If 4 is added to twice the number n, the result is the same as if n were increased by 7. What is the value of n?

For diagram A, the unsimplified equation represents the relationship between x and y is y = x + x/3.

For diagram B, the unsimplified equation represents the relationship between x and y is y = x + 2x/3.

For diagram C, the unsimplified equation represents the relationship between x and y is y = x - x/3.

For diagram D, the unsimplified equation represents the relationship between x and y is y = x - 2x/3.

Performing mathematical operations reduces an unsimplified equation to a simplified equation. A simplified equation is used for convenience.

Diagram A:

The value of x contains 3 congruent colored rectangles. The noncolored rectangle is 1. So, the value of the noncolored rectangle will be x/3.

Clearly, y will be the sum of x and x/3, that is, y = x + x/3.

Therefore, the obtained answer is y = x + x/3.

Diagram B:

The value of x contains 3 congruent colored rectangles. The noncolored congruent rectangles are 2. So, the value of the noncolored rectangles will be 2x/3.

Clearly, y will be the sum of x and 2x/3, that is, y = x + 2x/3.

Therefore, the obtained answer is y = x + 2x/3.

Diagram C:

The value of x contains 3 congruent colored rectangles. So, the value of 1 rectangle will be x/3.

Clearly, y will be the difference between x and x/3, that is, y = x - x/3.

Therefore, the obtained answer is y = x - x/3.

Diagram D:

The value of x contains 3 congruent colored rectangles. So, the value of 2 congruent rectangles will be 2x/3.

Clearly, y will be the difference between x and 2x/3, that is, y = x - 2x/3.

Therefore, the obtained answer is y = x - 2x/3.

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Answer:

12 Days

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

To find the ratio of the problem (days: pages) we can use this equation:

pages read ÷ days it took = pages read each day

Fitting the numbers into the equation:

168 ÷ 7 = 24

So, everyday Kelly reads 24 pages.

To find out how many more days Kelly needs to read, if she reads at the same rate, we can use this equation:

(456 - 168) ÷ 24 = days left

We can use this to check our work:

168 + (24 ×?) = 456

Solving for the first equation:

(456 - 168) ÷ 24 = days left

288 ÷ 24 = 12

Now, we can check our work.

168 + (24 ×?) = 456

Inserting 12 into the equation:

168 + (24 × 12) = 456

168 + 288 = 456

Therefore, to complete the book it will take Kelly 12 more days.

The boat that will cost Stephanie less to buy and use is boat B, and the difference between the cost is $11.7.

Let's calculate first the cost of each boat:

Boat A

cost + repairs + gasoline for 3 years= total cost

2400 + 600 + gasoline cost

gasoline cost = 40 / 15 = 2.66 gallons per month x 36 = 95.76 X 3.89 = 372.5

2400 + 600 + 372.5 = 3,372.5

Boat B

cost + repairs + gasoline for 3 years= total cost

2800 + 250 + gasoline cost

gasoline cost = 40 / 18 = 2.22 gallons per month x 36 = 79.92 X 3.89 = 310.88

2800 + 250 + 310.88 = 3,360.88

Difference: 3,372.5 - 3, 360.88 = 11.7

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Answer: A

Step-by-step explanation:

: 4x+25, 3x+15. x=10

The solution to the equation is (b) x = -18

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

X

= 6

-3

Represent the equation properly

So, we have the following representation

x/-3 = 6

Cross multiply the equation

This gives

x = -3 * 6

Evaluate the products

x = -18

Hence, the solution is (b) x = -18

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The value of x in the triangle is 6√5

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

The triangle

Using the above as a guide, we have the following:

x/20 = 9/x

Cross multiply the equation

so, we have the following representation

x^2 = 180

TAke the square root of hoth sides

This gives

x = 6√5

Hence, the solution of x is  6√5

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Answer:

AB = a - 8b

Step-by-step explanation:

AB = AO + OB

    = - OA + OB

     = - (4a + 7b ) + (5a - b )

    = - 4a - 7b + 5a - b ← collect like terms

     = a - 8b

Answer:

