Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4

Table F shows a proportional relationship and its points are plotted in the graph shown in the image attached below.

In Mathematics, the graph of any proportional relationship is represented by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously.

Mathematically, a proportional relationship can be represented or modeled by the following linear equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2 = 8/4 = 10/2

Constant of proportionality, k = 2.

Therefore, the linear equation for this proportional relationship can be correctly written as follows:

y = kx

y = 7.5x

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Answer:

85 inches

Step-by-step explanation:

7*12+1=84+1=85

Answer: Here it is

Step-by-step explanation:

a) The perimeter of a shape is the sum of the lengths of all its sides. In this case, the shape has sides with lengths of 4, 5h, 7, and 2h. Therefore, the expression for the perimeter of the shape can be written as:

Perimeter = 4 + 5h + 7 + 2h

To simplify this expression, we can combine like terms:

Perimeter = 4 + 7 + (5h + 2h)

Perimeter = 11 + 7h

So, the simplified expression for the perimeter of the shape is 11 + 7h

b) The perimeter of the shape is 42.

We can use this information and the expression we found in part a) to find the value of h. We know that:

Perimeter = 11 + 7h = 42

We can subtract 11 from both sides to get:

7h = 42 - 11 = 31

Finally, we can divide both sides by 7 to find the value of h:

h = 31/7

h = 4.428 (approximately 4.43)

Answer: To find the batting average of a player, we need to find the ratio of hits to total attempts.

Jana's ratio is 12/15, and Tasha's ratio is 9/10.

To compare these ratios, we can simplify both of them to a common denominator. In this case, the common denominator is 15.

Jana's ratio can be simplified to 12/15, which is equal to 0.8

Tasha's ratio can be simplified to (9/15), which is equal to 0.6

So, Jana has a ratio that means she has a better batting average (0.8) compared to Tasha (0.6)

Alternatively, we can convert these ratio to percentage by multiplying them by 100.

Jana's batting average is 12/15 * 100 = 80%

Tasha's batting average is 9/10 * 100 = 90%

By this way also we can see that Tasha's batting average is higher than Jana's batting average.

Step-by-step explanation:

Answer:

The quotient of two real numbers is not necessarily an integer. When dividing two real numbers, the result can be any real number, including a fraction or a decimal. It can be an integer only if the divisor is a factor of the dividend. In other words, if the remainder of the division is zero, the quotient is an integer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. The least square regression equation of Y on X is: Y = 3.08X - 127.82

b. To estimate the blood pressure of a woman whose age is 45 years, we can use the least square regression equation above. Substituting X = 45, we get: Y = 3.08(45) - 127.82 = 143.46. Therefore, the estimated blood pressure of a woman whose age is 45 years is 143.46.

The derivation of the function y = (4x+9x^2)(3x-7x^4) by the means of direct formulas is y = 12x^2 + 27x^3 - 28x^5 - 63x^6.

The direct formula method is a way to multiply two or more algebraic expressions together by applying the distributive property and combining like terms. It is also known as the "FOIL" method for multiplying binomials.

The direct formula method involves breaking down each expression into its individual terms and then using the distributive property to multiply each term in the first expression by each term in the second expression. After that, the resulting terms are combined according to the addition and subtraction rules of like terms.

To derive the function y = (4x+9x^2)(3x-7x^4) using the direct formulas method, we need to multiply the two expressions inside the parentheses:

y = (4x+9x^2)(3x-7x^4)

y = 4x3x + 4x-7x^4 + 9x^23x + 9x^2-7x^4

Using the distributive property, we can simplify the expression by combining like terms:

y = 12x^2 - 28x^5 + 27x^3 - 63x^6

y = (12x^2 + 27x^3) - (28x^5 + 63x^6)

So the final expression is y = 12x^2 + 27x^3 - 28x^5 - 63x^6

The direct formulas method uses the distributive property and the combination of like terms to derive the final expression of the function.

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The top of the hill have an altitude of 1391 feet above sea level

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

From the table, checkpoint 3 is at 1327 feet above sea level. Since the top of a hill rises 64 feet above checkpoint 3, hence:

Altitude of hill = 1327 + 64 = 1391 feet

The top of the hill is 1391 feet

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Answer:

a) The function is growth.

b) The growth rate in % is 4%. This can be determined by taking the natural logarithm of the coefficient (1.04) and multiplying it by 100.

ln(1.04)*100 = 3.98% ≈ 4%.

The quotient of these two expressions is not a finite value.

A quotient is a result obtained by dividing one quantity by another. It is the number that results from dividing one number by another.

Here,

Given : The quotient of

2-√√√8

and

4+√12

is not a finite value.

