154 + 13) = 180 - 167 = 13°

Therefore, using the Law of Sines, we can find the value of a.

[tex]\frac{a}{sin A}[/tex] =  [tex]\frac{b}{sin B}[/tex] = [tex]\frac{c}{sin C}[/tex]

a =  [tex]\frac{c*sin A}{sin C}[/tex]

a = [tex]\frac{75*sin(13^{0}) }{sin(154^{0}) }[/tex]

Now, you can use a calculator or a table of trigonometric values to find sin(13°) and sin(154°) and substitute them in the above equation to find the length of a. To the nearest tenth of a centimeter, a is approximately 18.6 cm.

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Answer:

  see attached

Step-by-step explanation:

You want to graph the piecewise defined function ...

  f(x) = 2x+9 for x < -3; 2x-2 for x > 4

You normally graph a line by finding (at least) two points on the line and drawing a line through them to make the graph. Often, it is convenient to start with the y-intercept. Here, it is convenient to start with the end point of the domain on which the line is defined. Additional points can be found by making use of the slope: rise 2 for each run of 1 to the right.

For x < -3, the value of y at x=-3 is ...

  y = 2(-3) +9 = 3

So, the point (-3, 3) will appear on the graph. This point is not actually in the domain, which is x < -3, so will be graphed as an open circle. The line goes down and to the left from there with a slope of 2.

For x > 4, the value of y at x=4 is ...

  y = 2(4) -2 = 6

So, the point (4, 6) will appear on the graph as an open circle, because x=4 is not actually in the domain of the function. The line will go up to the right from there with a slope of 2.

See the attachment for a finished graph.

To satisfied the solution of an equation after substituting the value of the variable left hand side value should equals to right hand side value.

As given in the question,

To satisfied the solution of the given equation we need to follow the following steps :

Therefore, to satisfied the solution of the given equation left hand side value should be equal to right hand side.

The above question is incomplete , the complete question is :

How do you satisfy the solution of an equation?

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Answer:

Below

Step-by-step explanation:

To find the slope of a line, we use the formula:

slope = (change in y-coordinates) / (change in x-coordinates)

In this case, if Akio recorded the distance he rode on his bike ride in hours, the slope of the line for the first two hours would be the change in the y-coordinates (distance) divided by the change in the x-coordinates (time) between those two points.

To find the slope of the line for all five hours, we will need to know the specific coordinates of all five points, otherwise, it's impossible to calculate the slope.

The slope of a line represents the rate of change in the y-coordinates (distance) per unit of change in the x-coordinates (time). In this situation, the slope represents Akio's speed, since the change in distance is divided by the change in time. A positive slope indicates an increase in distance over time, which means Akio is getting faster, whereas a negative slope indicates a decrease in distance over time, which means Akio is getting slower.

It's worth noting that a slope of zero would mean that there is no change in distance over time, which would mean that Akio isn't moving.

Answer:

Step-by-step explanation:

It's obvious 5x5=25

Therefore, the square root of 25 is 5.

The gradient of the line is 0.

A line's slope is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by the symbols y and x, respectively. where "m" represents the slope of a line. So, tan is the slope of a line.

According to the question

Given the equation of a line is y = -10.

The general equation of the line is y = mx + c

This is a horizontal line because, regardless of the value of x, the value of y is always less than 10. A horizontal line by definition has a slope of:

m = 0

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The inverse of a square root function looks like a half parabola which resembles the shape same as that of a quadratic function graph but we can not be certain about it.

Square root function graphs are usually curved. The curve above is, in reality, half of a parabola that is laying on its side. It represents half of the parabola that would result from graphing the equation y² = x.

f(x) = ax² + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.

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Answer:

The average marks = 31

Step-by-step explanation:

We know that the average can be measured using mean

Mean = Sum of observations /  no of observations

In the given data no of observations = sum of frequencies

                                                                 = 3+6+10+7+4

                                                                  =30

Sum of observations = No of marks * frequency 1 + No of marks * frequency 2+...

             =  10*3 +20*6+30*10+40*7+50*4

              = 930

Mean = 930/30

          = 31

The rounded number to the nearest tenth is 7.1

How to round to the nearest tenth?

Examine the hundredth number to determine the decimal number's nearest tenth. Add one to the tenth value if the number is more than 5. The tenth place value should remain unchanged if it is less than 5, but all subsequent numbers should be eliminated.

√50 = 7.071

hundredth number is 7 greater than 5

Add one to the tenth value if the number is more than 5

all subsequent numbers should be eliminated.

Thus, the rounded number to the nearest tenth is 7.1

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Answer:

I = 17deg, II = 73deg

Step-by-step explanation:

Let's say first angle is x, and then respectively, the second angle is 4*x + 5.

Their sum is 90 degrees, so:

x + (4*x+5) = 90

5x + 5 = 90

5x = 85 | :5

x = 17 degrees ==> first angle

4*x+5 = 73 degrees ==> second angle

the mid point of the side AB is (0,-1).

What is triangle?

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle containing the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane. A triangle's area is the region that each of its sides touches. A triangle's area varies from one triangle to another depending on the size of its sides and internal angles. Triangle area is measured in square units like m2, cm2, and in2.