(x+y)(8a - 1)

Step-by-step explanation:

For the first expression:

(a-7) - y(a-7)

We can factor out (a-7) from both terms:

(a-7)(1 - y)

So, the factored expression is:

(a-7)(1 - y)

For the second expression:

8a(x+y) - (x+y)

We can factor out (x+y) from both terms:

(x+y)(8a - 1)

So, the factored expression is:

(x+y)(8a - 1)

Answer: (1-y)(a-7) and (8a-1)(x+y)

Step-by-step explanation:

When the values in the parentheses are the same twice, they reappear only once after grouping. In the first problem, the coefficients are 1 and -y, therefore, the answer becomes (1-y)(a-7).

Hope this helps

MM

If we have four variables, then four equations will we have in our system of linear equations.

A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation that can be written in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point where the line intersects the y-axis.

Linear equations can be used to model a wide range of real-world phenomena, from simple physics problems such as calculating the speed of a moving object, to economic models that describe the relationship between price and demand. They are also widely used in fields such as engineering, finance, and statistics.

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The length of AC from the given triangle ABC is 10 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, in the right triangle ABC below, DE is parallel to AC, and DE is perpendicular to CB at E.

The length of AB is 26 units, the length of DE is 5 units, and the length of BE is 12 units.

Consider ΔABC and ΔBDE

∠BDE=∠BAC=90°

∠ABC=∠DBE (Reflexive property)

By AA similarity, ΔABC is similar to ΔBDE.

By midpoint line segment theorem,

AC=2DE

AC=2×5

AC=10 units

Therefore, the length of AC is 10 units.

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A step that is not performed in the process of solving n² - 12n - 10 = 0 by completing the square is: C. Factor n² - 12n - 10 = 0.

In order to solve the given quadratic equation, we would use the completing the square method as follows;

n² - 12n - 10 = 0

By keeping x terms on the left-hand side of the quadratic equation, we would move the constant term to the right-hand side of the quadratic equation by adding 10 on both sides as follows;

n² - 12n - 10 + 10 = 0 + 10

n² - 12n = 10

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

n² - 12n + (12/2)² = 10 + (12/2)²

n² - 12n + 36 = 10 + 36

n² - 12n + 36 = 46

(n - 6)² = 46

By taking the square root of each side, we have:

n - 6 = ±46

n = 6 ±46

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Complete Question:

Which step is NOT performed in the process of solving n² - 12n - 10 = 0 by completing the square?

Add 10 to each side

Add 36 to each side

Factor n² - 12n - 10 = 0

Take the square root of each side

The number of books to read per month is 3 or more.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

14x ≥ 42

Solve for x.

14x ≥ 42

Divide both sides by 14.

x ≥ 42/14

x ≥ 3

This means,

The number of books to read per month is 3 or more.

Thus,

The number of books to read per month is 3 or more.

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This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.

The interest rate in this situation is 19% compounded monthly. This means that each month, the interest rate is applied to the total balance. The formula to calculate the amount of interest owed is:Interest Owed = Balance x (Interest Rate/12) .In this case, the formula would be:Interest Owed = 16,783 x (0.19/12).This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.

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On solving the provided question, we can say that equation for getting amount spent by Daniel is y + 38 / 3 = x

A mathematical equatiοn is a formula that joins two statements and uses the equal symbοl (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equatiοn in algebra.

For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.

equatiοn for getting amοunt spent by Daniel -

x = y+38 / 3

Tracy then spent (in dοllars) accοrding to the provided descriptiοn (we don't write symbols like $ when writing equations because it is clear from the cοntext what the quantity stands fοr).

y = 3x - 38

y + 3x8 = 3x

y + 38 / 3 = x

equation for getting amοunt spent by Daniel is

y + 38 / 3 = x

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It's important to use sound statistical methods and careful analysis to ensure that the inferences drawn are as accurate as possible.

Statistical inference is the process of drawing conclusions or making predictions about a population based on data from a sample of that population. In other words, statistical inference involves using the principles of probability and statistics to make generalizations about a larger group based on information collected from a smaller group.