Explanation:

The square root of 8 is 2, so the first square root is 2, the second one is also 2, the third one is 2 again.

So the expression inside the first square root becomes 8, and the whole first square root becomes 2.

So the final expression would be:

2 - (2) = 0

On the other hand, √12 = √(223) = 2*√3

So the final expression would be:

4+2*√3

Hence, the quotient of these two expressions is not a finite value.

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The group of 20 students will save $144 by using the promotional deal. Half of the group, or 10 students, will get the free cotton candy, so that's $30 saved. 14 of the students will get the free soda, so that's another $28 saved. Added together the group of 20 students will save $58 on the cotton candy and $28 on the soda for a total savings of $144.

If h(x) is equal to the composition between functions f(x) and g(x), then we must have:

f(x) = 1/x.

Here we have the function:

h(x) = 1/(x - 5)

And we know that we can write function h as a composition of other two functions:

h(x) = f( g(x) )

Where we know that:

g(x) =x - 5

Remember that the composition of two functions means that we are evaluating one in the other, in this case is rater easy to notice that we must have:

f(x) = 1/x

Then when we evaluate this in g(x) we will get:

f(g(x)) = 1/g(x)

Now we can replace g(x) by the actual function:

f(g(x)) = 1/g(x) = 1/(x - 5)

And that is h(x).

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Answer

[tex] - 5 \sin(5x) [/tex]

Answer:

(a) The central 95% of IQ scores in a standardized test would be found in the interval from 85 to 115. This is because a normal distribution is symmetric around the mean, and 95% of the data falls within two standard deviations of the mean. So, the interval would be mean - 2standard deviation to mean + 2standard deviation i.e. 100 - 215 to 100 + 215 = 85 to 115

(b) About 2.5% of people should have IQ scores above 115. This is because the IQ scores follow a normal distribution and IQ scores above 115 are considered to be in the top 2.5% of the distribution.

(c) About 16% of people should have IQ scores between 70 and 85. This is because the IQ scores follow a normal distribution, and IQ scores between 70 and 85 fall within one standard deviation of the mean (85 is one standard deviation below the mean and 70 is one standard deviation below that)

(d) About 0.1% of people should have IQ scores above 130. This is because IQ scores above 130 are considered to be in the top 0.1% of the distribution.

Step-by-step explanation:

Answer: We can write an inequality to show how many more inches Bobby needs to grow to reach his desired height by using the following information:

Bobby hopes that he will someday be more than 72 inches tall.

He is currently 59 inches tall.

We can use the inequality x + 59 > 72, where x is the number of inches Bobby needs to grow to reach his desired height.

This inequality represents the total height (x + 59) being greater than the desired height (72).

To solve this inequality, we can subtract 59 from both sides:

x > 72 - 59

x > 13

So, Bobby needs to grow 13 inches or more to reach his desired height.

Step-by-step explanation:

Answer: Here it is

Step-by-step explanation:

A.

Arithmetic Mean: 30.57

Median: 32

Mode: 41

Range: 41-23 = 18

B.

Upper Quartile: 39

Lower Quartile: 25

D7: 25

P50: 32

C.

Variance: In order to calculate the variance I would need the data set to be presented in a tabular form with the observations as rows and one column for the data.

Coefficient of Variation: Same as above.

D.

Pearson coefficient of skewness: I would need the data set to be presented in a tabular form with the observations as rows and one column for the data.

Kurtosis: Same as above.

Polar form of the given problem are expressed below

In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modelled as a union of argument and modulus.

Given, Some numbers that we need to write in polar form

General formula of polar form = r * [tex]e^{ia}[/tex]

For polar/rectangular conversion we use the following transformations

r² = x² + y²

x = r cosa

y = r sina

Where a is angle

For (a) 1/5

r = 1/5

a = 0

Since angle is 0

Polar form = 1/5

For  (b) 4 +4i

r = √4² + 4² = 4√2

a = tan(4/4) = tan (1) = pi/4

Polar form = 4√2 [tex]e^{ipi/4}[/tex]

For (c) -6 + 6 i

r = √-6² + 6² = 6√2

a = tan(-6 /6)

a = -pi/4

Polar form = 6√2[tex]e^{-ipi/4}[/tex]

Therefore, polar form of the given questions written above.

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The altitude of the hill whose top rises 64 feet above checkpoint -213, is 277 feet above sea level.

The altitude refers to the vertical distance or height of an object or point in relation to sea level (true altitude) or ground level (absolute altitude).

The altitude of a hill refers to its height measured from the ground level or the sea level, as the case may be.

In this situation, we can compute the altitude of the hill as the difference between the rise of the hill or mountain above the checkpoint and the given checkpoint.