A = (2,-3)

B = (-2,1)

Mid point will be 1+3/2, -2-2/2

Mid point is (0,-1)

Hence the midpoint of the side AB is (0,-10).

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Answer:

3.2

Step-by-step explanation:

......................

The set of -values that are appropriate in the given situation is known as the practical domain. Solution: F (x) = 2 x is the function's formula.

You are not accounting for or measuring any rainfall that occurred prior to the storm's onset, thus there is a total of 0 inches of precipitation at that time. Six and a half hours are spent in the storm.

Example :

Miami, Florida, experiences heavy rainfall due to a powerful hurricane. A 2 inch per hour downpour is occurring. In 6 and a half hours, the storm is over. The total amount of rain that has fallen throughout time should be modeled mathematically. The function is plotted. For this situation, identify the practical domain. The set of -values that are appropriate in the given situation is known as the practical domain.

Solution: Since there was no rain measured or included before the storm began, the function is as follows:

f(x)= 2x

There was 0 inches of rain at the moment the storm began. Six and a half hours are spent in the storm. f(6.5) = 2(6.5) = 13 inches of rain had been recorded at 6.5 hours, or so. It follows in words what the domain and range are:

Domain :

All real numbers between and including 0 and 6.5 hours.

Range :

All real numbers between and including 0 and 1.3 inches.

Domain and range can be expressed more easily with the help of some helpful notation, such as the following:

Domain { x∈R,0≤ x ≤ 6.5} [0,6.5]

Range { x∈R,0≤ x ≤ 6.13 [0,13].

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Answer:

Step-by-step explanation:

first we subtract 92.1 from 41 which gives us 51.1 now we want to see how many hours we can keep the room for while staying under 91.1 so we divide the value of 51.1(as we have to first pay the fee of $41) by 7.3 as that is the amount they are charging per hour(51.1/7.3) which gives us 7 so we can rent the roof for 7 hours max or just for 1,2,3,4,5 or 6 hours

Answer:

$18.30

Step-by-step explanation:

125 x 18 = 2250

2250/500 = 4.5 (round up to 5)

5 x 3.66 = $18.30

Therefore , light of the fact that the three equations equal x2 + 6x - 16, they all represent the same function.

In a mathematical formula, the equal symbol (=) is used to denote that the statements are equivalent. It is demonstrated that many quantitative variables are comparable using mathematical equations, which are statements of reality. The equal sign, for instance, separates the numbers 12 and b + 6 into 2 halves within the equation y + 6 = 12. It is possible to calculate how many expression words each edge of a symbol represents. The meaning of a symbol usually contradicts itself.

Here,

It is important to understand that the function Corey wrote is:

=>y = (x + 8)(x - 2) (x - 2)

=> y = x² - 2x + 8x - 16

=> y = x² + 6x - 16

Kimberly spelled out y = x + 6x - 16

Joshua spelled out (x + 3)² - 25.

=>  (x + 3)(x + 3) - 25

=>  x² + 3x + 3x + 9 - 25

=>  x² + 6x - 16

In light of the fact that the three equations equal x2 + 6x - 16, they all represent the same function.

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There are 21 states landlocked and 27 states do not border an ocean.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Since there are 48 states in the continental United States, some of which are on the border of an ocean and some of which are not.

According to the question,

The ratio of the states having the border to the ocean and not having the border to the ocean = 7 : 9

Let the states having the border to the ocean = 7x

The states do not have a border to the ocean = 9x

Thus, 7x + 9x = 48

⇒ 16x = 48

⇒ x = 3

So, the states do not have a border to the ocean = 7 × 3 = 21

And, the states do not have a border to the ocean = 9 × 3 = 27

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To write 149600000000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point. 149600000000 in standard form would be written as 1.496 x 10^11.

To arrive at this form, we move the decimal point 11 places to the left (since there are 11 zeros in 149600000000) and add the power of 10 notation, indicating that we moved the decimal point 11 places to the left. The number 1.496 is the coefficient and 11 is the exponent. This way, we get 1.496 x 10^11 which is the standard form of 149600000000.

Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers. To write a number in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point. The number of places the decimal point is moved is indicated by a power of 10

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Yes, 1/4 and 2/8 equivalent fractions.

Mathematical fractions that have the same denominator but different numerators are called equivalent fractions. As an illustration, since 2/4 and 3/6 both equal 1, they are both comparable fractions. The total is divided into fractions. When referring to identical components of the total, equivalent fractions are utilized.

By multiplying the numerator and denominator by the same integer, it is possible to determine the equivalent fraction of each fraction. In spite of differences in appearance, equivalent fractions signify the same value. For instance, if you take one piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.

=  1/4 = 2/8

= 1/4 = 1/4

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Correct Question:

Are 1/4 and 2/8 equivalent fractions?.

The recursive formula represents the total amount of money in Victoria’s account at the end of the nth year

Generally, The recursive formula representing the total amount of money in Victoria's account at the end of the nth year is:

A(n) = A(n-1) + 15 + 0.02 * A(n-1)

where

To get the first value of A(n) we can use the initial condition

A(1) = 200 + 15 + 0.02 * 200

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