The equation 1 – 4∕3x = 1∕2(–x + 7) has what type of solution set?
Question 14 options:

A)

One solution

B)

Infinitely many solutions

C)

Two solutions

D)

No solutions

Answer: AS 1

Step-by-step explanation:

The best estimation of the equation 7/8 − 6/11 is 1/3

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

the best estimation of the equation 7 8 − 6 11

Express properly

So, we have

7/8 - 6/11

Take the LCM

This gives

7/8 - 6/11 = (77 - 48)/88

Evaluate the difference

7/8 - 6/11 = 29/88

Approximate

7/8 - 6/11 = 30/90

So, we have

7/8 - 6/11 = 1/3

Hence, the estimate is 1/3

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The quadratic regression in this case is y = 126.01x2 - 312.04x + 888.88.

An analysis tool called quadratic regression is implemented to identify the parabola equation that perfectly matches a given collection of data. Finding the equation of the straight line that most closely matches a collection of data is the goal of this sort of regression, which is an expansion of simple linear regression.

Step 1:  Input the data sets into the graphing calculator.

Step 2: Choose "Scatter Plot" from the graphing calculator's interface.

Step 3: Choose "Quadratic Regression" from the graphing calculator's toolbar.

Step 4: The calculator will create the equation y=ax2+bx+c, where a, b, and c are constants.

Step 5: Round the constants to the hundredths place, and the best-suited quadratic model's equation will be: y = 0.06x2 - 3.12x + 4.00.

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Answer:

Mike is incorrect.

Step-by-step explanation:

In this figure, corresponding angles are equal. However there is no guarantee that the corresponding sides are equal. For example, ΔDEF may be ΔABC dilated by a scale factor of 10, say. This means the angles will remain the same but the sides will be different

So Mike is incorrect.

Answer:

On the Venn diagram, these common elements are located inside the intersection of the three circles representing sets A,B and C . From the figure, we see that 7 and 4 belong to this mutual intersection. So, the roster form of set A∩B∩C A ∩ B ∩ C is given as {4,7}

i hope that help, i am not sure if i am correct

10.44 Percent of increase in the price of a basketball .

A percentage is a number or ratio that is expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to denote it. A percentage is a dimensionless number; there is no specific unit of measurement for it.

By divided the number by the entire value and multiplying the outcome by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

The price of basketball increased = $18.50 -$16.75 = 1.75$

Now the percent of increase in the price= 1.75/16.75×100

= 10.44%

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Answer:The missing length can be found using the formula for the area of a triangle, which is:

Area = (base * height) / 2.

We know the base is 18.7 inches and the area of the shaded region is 152.405 in^2.

So, the height can be found using the formula:

152.405 = (18.7 * height) / 2

Solving for height:

height = 2 * 152.405 / 18.7

height = approximately 12.67 inches.

The expression that presents the number of trees that Shannon planted will be 6 - t.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Shannon planted t fewer trees than toby. Toby planted 6 trees.

Then the number of trees that Shannon planted will be given as,

⇒ 6 - t

The expression that presents the number of trees that Shannon planted will be 6 - t.

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Therefore , the solution of the given problem of ratio comes out to be

 x = 13/22 cups of dish soap.

A set of equivalent variables "a" and "b" can be defined using the straightforward formula "a / b," where "b" may be bigger than zero. Two ratios are combined to make one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. 3/4 of the group are girls, while 1/4 are boys. Parts can be a division between one or more items, a number, or a portion of the volume of a component.

Here,

Given:

=> 1/2 cup of dish soap

=> 11/2 cups of water

and,

Ratio of dish soap and water is

=> 1/2 : 11/2

=> 1 : 11

After 1 cup addition of water:

=> 11/2 + 1 = 13/2

and

Let x be the new cup of dish soap

So, ratio :

=>  x : 13/2 =  1 : 11

=> 2x : 13 = 1:11

=> 13 = 22x

=> x = 13/22

Therefore , the solution of the given problem of ratio comes out to be

 x = 13/22 cups of dish soap.

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The solution is Option B.

The scale factor of the translated triangle is S = 16

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the perimeter of the first triangle be P

The value of P = 3 m

Now , the triangle is translated by a scale factor of S

And , the perimeter of the translated triangle = 48 m

So , the scale factor = perimeter of the translated triangle / perimeter of the first triangle

Substituting the values in the equation , we get

The scale factor of the translation S = 48/3

The scale factor of the translation S = 16

Hence , the scale factor is 16

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The scale factor of the triangles will be 16:1. The correct option is B.