The rise of the top of a hill = 64 feet

Given checkpoint = -213

The altitude of the hill = 277 feet [64 - (-213)]

Thus, the position or altitude of the hilltop in relation to the ground or sea level is 277 feet.

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There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson. The road junction to Timpson is option B. 20.57 miles.

To find the distance between Timpson and the junction point, we can use the Pythagorean theorem. Let's call the distance "d".

d^2 = (60 - 22)^2 + 12^2

d^2 = 38^2 + 144

d^2 = 1444

d = √(1444) = 38.03

So the distance between Timpson and the junction point is 38.03 miles. The distance between the junction point and Ashburn is simply 22 miles, so the total distance from Timpson to Ashburn is 20.57 miles (38.03 + 22).

Therefore, the distance between the road junction to Timpson is option B. 20.57 miles

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The complete question goes thus:

There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson. How far is the road junction to Timpson

A. 21.57miles

B. 20.57miles

C. 10.57miles

D. 57.12 miles

The vertex form of the parabola is y + 1 = - 4 · (x + 1)².

Graphically speaking, parabolae can be generated by quadratic equations, whose forms are described below: (Please notice that the parabola described by statement is parallel to y-axis since axis of symmetry is a vertical line)

Standard form

y = a · x² + b · x + c

Vertex form

y - k = C · (x - h)²

Where:

If we know that h = - 1, k = - 1 and (x, y) = (0, - 5), then the equation of the parabola in vertex form is:

C = (y - k) / (x - h)²

C = (- 5 + 1) / (0 + 1)²

C = - 4 / 1²

C = - 4

The equation of the parabola in vertex form is equal to y + 1 = - 4 · (x + 1)².

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Considering the context of the question and the mathematical expression, the height of the frame. after the width is reduced to 3 inches will be 1.8 inches.

Dimension is a term that is used to describe the measurement of the size or distance of an object or region or space in one direction.

Generally, the term dimension is the measurement of the length, width, and height of anything.

In this case, as given in the question

A frame is 10in wide and 6 in tall.

reduces to a width of 3 in

let us assume that the height of the frame after reducing the width to 3in be = x

then the equation becomes original width/ original length = reduced width/reduced length

put all the value, we get

[tex] = 10 \div 6 = 3 \div x[/tex]

solve the above

[tex]x = (6 \times 3) \div 10 \\ x \: = 1.8in[/tex]

Therefore, in this case, it is concluded that the correct answer is 1.8in, which will be the tall or height of the frame.

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The geometric shape formed is a rhombus.

A quadrilateral is a four-sided shape enclosed shape, where the sum of the internal angle is 180°.

Here,
It is mentioned in the question, we have to construct a quadrilateral with two pairs of parallel sides and two angles measuring 125°.
So, the construction of a quadrilateral is shown.
As seen in the figure, the figure is of a rhombus.

Thus, the geometric shape formed is a rhombus.

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Area of figure 1 is 468 cm² and figure 2 is 45 cm².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

In these given figure for calculating the area of them we need to divide them into two or more shape like rectangle, triangle or square. For example, I will take Figure 1 and 2

For figure 1

Length of base = 16 + 14 =  30 cm

Length of right rectangle whose side is 14 and 14(smaller one)

Thus, its area = 14 * 14 = 196

Area of left rectangle whose side is 16 and 17 = 16 * 17 = 272

Total area of the figure = 272 + 196 = 468 square cm

For figure 2

If we split them into two shape they will become a square and a triangle

Area of triangle = 1/2 base * height = 1/2 * 6 *3 = 9

Area of square = side * side = 6*6 = 36

Thus, total area = 9 + 36 = 45 square cm

Therefore, Area of these given figures(in unit square) are:

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The total surface area of the rectangular prism is 160 inches².

Since the base of the rectangular prism is a square, we know that the edge length of the base is the square root of the area of the base. The area of the base is 16 square inches (since it can be completely covered by 16 squares with edge length of 1 inch), so the edge length of the base is 4 inches.

Since the height of the prism is twice the edge length of the base, the height of the prism is 8 inches.

The total surface area of a rectangular prism is given by the formula:

2lw + 2lh + 2wh

Where l is the length, w is the width and h is the height

So, the total surface area of the rectangular prism is:

2(4 inches * 4 inches) + 2(4 inches * 8 inches) + 2(4 inches * 8 inches)

= 160 square inches

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Answer:

Step-by-step explanation:

Linear functions can be used in many real-world applications such as:

Economics: Linear functions can be used to model the relationship between the price of a product and the quantity of the product that will be sold.

Engineering: Linear functions can be used to model the relationship between force and displacement in elastic materials.

