what is the difference between 7 and 10

The answer is decreases.

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression.

The algebraic equation can be written in the many forms. It can be in one variable , two variable or even three or four variable. There are also many ways to put all into the equations.

So, as the question stated As x is increases, the value of the expression decreases.

Therefore, the answer is decreases.

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We need to use the formal definition of a limit, The definition is:

Let be L be a real number. Then:

if, for every ε > 0, there exists a δ > 0 such that if 0 < |x - a| < δ, then |f(x) - L| < ε

In this case, we need to prove:

Then, we need to find a relationship between ε and δ, so for any value of ε> 0 we can find a value of δ.

We know that, for a given ε > 0, |(5x -7) - 3| < ε, and 0 < |x - 2| < δ

Then:

Now we can divide each side by 5.

We are now really close from relate the ε and δ.

We can use the triangle inequality:

Then, we can add and subtract 1 inside the absolute value:

We have:

By the triangle inequality:

And since the absolute value of any number is bigger or equal than 0:

And we have:

And since ε > 0, ε/5 > 0, we can define:

And we have proven that:

For a given ε > 0, exists δ = ε/5 such that, if 0 < |x - 2| < δ = ε/5, then |f(x) - L| < ε

The point estimator of the mean percentage of airline reservations canceled on the day of the flight is the midpoint of the 95% confidence interval, which is (3% + 9%) / 2 = 6%.

The point estimator of the mean percentage of airline reservations being canceled on the day of the flight is the midpoint of the confidence interval, which is (3% + 9%) / 2 = 6%. Therefore, the point estimator of the mean percentage of reservations that are canceled on the day of the flight is 6%.

This means that based on the data, we can estimate that the mean percentage of airline reservations being canceled on the day of the flight is around 6%. However, since this is a point estimate, there is some uncertainty associated with it. The 95% confidence interval provides a range of values within which we can be 95% confident that the true mean percentage of cancellations falls. In this case, we can be 95% confident that the true mean percentage of cancellations on the day of the flight falls between 3% and 9%.

Overall, the interval and the point estimator provide us with useful information about the mean percentage of airline reservations being canceled on the day of the flight and allow us to make informed decisions and predictions about future cancellations.

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Answer:

-2(-5)^2+7

-2(25)+7

-50+7

-43

Answer:

10,000

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

A sensible original hypothesis that suggests a positive relationship between two variables could be: "Hypothesis: Increased physical exercise is positively associated with improved cardiovascular health."

The hypothesis suggests that there is a positive relationship between increased physical exercise and improved cardiovascular health. This means that as the level of physical exercise increases, it is expected to result in an improvement in cardiovascular health.

To explain further, the hypothesis is based on the understanding that physical exercise has various beneficial effects on the cardiovascular system. Regular exercise can lead to improvements in heart function, increased blood flow, lower blood pressure, improved cholesterol levels, and better overall cardiovascular fitness.

By proposing this hypothesis, we are suggesting that individuals who engage in more physical exercise will experience greater improvements in their cardiovascular health compared to those who engage in less or no exercise. This hypothesis can be tested through research studies, where data on exercise habits and cardiovascular health measures are collected and analyzed to determine if a positive relationship exists between the variables.

It is important to note that while the hypothesis suggests a positive relationship, further research is needed to provide concrete evidence and establish a causal link between increased physical exercise and improved cardiovascular health.

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The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.

To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.

Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.

With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.

To calculate the required percentage reduction in overtime hours, we can set up the following equation:

(1.05R) * (1 - x) * H = 1.03B

where x represents the required percentage reduction in overtime hours.

Simplifying the equation, we have:

(1 - x) * H = (1.03B) / (1.05R)

Now, let's solve for x:

1 - x = (1.03B) / (1.05R * H)

x = 1 - [(1.03B) / (1.05R * H)]

Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.

It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.

By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.

Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.

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The slope of a line parrallel to the line whose equation is 8x+10y = 60 is -4/5

The standard form of a equation of a line is y = mx + c

The line whose equation is 8x+10y = 60

10y = -8x + 60

y = 1/10(-8x + 60)

y = -4/5 x + 6

The slope of the line is -4/5

When two lines are parallel the slope of both the lines is equal

so, the slope of the line parallel is same as the slope of the line  8x+10y = 60

Therefore, the slope of a line parrallel to the line whose equation is 8x+10y = 60 is -4/5

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Answer:

sinple interest= principle*rate*time/100

SI= 2400*3*1.5/100

SI= 108

AMOUNT= SI + PRICIOLE

AMOUNT= 108+2400

AMOUNT= 2508

{ I converted 18 months to 1.5 years}

The correct statement is end behavior is decreasing to the left and increasing to the right, which statement must be true about the function is The order is odd and the leading coefficient is negative.

