Does (5, 6) satisfy the inequality 2x - 3y> 6?

The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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Answer:

800

Step-by-step explanation:

2 times 4 is 8, 20 has one zero and 40 has one zero. Just add both zeros to 8, if you know the answer to 2x4.

The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

We have,

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:

mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6

Next, we calculate the deviation of each data point from the mean:

|4 - 6.6| = 2.6

|5 - 6.6| = 1.6

|7 - 6.6| = 0.4

|9 - 6.6| = 2.4

|8 - 6.6| = 1.4

Then we find the average of these deviations, which gives us the mean absolute deviation:

MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6

Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

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Answer:

2πr

Step-by-step explanation:

Answer:

------------------

Let the amount deposited be x. It is assumed we are talking about simple interest.

After 4 years the interest amount is:

95% of this amount is Rs 4940:

Mrs Majhi deposited Rs 20000.

Mrs. Majhi deposited Rs 20000 in her bank account. This was calculated by first finding the total interest (before tax) and then using the formula for simple interest to determine the principal amount.

The question is based on the concepts of Simple Interest and taxation. We know that Mrs Majhi received Rs 4940 as net interest after 4 years and this amount is 95% of the total interest (since 5% was paid as income tax). The total interest can be calculated as (4940 / 95) * 100 = Rs 5200.

The rate of interest is given as 6.5% per annum. Thus, the money deposited (Principal) by her can be calculated using the formula for simple interest (I = PRT/100), where P is the Principal, R is the rate of interest, and T is the time. Re-arranged to calculate the Principal (P), it becomes P = I / (R*T) = 5200 / (6.5*4) = Rs 20000.

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The given zeros are 4 with a multiplicity of 2 and -5 with a multiplicity of 1. As a result, the factored form of the polynomial is:f(x)

= (x - 4)²(x + 5)To calculate the leading coefficient, we must multiply the expression above by some constant K:f(x)

= K(x - 4)²(x + 5)Since the leading coefficient is 2, we obtain :K

= 2/[(4 - 4)²(- 5)]K

= -2/125Therefore, the polynomial function is:f(x)

= -2/125(x - 4)²(x + 5)

We know that the degree of the polynomial function is 5, and the leading coefficient is 2.Thus, let's consider the factored form of the polynomial function first:f(x)

= a(x - 4)²(x + 5)Here, the zeros of the function are 4 and -5. However, since the zero of 4 has a multiplicity of 2, we need to multiply one of these zeros by itself and leave the other one as it is. Since the degree is 5, it means that the product of the highest degrees of all the factors must be x^5. We must have two factors of (x - 4)  Therefore, the highest degree in the factored form is (x - 4)^2(x + 5), which equals x^3 + 6x^2 - 55x - 200.This means that we must multiply this by 2 to get the leading coefficient of the polynomial.Thus, the polynomial function is:f(x) = 2(x - 4)²(x + 5)

Now, we need to find the value of 'a'. Here, the leading coefficient of the polynomial is 2, and we know that one factor is (x - 4)² and the other factor is (x + 5).Therefore, we can say that: f(x) = 2(x - 4)²(x + 5)

= 2(x - 4)(x - 4)(x + 5)

= 2(x - 4)³(x + 5)To get the value of 'a', we compare the coefficient of x^5 in this equation to the coefficient of x^5 in the equation we derived earlier, which is (x - 4)^2(x + 5).Therefore, we can say that:2(x - 4)³(x + 5)

= a(x - 4)²(x + 5)x² + 6x - 55

= a(x² - 8x + 16)(x + 5)x² + 6x - 55

= a(x³ - 8x² + 16x + 5x² - 40x + 80)We can simplify this to get:x³ - 3x² - 14x + 16

= a(x³ - 3x² - 40x + 80)Comparing coefficients of x³, we get:1

= aComparing coefficients of x², we get:-3

= -37aThus, a = 3/37.Comparing coefficients of x, we get:-14

= 43aThus, a = -14/43.Comparing constant terms, we get:16

= 80aThus,

Therefore, a = 2/5.

Thus, we can f(x) = 2/5(x - 4)²(x + 5).

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To find the point at which the line intersects the given plane, we will first substitute the parametric equations of the line into the equation of the plane and then solve for the parameter 't'.

The parametric equations of the line are:

x = 3 - t
y = 2t
z = 2t

The equation of the plane is:

x - y + 5z = 9

Step 1: Substitute the parametric equations of the line into the plane equation:

(3 - t) - (2t) + 5(2t) = 9

Step 2: Simplify the equation and solve for 't':

3 - t - 2t + 10t = 9
7t - t = 6
6t = 6
t = 1

Step 3: Substitute the value of 't' back into the parametric equations of the line to find the intersection point (x, y, z):

x = 3 - t = 3 - 1 = 2
y = 2t = 2(1) = 2
z = 2t = 2(1) = 2

Therefore, the point at which the line intersects the given plane is (2, 2, 2).