A scale factor is a numerical value that is used to represent an object's enlarged or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its original size.

It aids in altering the figure's size but not its shape. The scale factor is defined as the proportion of the new image's size to that of the previous image.

Given that a triangle with a perimeter of 48 meters was created from a triangle with a perimeter of 3 meters using a scale factor.

The scale factor will be calculated as:-

Scale factor = 48 / 3

Scale factor = 16: 1

Therefore, the scale factor of the triangles will be 16:1. The correct option is B.

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Answer:

4x - 7

Step-by-step explanation:

The x represents Bob's age since, we don't know what it is, I put it as a variable.

2x      This represents Jeff who is 2 times Bob's age.

x - 7    Peter is younger than Bob by 7 years so we need to take away 7                    from Bob's age

2x + x - 7 + x    This would be the expression

4x - 7                Now just combine the like terms. We don't have Bob's age so the expression will stay like this.

The equivalent markup price will be $31.675.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that the cost is $25 and the markup percentage is 26.7%. The markup cost will be calculated as:-

Price = cost x Percentage increase

Price = 25 x 1.267

Price = $31.675

Therefore, the equivalent markup price will be $31.675.

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Yes, these steps are correct for solving a linear equation with one variable.

Variables on the same side: This step involves rearranging the equation so that all the terms with the variable are on one side and all the constant terms are on the other. This is done so that we can isolate the variable and find its value.

Use distributive property to remove parentheses: If there are parentheses in the equation, we can use the distributive property to remove them. For example, if the equation is 3(x + 2) = 9, we can distribute the 3 to get 3x + 6 = 9.

Combining like terms involving the variable: After distributing, we can combine like terms, i.e., terms with the same variable, to get a simplified equation. For example, if the equation is 3x + 2x = 5, we can combine the terms to get 5x = 5.

Subtracting non-variable terms from both sides: If there are any constant terms on the side with the variable, we can subtract them from both sides to isolate the variable even further. For example, if the equation is 5x = 5, we can subtract 5 from both sides to get 0 = 0.

Isolate the variable: The final step is to divide both sides by the coefficient of the variable to find its value. For example, if the equation is 0 = 0, we can divide both sides by 5 to get x = 1.

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Answer:

see below

Step-by-step explanation:

2x+5y=50.25

3x+4y=53.50

use 2nd equation minus first equation to get

x-y=3.25

so x = 3.25+y

substitute x with above equation

2*(3.25+y) +5y =50.25

so 6.5+2y+5y = 50.25

7y = 43.75

y=6.25

x=3.25+y =9.5

The solution set of the given equation is; -10

The equation is expressed as;

(2x + 5)/2 - 3x/(x - 2) = x

Multiply through by 2(x - 2) to get;

(2x + 5)(x - 2) - 6x = 2x(x - 2)

2x² + 5x - 4x - 10 - 6x = 2x² - 4x

2x²  will cancel out to get;

-5x - 10 = -4x

5x - 4x = -10

x = -10

Thus that value of x is the solution

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Gina Wilson is an Australian intersex human rights activist. She was the founding president of Intersex Human Rights Australia

Define parallel lines?

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Following are the different sides of the triangles -

The line segment that divides a triangle in half and connects one vertex to the middle of the other side is known as the median in geometry. There are an equal number of medians at each vertex of a triangle, and they all intersect at the triangle's centroid.

The triangle's three medians are the line segments with endpoints at the triangle's vertices and the midpoint of the opposite side. The point where all medians converge is known as the centroid.

1. The sides are in same ratio,

[tex]\frac{24}{9} = \frac{32}{x}\\[/tex]

⇒ [tex]x = \frac{32 \times 9}{24}[/tex]

⇒ [tex]x = 12[/tex]

2. [tex]\frac{20}{14} = \frac{33}{x}[/tex]

⇒ [tex]x = \frac{33 \times 14}{20}[/tex]

⇒ x = 23.1

3. [tex]\frac{x+ 5}{30} = \frac{16}{20}[/tex]

⇒ [tex]x = \frac{16 \times 30 }{20} - 5\\x = 19[/tex]

4. [tex]\frac{x+8}{2x - 5} = \frac{20}{22.5}[/tex]

⇒ [tex]22.5x + 180 = 40x - 100\\[/tex]

⇒ [tex]17.5 x = 280[/tex]

⇒ [tex]x = 16[/tex]

8. [tex]\frac{33}{41.8} \neq \frac{45}{57}[/tex]

∴ ST is not parallel to PR.