As x approaches infinity it is detected by its limit. On the left side, it is given by:

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Answer: 40 pages in total

Explanation: Porter has read 20% of the book and this translates to 8 pages of the book.

20% = 8 pages

Assume the total number of pages is x:

20% * x = 8

0.2x = 8

x = 8 / 0.2

x = 40 pages in total

Answer:

40 pages in the book

Step-by-step explanation:

8/40 = .20

Answer:

D. 360 square feet

Step-by-step explanation:

The area of Tara's wall is 24 times 15 which equals 360 sq. feet. This means she would need the same amount of wallpaper to cover it.

Answer:

B) 50%

Step-by-step explanation:

It says or so it includes both as a probability, since drawing one of the four suits is 25% adding them together would increase the probability for two either two suits to 50%

Answer:  3, 5, 7

Step-by-step explanation:

There is a "trick" to determine divisibility by 3: if the sum of the digits is divisible by 3, the number is divisible by 3.

3 + 1 + 5 = 9 which is a multiple of 3, so 315 is divisible by 3.

It works for 9 also. since the sum of the digits is 9, 315 is divisible by 9.

Divisibility by 5: any number that has the units digit 5 or 0 is divisible by 5.

For 7, I just tried it  315÷7= 45

Only even numbers are divisible by 2.

If a 3-digit number is divisible by 11, the middle digit will be the sum of the first and last digits.   (That is not the case for 315)  But 385 is divisible by 11, also 495, 253, and many others you can try for fun.

Using what we know about right and similar triangles, we will see that x = 25.

First, we can find the hypotenuse of the smallest triangle by using the Pythagorean theorem.

6^2 + 8^2 = H^2 = 100

H = √100 = 10

Then the perimeter of the smaller triangle is:

6 + 8 + 10 = 24

Now, the triangles are similar, then the perimeter of the larger triangle is "k" times the perimeter of the smaller triangle, so we can write.

60 = k*24

Where k is the scale factor between the triangles.

k = 60/24 = 30/12 = 10/4 = 5/2

Then, x will be 5/2 times the hypotenuse of the other triangle, this gives:

x = (5/2)*10 = 25

The value of x is 25.

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Answer:

(1) 8 (2) 12

Step-by-step explanation:

PEMDAS

Answer:

because SAS , NYC , PAC all are together

Step-by-step explanation:

The given statement in the question is SAS.

We are given that;

Trapezoid NYAP

Now,

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

One possible given statement is that ∠NYC = ∠PAC.

This is because the base angles of an isosceles trapezoid are congruent. Since C is the midpoint of YA,

we know that YC = CA by the definition of midpoint.

Also, NC = CP is given.

by SAS, we can conclude that △NYC ≅ △PAC.

Therefore, by congruent triangles the answer will be SAS.

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Hi there!

~

⇒ \(- \frac{1}{2(x + 3)} + \frac{1}{2(x - 3)}\)

Step by Step :

∴ Factor \(x^2 - 9\) : \(( x+ 3 ) ( x - 3)\)

\(= \frac{3}{(x +3)(x - 3)}\)

∴ Create the partial fraction template using the denominator \(( x + ) ( x - 3)\)

\(\frac{3}{( x + 3) ( x -3)} = \frac{a^0}{x + 3} + \frac{a^1}{x - 3}\)

∴ Multiply the equation by the denominator.

\(\frac{3(x+3)(x-3)}{( x+3)(x-3)} = \frac{a^0(x +3)(x-3)}{x + 3} + \frac{a^1 (x+3)(x-3)}{x - 3}\)

∴ Simplify.

\(3 = a^0 ( x - 3) + a^1 ( x+3)\)

∴ Solve the unknown parameters by plugging the real roots of the denominator : - 3,3

⇅

∴ Solve the denominator root -3 : \(a^0 = -\frac{1}{2}\)

∴ For the denominator root 3 : \(a^1 = \frac{1}{2}\)

\(a^0 = -\frac{1}{2} , a^1 \frac{1}{2}\)

∴Plug the solutions to the partial fraction parameters to obtain the final result.