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Answer:

C!

Step-by-step explanation:

By applying the definition of a definite integral and partitioning the interval [1, 2] into subintervals, we can approximate the integral as the sum of the areas of right rectangles. The evaluation results in an approximation of 2.71875.

To evaluate the definite integral using the right endpoints, we divide the interval [1, 2] into n subintervals of equal width. The width of each subinterval, denoted by Δx, is given by (2 - 1)/n = 1/n. We can then choose the right endpoint of each subinterval as our sample point. Let's denote this sample point as xi, where xi = 1 + iΔx for i = 0, 1, 2, ..., n-1. Using the sample points, we can approximate the integral as the sum of the areas of right rectangles: ∫(1 to 2) √(1 + 4x) dx ≈ Δx * [√(1 + 4x0) + √(1 + 4x1) + √(1 + 4x2) + ... + √(1 + 4xn-1)]. Simplifying this expression, we have: ∫(1 to 2) √(1 + 4x) dx ≈ (1/n) * [√(1 + 4(1)) + √(1 + 4(1 + 1/n)) + √(1 + 4(1 + 2/n)) + ... + √(1 + 4(1 + (n-1)/n))].

Taking the limit as n approaches infinity, this approximation converges to the exact value of the integral. By evaluating the above expression for a large value of n, we can approximate the definite integral. For this specific integral, we have: ∫(1 to 2) √(1 + 4x) dx ≈ (1/n) * [√5 + √(1 + 4(1 + 1/n)) + √(1 + 4(1 + 2/n)) + ... + √(1 + 4(1 + (n-1)/n))]. Let's consider a value of n = 8. Evaluating the expression above, we obtain an approximation of 2.71875 for the definite integral. Therefore, using the definition of a definite integral with right endpoints, the approximation of the integral ∫(1 to 2) √(1 + 4x) dx is 2.71875.

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Answer:

A. \( \frac{1}{5} \)

Step-by-step explanation:

The scale factor of dilation is the ratio of the length of any of the corresponding sides of rectangle R'S'T'Q to rectangle PQRS.

R'S' = 3

RS = 15

Thus,

Scale factor = \( \frac{R'S'}{RS} = \frac{3}{15} \)

Simplify

Scale factor = \( \frac{1}{5} \)

The answer can be checked by multiplying the divisor, quotient, and remainder, and then adding the quotient to the result.

After performing polynomial long division, the answer may be checked by following these steps:

1. Multiply the divisor by the quotient obtained from the division.

2. Add the obtained product to the remainder.

3. The result should be equal to the dividend.

In other words, you can check the answer by multiplying the divisor, quotient, and remainder, and then adding the quotient to the result.

This should give you the dividend.

To explain this step-by-step:

1. Perform the polynomial long division to obtain the quotient and remainder.

2. Multiply the divisor by the quotient obtained in the division.

3. Add the obtained product to the remainder.

4. The result should be equal to the dividend.

Remember to follow the correct order: multiply the divisor by the quotient first, and then add the remainder.

This method allows you to verify the correctness of the division.

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taking a peek at the pyramid, is really just 4 triangles stemming from a common top and touching a squarish base at the edges.

so hmmm to get the surface area of the pyramid, we can simply get the area of all those four triangles and the square and sum them up.

\(\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{four triangles}}{4\left[\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{4}) \right]}~~ + ~~\stackrel{square}{(10)(10)}}\implies 80~~ + ~~100\implies 180~in^2\)

a) The number of page faults for the First In First Out (FIFO), Least Recently Used (LRU), and Optimal page replacement (OPT) algorithms with 4 frames in physical memory are compared for the given page reference string. , b) The effect on the page fault rate is discussed when the number of frames is reduced to 3 frames in each algorithm.

a) To compare the number of page faults for the FIFO, LRU, and OPT algorithms with 4 frames, we simulate each algorithm using the given page reference string. FIFO replaces the oldest page in memory, LRU replaces the least recently used page, and OPT replaces the page that will not be used for the longest time. By counting the number of page faults in each algorithm, we can determine which algorithm performs better in terms of minimizing page faults.

b) When the number of frames is reduced to 3 in each algorithm, the page fault rate is expected to increase. With fewer frames available, the algorithms have less space to keep the frequently accessed pages in memory, leading to more page faults. The reduction in frames restricts the algorithms' ability to retain the necessary pages, causing more page replacements and an overall higher page fault rate. The specific impact on each algorithm may vary, but in general, reducing the number of frames decreases the efficiency of the page replacement algorithms and results in a higher rate of page faults.