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Answer:

below

Step-by-step explanation:

This is isosceles because you have TWO equal sides

Equilateral has THREE equal sides

The length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.

Now, According to the question:

The area of a rectangular page can be calculated using the area of a rectangle which is just the product of the length and the width of the page.

                                                         A = lw

Here, l represents the length of the page and w represents the width of the page.

Determine the dimensions of a page given that the printed area is [tex]30in^2[/tex]

and the page has margins on each side, each having a width of 1in.

We will first set up an equation using the details that we know. We know that the printed area is  [tex]30in^2[/tex] We can let x be the length of the printed area and y be the width of the printed area. Assuming that the printed area is rectangular, the area is

[tex]A_p=xy[/tex]

30 = xy

[tex]y = \frac{30}{x}[/tex]

Now, we want to minimize the amount of paper used. The length of the entire page would be x + 2 since we have to consider the 1-in margins at the top and the bottom. Similarly, the width would be y+ 2  since we have to consider the margins at the sides. The area of the page is as follows.

A = (x+2)(y + 2)

We can substitute the value of y in terms of x.

A(x) = (x + 2)([tex]\frac{30}{x} +2[/tex])

A(x) = x ([tex]\frac{30}{x}[/tex]) + 2x + 2[tex](\frac{30}{x} )[/tex] + 4

A(x) = 30 + 2x + [tex]\frac{60}{x}[/tex] + 4

A(x) = 34 + 2x + [tex]\frac{60}{x}[/tex]

We want to minimize this area, so we will apply differentiation to this function. By finding its derivative and equating it to zero, we can find the value/s of x that will minimize the area.

A'(x) = [tex]2-\frac{60}{x^2}[/tex]

0  = [tex]2-\frac{60}{x^2}[/tex]

[tex]2 =\frac{60}{x^2}[/tex]

[tex]2x^2=60\\\\x^{2} =\frac{60}{2}\\ \\x^{2} =30\\\\x =[/tex]±[tex]\sqrt{30}[/tex]

Since we are dealing with dimensions, we can only choose the positive value, x =√30. Now, to determine if this would really minimize the area of the page, we can substitute it into the second derivative of the function. If the result is positive, the value of x would give the minimum area.

A"(x) = [tex]\frac{120}{x^3}[/tex]

[tex]A"(\sqrt{30} )=\frac{120}{(\sqrt{30})^3 }[/tex]

[tex]A"(\sqrt{30} )=0.73[/tex]

We can now use the value of x to find the dimensions of the page. Take note that the dimensions of the page are x + 2 and y + 2

x + 2 = √30 + 2

y + 2 = [tex]\frac{30}{x}[/tex] + 2

y +2  = [tex]\frac{30}{\sqrt{30} }[/tex] + 2

y + 2 = [tex]\sqrt{30}+2[/tex]

Therefore, the length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.

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The equation that represents the total cost that Debra paid is: C = 5N

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Information about the problem:

The function that models the situation is the following:

C = 5N

Where:

Number of notebooks = N

Cost of each notebook = $5

Total cost = C

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Correctly written question:

Debra purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Debra paid.

Refer to the images attached. Edit: I realized after uploading this answer that the integral in terms of y is MUCH easier, so I attached that as well :) But at least you know it can be done both ways!

Step-by-step explanation:

The Organisation for Economic Co-operation and Development (OECD) is an international organization that aims to promote economic growth and prosperity, as well as to improve social well-being through research and policy analysis.

Five research activities related to corporate governance by OECD are:

Corporate Governance Principles and Guidelines

Board Diversity and Gender Equality

Board Evaluation and Succession Planning

Shareholder Engagement and Activism

Anti-Corruption and Integrity in Corporate Governance.

Therefore , the solution of the given problem of velocity comes out to be (-8*(1 + h)² + 24*(1 + h)) - 16 / h

Velocity is a vector quantity that measures the rate of change of an object's position in space. It is defined as the rate of change of an object's displacement over a specific interval of time .

In physics, velocity is one of the most important quantities used to describe the motion of an object. It is used to calculate the acceleration of an object, the work done on an object, and the force required to change the velocity of an object.