Sciences: Linear functions can be used to model the relationship between the concentration of a substance in a solution and the time it takes for that substance to be consumed or produced.

Business and Finance: Linear functions can be used to model the relationship between the cost of a product and the number of products produced.

Graphing: Linear functions can be used to graph the relationship between different variables.

Transportation: Linear functions can be used to model the relationship between the distance traveled and the time it takes to travel that distance at a constant speed.

Construction: Linear functions can be used to model the relationship between the height of a building and the number of floors in the building.

Weather forecasting: Linear functions can be used to model the relationship between temperature and time of the day.

I'm going to provide a real life case for this answer. I own and manage an online soccer jersey store and the process behind it is quite simple:

1. Receive order

2. Buy jerseys from supplier

3. Resell at an slighly higher price

4. Pay taxes + shipping

Now, say that "x" is the amount of jerseys my store sells in a month. I can use functions to create an expression that tells me what is the total net revenue I get from selling "x" amount of jerseys a month.

For example, say that the jerseys cost $50 and you sell them for 60$. You also need to pay the shipping for each jersey (say it is $5 per jersey). Then, we can form a function like this:

[tex]y=60x-50x-5x[/tex]

As you can tell, the money that comes back to the seller ($60 dollars per jersey) is expressed as a possitive coefficient for variable "x" (number of sold jerseys). And, all the other costs, which is money that you spend in order to sell the jerseys, are expressed with a negative coefficient meaning that they are not net revenue, it isn't profit. Now, to see how much money you can make by selling 2 jerseys, simplify the function and substitute variable "x" (number of sold jerseys) by 1:

[tex]y=60x-55x\\ \\y=5x[/tex]

Say "y" is the net revenue:

[tex]y=5(2)\\ \\y=10[/tex]

You can also use functions to determine things such as, how many jerseys do I need to sell in order to make $750 of net revenue? In that case you do the following:

[tex](750)=5x\\\\x=\frac{750}{5} \\ \\x=150[/tex]

From this analysis, you can conclude that you need to sell 150 jerseys ij order to amke a net revenue of $750.

In conclusion, linear functions can be used to see how a variable value (normally called "x") can affect in the results in multiple daily situations: how many miles can your car run with a full tank, how much time do I need to work so I can buy a product, how much money I can spend in something so I can have saving of "x" amount at the end of the year, etc...

To complete the hole on schedule the minimum amount of time the drill must continue to work is 18 hours

The rate of the drill for the remaining part of creating the whole is 56 feet per hour of digging

The remaining depth of the hole = the total hole - the depth before the rock

The remaining depth of the hole = 1012 - 2.75

The remaining depth of the hole = 1009.25

At a rate of 56 feet per hour the number of hours to dig 1009.25

56 feet = 1 hour

1009.25 feet = ?

cross multiplying

? * 56 = 1 * 1009.25

? = 1009.25/56

? = 18  

approximately 18 hours will take the drill to reach complete the hole

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Sherree's score on her 12th game is 86.67 in her golf game using equation.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

In order to have ordered pairs of the kind, relations and functions provide a mapping between two sets (Inputs and Outputs) (Input, Output). In algebra, relationship and function are crucial ideas. They are commonly employed in both real life and mathematics.

At games =2 score was 120

At games = 8 score was 100

so the equation is

y - 2 = (8-2)/(100-120) *(x-120)

⇒ (y-2)*(-20) = 6(x - 120)

⇒ -20y + 40 = 6x -720

⇒ 6x + 20y = 760

⇒ 3x + 10 y = 380

So, for y = 12

3x + 12*10 = 380

⇒ 3x +120 = 380

⇒ x = 260/3 = 86.67

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The length of the rectangle is [tex]x^{4}[/tex]- 7 units.

We know that,

                  Area of a rectangle = length* width

           So,                       Length = Area/width

According to the question,

                                    Area = [tex]7x^{5} - 49x[/tex]

                                   Width = [tex]7x[/tex]

             Length of the given rectangle = Area/width

                                                                = [tex]\frac{7x^{5}- 49x}{7x}[/tex]

                                                                = [tex]\frac{7x(x^{4}- 7)}{7x}[/tex]

                                                                = [tex]x^{4} - 7[/tex]

Hence, the length of the rectangle is [tex]x^{4} - 7[/tex] units.

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The complete question is:

A rectangle has an area of [tex]7x^{5}- 49x[/tex]. Its width is 7x units. What is its length?

Explanation:

The points do not fall on the same line, but the points trend upward as we move to the right. This means that a straight line can get somewhat close to all of the points to represent the average trend of what's going on.

Answer:

linear :)

Step-by-step explanation:

ive already answered this question and got it right <3