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The correct answer is (c) depending on the benchmark interest rates. The liquidity premium can be positive or negative, depending on market conditions and the risk associated with specific securities.

It seems like there are some typos in your question, but I believe you're asking about the liquidity premium when the yield curve is inverted. In this context, I'll include the terms "ratio," "liquidity, and "negative" in my answer.

The liquidity premium is the additional return that investors demand by holding securities with lower liquidity or higher risk. When the yield curve is inverted, it generally indicates that short-term interest rates are higher than long-term interest rates. This can be a result of higher demand for long-term bonds, which drives their prices up and yields down.

In such a situation, the liquidity premium is:

a) not always negative, because an inverted yield curve doesn't necessarily mean that the liquidity of the market is negatively impacted. The ratio of liquid to illiquid assets can still be favorable even when the yield curve inverts.

b) not always positive, as the premium depends on the overall market conditions and risk factors associated with specific securities.

c) It depends on the benchmark interest rates, which are a key determinant of the yield curve shape. When benchmark interest rates change, the yield curve can either steepen, flatten, or invert, affecting the liquidity premium accordingly.

So the correct answer is (c) depending on the benchmark interest rates. The liquidity premium can be positive or negative, depending on market conditions and the risk associated with specific securities.

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The present value of Mark's prize, considering the $10,000 annual payments for 10 years and the subsequent $20,000 annual payments for 30 years, with an 8% discount rate, amounts to $171,391.44.

To calculate the present value of Mark's prize, we need to determine the current worth of the future cash flows he will receive. The $10,000 annual payments for 10 years can be considered an annuity, while the subsequent $20,000 annual payments for 30 years can be viewed as a perpetuity starting from the 11th year.

First, we calculate the present value of the annuity using the formula for the present value of an ordinary annuity:

PV_annuity = \(C * [1 - (1 + r)^(-n)] / r\),

where PV_annuity is the present value of the annuity, C is the annual cash flow, r is the discount rate, and n is the number of years. Plugging in the values, we have:

PV_annuity = $10,000\(* [1 - (1 + 0.08)^(-10)] / 0.08\) = $85,394.45.

Next, we calculate the present value of the perpetuity using the formula for the present value of a perpetuity:

PV_perpetuity = C / r,

where PV_perpetuity is the present value of the perpetuity. Plugging in the values, we have:

PV_perpetuity = $20,000 / 0.08 = $250,000.

Finally, we sum up the present values of the annuity and the perpetuity to obtain the total present value:

Total present value = PV_annuity + PV_perpetuity = $85,394.45 + $250,000 = $335,394.45.

Therefore, with an 8% discount rate, the present value of Mark's prize is $171,391.44.

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Answer:

\(6x + 6x + 6 + x = 13x + 6\)

The correct option for the given vector is the third one:

If the initial point is (0, 0), then the component form of the vector is just equal to the terminal point of the vector.

Then we have:

u = (5, -8)

For a vector w = (x, y) the magnitude is:

\(||w|| = \sqrt{x^2 + y^2}\)

In this case, the magnitude will be:

\(||u|| = \sqrt{5^2 + (-8)^2} = \sqrt{89}\)

Then the correct option is the third one.

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Answer:

(2x+3)^2 = 16/25

(2x+3) = √(16/25)

2x+3 = 4/5

2x = 4/5 - 3

x = -1 .1

To be a function, each input can only go to one output

A. The input 1 goes to two different output values

(1,6) (1,7) causes it not to be a function

B. This is a function. Each input has only one output value

C. The input 0 goes to two different output values

(0,-5) snf (0,4) causes it not to be a function

The billing period is 31 days, so the average daily balance is $1,437.73.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and understand relationships between variables. Algebra uses letters and symbols to represent quantities and their relationships, and it involves solving equations and inequalities, working with graphs and functions, and manipulating expressions.

Algebraic concepts and techniques are used extensively in many areas of science, engineering, economics, and other fields. It is a foundational subject in mathematics, and is often studied as a prerequisite for more advanced courses in mathematics and other sciences.

To find the average daily balance, we need to calculate the total balance over the billing period and divide it by the number of days in the billing period.

The total balance is:

10 days at $778.12 = $7,781.20

8 days at $1,876.00 = $15,008.00

3 days at $2,112.50 = $6,337.50

10 days at $1,544.31 = $15,443.10

Total balance = $44,569.80

The billing period is 31 days, so the average daily balance is:

$44,569.80 / 31 = $1,437.73

Rounding this to the nearest cent, we get an answer of $1,437.74, which is option C.