\(\frac{(-\frac{1}{2}) }{x + 3} + \frac{\frac{1}{2} }{ x- 3}\)

∴ Simplify

\(- \frac{1}{2(x + 3)} + \frac{1}{2(x - 3)}\)

Hope this helped you!

Answer:

it's going to be d.

Answer: c

Step-by-step explanation:

2*6=12

12+3=15

15 is not less than 10

2*4=8

8+3=11

11 is not less than 10

2*2=4

4+3=7

7 is less than 10

10*2=20

20+3=23

23 is not less than 10

The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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Answer:

Plug the x and y values to get it

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part A:

This data modeling an exponential function because the y-coordinate values are increasing by multiplying the previous value by 2, which is the common ratio.

Part B:

To write a function to represent the data, we can use the formula for an exponential function: y = a(b)^x, where a is the initial value, b is the common ratio, and x is the input value (station number in this case).

Using the given data points, we can write two equations:

2 = a(b)^1

16 = a(b)^4

Dividing the second equation by the first equation, we get:

8 = (b)^3

Taking the cube root of both sides, we get:

b = 2

Substituting b = 2 in the first equation, we get:

2 = a(2)^1

2 = 2a

a = 1

Therefore, the function that represents the data is: y = 1(2)^x, or y = 2^x.

Part C:

To find the average rate of change between station 2 and station 4, we need to calculate the slope of the line passing through the points (2, 4) and (4, 16).

Using the formula for slope, we get:

slope = (y2 - y1) / (x2 - x1)

slope = (16 - 4) / (4 - 2)

slope = 6

Therefore, the average rate of change between station 2 and station 4 is 6 minutes per station.

It will take them 3 days to paint the building if they work together on it except for 1 day when the painter is ill and the apprentice works alone is the answer.

Given that a painter can paint a building in 4 days and his apprentice can do it in 6 days, the following steps can be taken to find out the time taken to paint the building when they work together on it except for 1 day when the painter is ill and the apprentice works alone.

Step 1: Let's find the painter's work efficiency.

The painter can paint a building in 4 days. It means, in 1 day, the painter can complete 1/4 of the work.(1/4) × (4 days) = 1 work done

Therefore, the painter can complete 1 work in 1 day.

Step 2: Let's find the apprentice's work efficiency.

The apprentice can paint a building in 6 days. It means, in 1 day, the apprentice can complete 1/6 of the work. (1/6) × (6 days) = 1 work done

Therefore, the apprentice can complete 1 work in 1 day.

Step 3: Let's find out their combined work efficiency.

In 1 day, the painter can complete 1 work and the apprentice can complete 1 work.

So, in 1 day, their combined work efficiency = 1 + 1 = 2 works done.

Step 4: Let's find out the time taken to complete the work if they work together on it except for 1 day when the painter is ill and the apprentice works alone. If they work together for x days (except for 1 day when the painter is ill and the apprentice works alone), then, the following equation can be formed: Painter's work done in x days + Apprentice's work done in x days = Total work to be done.

Painter's work done in x days = (1/4) × (x - 1) = (x - 1)/4.

Apprentice's work done in x days = (1/6) × x = x/6.

Total work to be done = 1.

So, the equation becomes:(x - 1)/4 + x/6 = 1.

⇒ 3(x - 1)/12 + 2x/12 = 1.

⇒ (3x - 3 + 2x)/12 = 1.

⇒ 5x - 3 = 12.

⇒ 5x = 15.

⇒ x = 3.

Therefore, it will take them 3 days to paint the building if they work together on it except for 1 day when the painter is ill and the apprentice works alone.

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Answer:

Step-by-step explanation:

+18-9+5-3 = 11

It's on the eleventh floor and must go down 11 floors to return to the ground floor.

Answer:

Blank 1 = -1

Blank 2 = 2

Blank 3 = 4

Blank 4 = 7

Blank 5 = 79

Step-by-step explanation:

Blank 1 has an input of 1 we have to square 1

1 squared = 1

Then we subtract 2

1 - 2 = -1

Blank 2 has an input of 2 we have to square 2

2 squared = 4

Then subtract 2

4 - 2 = 2

Blank 3 has an output so we have to do the opposite of what we would for an input

Blank 3 has an output of 14 so we add 2

14 + 2 = 16

then we have to do the square root

The Square root of 16 = 4

So the input was 4

Blank 4 has an output of 47

47 + 2 = 49

The square root of 49 = 7

So the input was 7

Blank 5 has an input of 9

9 squared = 81

81 - 2 = 79

So the output is 79

Answer:

D

Step-by-step explanation:

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