For example, a political survey may be conducted to gather opinions from a sample of voters about a particular issue or candidate. The data collected from this sample can be used to make inferences about the opinions of the larger population of voters. Statistical inference allows us to estimate the opinions of the larger population based on the information gathered from the smaller sample.

To illustrate this, suppose a survey is conducted on a random sample of 1000 voters in a city, and 600 of them indicate that they support a particular candidate. Based on this sample, the surveyors can use statistical inference to estimate the proportion of voters in the entire city who support that candidate. A confidence interval could be constructed to provide a range of values within which the true proportion of voters who support the candidate is likely to lie. This estimate can be used to inform political strategy and decision-making.

However, it's important to note that statistical inference is subject to certain assumptions and limitations, and there is always a degree of uncertainty associated with making predictions or generalizations based on a sample. Therefore, it's important to use sound statistical methods and careful analysis to ensure that the inferences drawn are as accurate as possible.

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Each of the following measurements contain a) 1, b) 4,c) 3,d) 1,e) 2,f) 4,g) 2  significant figures.

Significant digit -Precision refers to the number of digits to which a value can be assigned. Therefore, numbers that can have a value of digits are called significant digits.

Below are the key figures for each value reported.

(a) 2- 1significant digits

(b) 81.640 - 4 significant digits;

(c) 7.03 - 3 Significant Figures

(d) 0.003 - 1significant digits

(e) 0.0086 to 2 significant digits

(f) 3236 - 4 significant digits

(g) 8700 - 2 significant digits

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The standard deviation of the sampling distribution of x bar (the mean of a sample) is always less than the standard deviation of the population from which it is sampled.

Central Limit Theorem states that as the sample size increases, the sampling distribution of x bar approaches a normal distribution with a mean equal to the population's mean and a standard deviation equal to the population's standard deviation divided by the square root of the sample size.

Standard deviation of the sampling distribution of x = σ / √N,

where:

σ  = standard deviation of the population

N = sample size

As a result, the standard deviation of the sampling distribution of x bar is also less variable than the standard deviation of the population.  

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If the presented hypothesis is confirmed, it can be assumed that individuals in the experimental group suffer from headaches more frequently than those in the control group.

The study examines how stress affects headaches. The theory can be stated as follows: People who encounter stress episodes more than twice per day would feel headaches more frequently than people who do not experience stress. This question concerns a cause and effect analysis, which can be done with reliable results when using an experimental investigation. Therefore, it is advised to use an experimental design for dealing with headaches brought on by stress. Stress events are the only unchanging factor in our study, however they do cause changes in the frequency of headaches. The degree of headaches, which fluctuates when the independent variable is changed, can be thought of as the dependent variable. Here, the technique can be applied as follows: Informed consent is obtained from a sample of 400 persons, all of whom fall within the age range of 25 to 40 (to lessen the impact of any auxiliary variables on the results). The volunteers are divided into two groups at random, one of which is the experimental group and the other the control group (double-blind design to avoid any potential biases). Three times a day, participants in the experimental group are exposed to a show that is heavy on the negative feelings that can lead to stress; in contrast, individuals in the control group are not exposed to any of the shows mentioned above. Then, the presence of headaches is assessed in both groups' members.

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Answer:

5.6lbs

Step-by-step explanation:

multiply 180 by .08

8%=14.4

14.4-180=165.6

165.6-160= 5.6

Answer:

x = 72

Step-by-step explanation:

x : 4 = 54 : 3

express the ratios in fractional form

[tex]\frac{x}{4}[/tex] = [tex]\frac{54}{3}[/tex] = 18 ( multiply both sides by 4 to clear the fraction )

x = 4 × 18 = 72

The area of the sidewalk in terms of x would be 3 x ² + x + 2

The area of the sidewalk would be :

= Area of rectangular area - Area of rectangular garden

Area of rectangular area = 2 x ( 2x + 1 )

Area of rectangular garden = x ( x + 1 )

The area of the sidewalk in terms of x is therefore :

= ( 2 x ( 2x + 1 ) ) - ( x ( x + 1 ) )

= ( 4 x ² + 2 ) - ( x ² + x )

= 4 x ² + 2 -  x ² + x

= 4 x ² - x ² + x + 2

= 3 x ² + x + 2

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Answer:

-0.061 dollars per day.