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We need to know the shape of the base and at least one other dimension, such as height or slant height. Therefore, Base Area is the area of the base and Height is the height of the pyramid.

The formula for the area of the base of a pyramid will depend on the shape of the base. If the base is a square with side length s, then the area of the base is given by:

Area = s^2

If the base is a rectangle with length l and width w, then the area of the base is given by:

Area = l*w

If the base is a triangle with base length b and height h, then the area of the base is given by:

Area = (1/2)bh

If the base is a polygon with n sides, then we can divide it into n triangles and sum up the areas of each triangle to find the area of the base. The formula for the area of a triangle can be used for each individual triangle.

Once we know the area of the base and the height of the pyramid, we can use the formula for the volume of a pyramid to find the total volume of the pyramid. The formula for the volume of a pyramid is given by:

Volume = (1/3)Base AreaHeight

where Base Area is the area of the base and Height is the height of the pyramid.

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Answer: 0.514285714286 ≈

Step-by-step explanation: 18/35 is already in the simplest form. It can be written as 0.514286 in decimal form

The employee's yearly salary is calculated as $37,440 using the arithmetic operations.  

The employee earns $18 per hour and works 40 hours per week. To calculate the weekly salary, we multiply the hourly wage by the number of hours worked:

Weekly salary = Hourly wage × Hours worked per week

Weekly salary = $18/hour × 40 hours/week = $720

Next, to calculate the yearly salary, we use the multiplication operation the weekly salary by the number of weeks in a year:

Yearly salary = Weekly salary × Weeks in a year

Yearly salary = $720/week × 52 weeks/year = $37,440

Therefore, the employee's yearly salary is $37,440. This calculation assumes a 40-hour work week and 52 weeks in a year. It's important to note that this calculation does not account for overtime pay or any other additional benefits or deductions that may affect the employee's total annual income.

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Answer:

96 cm^3

Step-by-step explanation:

I hope this helped!

Opposite angles are equal, so:

78 = 12x + 18

solve for x

78 - 18 = 12x

60 = 12 x

60/12 = x

x= 5 (option A)

Answer:

1221.2 factor increase

Step-by-step explanation:

It is difficult interpreting the numbers.  I'll assume:

2.25x10^2 and 2.75x10^5

----

225

275000

The difference(increase) is 274775, or 2.75 x 10^5 to 3 sig figs

There is a (2.75 x 10^5)/(2.25x10^2) or 1221.2 factor increase in bacteria between the two weeks.

The measure of angle ZWYZ is 180 degrees minus the sum of the measures of angles WZY and VY.

The measure of angle ZWYZ can be found using the following steps:

Find the measures of angles WZY and VY.

Add the measures of angles WZY and VY together.

Subtract the sum of the measures of angles WZY and VY from 180 degrees.

The measures of sides WZ and WY are equal, so the lines WZ and WY are parallel. This means that angles WZY and VY are supplementary, so their measures add up to 180 degrees. Therefore, the measure of angle ZWYZ is 180 degrees minus 180 degrees, or 0 degrees.

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Answer:

122

Step-by-step explanation:

Given information, line t is parallel to line s.

angle 1 and angle 2 are alternate angles and so their measure is equal to each other:

10x + 2 = 12x - 22 transfer like terms to the same side of the equation

2 + 22 = 12x - 10x

24 = 2x divide both sides by 2

12 = x to find the measure of angle 2 replace x with the value we found

12*12 - 22 = 122

Answer:

5.8

Step-by-step explanation:

\( \sqrt{ {5}^{2} } + \sqrt( { - 3}^{2} )\)

\( \sqrt{25 + 9} \)

\( \sqrt{34} \)

5?8

The statement is False. A matrix A can be expressed in the form of A = UΣVT, where Σ is an m x n matrix whose diagonal entries are non-zero.

The statement is not accurate. The correct statement is that A can be expressed in the form of A = UΣVT, where Σ is an m x n matrix whose diagonal entries are non-zero.

This form represents the singular value decomposition (SVD) of a matrix A. In the SVD, U is an m x m orthogonal matrix, Σ is an m x n diagonal matrix with non-zero diagonal entries, and VT is the transpose of an n x n orthogonal matrix.

The diagonal entries of Σ, called the singular values, represent the magnitudes of the singular vectors in U and VT and can be non-zero. Therefore, the correct statement is that the diagonal entries of Σ are non-zero, rather than zero.

The SVD is a powerful tool in linear algebra and has various applications in areas such as data analysis, image processing, and signal processing.

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