Here,

The average velocity of an object over an interval [t1, t2] is given by the formula:

V = (x(t2) - x(t1)) / (t2 - t1)

where x(t) is the position function.

a) Average velocity over [1, 4]:

V = (-84² + 244) - (-81² + 241) / (4 - 1)

= (-816 + 96) - (-81 + 24) / 3

= (96 - 128) / 3

= -32 / 3

b) Average velocity over [1, 3]:

V = (-83² + 243) - (-81² + 241) / (3 - 1)

= (-89 + 72) - (-81 + 24) / 2

= (72 - 64) / 2

= 8 / 2

= 4

c) Average velocity over [1, 2]:

V = (-82² + 242) - (-81² + 241) / (2 - 1)

= (-84 + 48) - (-81 + 24) / 1

= (48 - 32) / 1

= 16

d) Average velocity over [1, 1 + h]:

V = (-8*(1 + h)² + 24*(1 + h)) - (-81² + 241) / ((1 + h) - 1)

= (-8*(1 + h)² + 24*(1 + h)) - (-8 + 24) / h

= (-8*(1 + h)² + 24*(1 + h)) - 16 / h

The value of h is any real number greater than 0, so the answer is a general expression that depends on the specific value of h.

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The monthly rate percentage is given as follows:

r = 0.65%.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which the parameters are given as follows:

To obtain the monthly interest, we must consider that:

[tex]\left(1 + \frac{r}{12}\right)^{12 \times \frac{1}{12}} = 1.0777[/tex]

Hence the equation is simplified as follows:

r = 0.0777/12

r = 0.0065.

r = 0.65%.

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The average cost of gas in June 2022 is $5.01

In September of 2021, gas cost $3.17 on average in the United States.

By June of 2022, the cost of gas had increased by 58%, so we can calculate the increase as:

Increment = 3.17 * 0.58 = 1.84

Adding the increase to the starting price:

3.17 + 1.84 = 5.01

So in June of 2022, gas cost $5.01 on average in the United States.

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$120.00 increased by 20% is $144.00

Answer:

3,636.36

Step-by-step explanation:

Let x be the number

19.8% de x = 720

19.8% =19.8/100 = 0.198

0.198x = 720

x = 720/0.198 =  3,636.36

The variance of x is 258.2, rounded to the first decimal place.

The variance of a discrete probability distribution with values x and corresponding probabilities f(x) is given by the formula:

Var(x) = Σ[x^2 × f(x) - (Σ[x × f(x)])^2]

To find the variance of x, we need to first find the mean of x, which is given by the formula:

mean(x) = Σ[x × f(x)]

Using the given probability distribution f(x), we can calculate the mean and variance as follows:

mean(x) = Σ[x × f(x)] = 0 × (15!/0!(15-0)!) × (1/5)^0 × (4/5)^(15-0) + 1 × (15!/1!(15-1)!) × (1/5)^1 × (4/5)^(15-1) + 2 × (15!/2!(15-2)!) × (1/5)^2 × (4/5)^(15-2) + ... + 15 × (15!/15!(15-15)!) × (1/5)^15 × (4/5)^(15-15) = 15 × (1/5) = 3

Var(x) = Σ[x^2 × f(x) - (Σ[x × f(x)])^2] = 0^2 × (15!/0!(15-0)!) × (1/5)^0 × (4/5)^(15-0) + 1^2 × (15!/1!(15-1)!) × (1/5)^1 × (4/5)^(15-1) + 2^2 × (15!/2!(15-2)!) × (1/5)^2 × (4/5)^(15-2) + ... + 15^2 × (15!/15!(15-15)!) × (1/5)^15 × (4/5)^(15-15) - (mean(x))^2 = 267.2 - (3)^2 = 267.2 - 9 = 258.2

The variance of x is 258.2, rounded to the first decimal place.

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Answer: y = -11

Step-by-step explanation:

-5x + 2y + 10 = 8

(If x= -4, then...)

or -5(-4) + 2y+10=8

or 20 + 2y + 10 = 8

or 2y = 8-20-10

or 2y = -22

or y = -22/

or y = -11

Explanation:

The equation y = 2 is horizontal. Anything parallel to this will also be horizontal. The answer is of the form y = k, where k is some real number. We replace k with 1 since we need the answer to go through (4,1). All points on the answer line have a y coordinate of 1.

The equation y = 1 is the same as y = 0x+1, which shows we have a slope of 0.

The number of number plates assigned is 40,219,200.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Given that, a seven-digit license plate with the following pattern: L L N – L N N N.

There are 3 letters with the restriction of no vowels and 4 numbers between 0-9.

With no vowels, we have 21.

= 21!/3!(21-3)! + 10!/(10-4)!

= 7980×5040

= 40,219,200

Therefore, the number of number plates assigned is 40,219,200.

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