Step-by-step explanation:

(R(t + h) - R(t)) / h

We can use this formula to find the average rate of change of R(t) over various time intervals h, starting with t = 3:

For h = 1 day:

R(3 + 1) = 30(3 + 1) - 3(3 + 1)^2 = 27 - 6 = 21

Average rate of change = (21 - 30(3) + 3(3)^2) / 1 = (21 - 27) / 1 = -6

For h = 0.1 day:

R(3 + 0.1) = 30(3 + 0.1) - 3(3 + 0.1)^2 = 29.7 - 8.91 = 20.79

Average rate of change = (20.79 - 30(3) + 3(3)^2) / 0.1 = (20.79 - 27) / 0.1 = -0.61

For h = 0.01 day:

R(3 + 0.01) = 30(3 + 0.01) - 3(3 + 0.01)^2 = 29.93 - 8.9699 = 20.9601

Average rate of change = (20.9601 - 30(3) + 3(3)^2) / 0.01 = (20.9601 - 27) / 0.01 = -0.061

As we can see, as the value of h decreases, the average rate of change approaches a more accurate value. The average rate of change of R(t) at t = 3 days is approximately -0.061 dollars per day.

Answer:

[tex]p(3and7)andq(1and9)[/tex]

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is 5/52

probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations.

Given that, if each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits

Like the 4 distinct letters be A,B,C,D

4 distinct nonzero digits are 2,3,4,5

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to the 10/104 = 5/52

Here the probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations and the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to 5/52

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The M.A.S motion for two different time periods {T} = 2s and

{T} = 2/3s is calculated above.

The general equation is -

y{t} = A sin(ωt + Ф)

Given is a body describes an M.A.S according to the function -

{x} = 2 cos{(π/2)T+ π)r

Now -

For {T} = 2, we can write -

{x} = 2 cos{(π/2) x 2+ π)r

{x} = 2 cos{2π}r

{x} = 2 x 1 x r

{x} = 2r

For {T} = 2/3, we can write -

{x} = 2 cos{(π/2) x 2/3+ π)r

{x} = 2 cos{π/3}r

{x} = 2 x -0.33 x r

{x} = - 0.66r

Therefore, the M.A.S motion for two different time periods {T} = 2s and

{T} = 2/3s is calculated above.

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{Question in english -

a body describes an M.A.S according to what is specified.

x= 2 cos (π/2 T+π) r

Find its elements in:

T= 2

T= 2/3 sec

K=f/x}

The volume of the given 3 - D figure is 156.36 cubic inches.

A volume is a collection of a three dimensional coordinate points enclosed by a two dimensional coordinate points.

Given is the 3 - D figure as shown in the image.

We can write the volume as -

V = πr²h/3 + lbh

V = (3.14 x 3 x 3 x 8)/3 + (9 x 9 x 1)

V = 156.36 cubic inches

Therefore, the volume of the given 3 - D figure is 156.36 cubic inches.

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The set representing the ordered numbers is given as follows:

0.45, 52%, 10/11, 31.

The numbers for this problem are given as follows:

For the three numbers with an integer part of zero, we order them according to the decimal part, hence:

0.45, 52%, 10/11.

31 has an integer part of 31 and is greater than the other numbers, hence the ordered data-set is given as follows:

0.45, 52%, 10/11, 31.

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The compound interest rate charged is given as follows:

13% per year.

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 for this problem are given as follows:

P = 12000, A(t) = 22109.22, n = 1, t = 5.

Hence the interest rate is obtained as follows:

22109.22 = 12000(1 + r)^5

(1 + r)^5 = 22109.22/12000

1 + r = (22109.22/12000)^(1/5)

1 + r = 1.13

r = 1.13 - 1

r = 0.13.

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