select yes if the determinant shows that the matrix will reduce to an identity matrix; select no if it does not. [ 3 0 5 1 ]

Rounded to the nearest integer, this is 140165 lb.

The height of the water above the gate is 25 ft - 5 ft = 20 ft.

The width of the water perpendicular to the gate is half the width of the dam, or 60 ft / 2 = 30 ft.

The area of the equilateral triangle is (8 ft)^2 * √(3) / 4 = 8 * 8 * √(3) / 4 = 16 * √(3) ft^2.

The volume of the water pressing against the gate is the product of the height, width, and area:

20 ft * 30 ft * 16 * √(3) ft^2 = 2400 ft^3 * √(3).

Finally, the hydrostatic force is the product of the volume, the density of water, and g (acceleration due to gravity):

2400 ft^3 * √(3) * 62.4 lb/ft^3 * 9.8 m/s^2 = approximately 140164.96lb

Therefore, Rounded to the nearest integer is 140165 lb.

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If a polygon has four congruent angles then it can be a square and rectangle. Therefore the converse is not always true because square also have this property

The 4 basic property of a rectangle are;

1. A rectangle is a quadrilateral.

2. The opposite sides are parallel and equal to each other.

3. Each interior angle is equal to 90 degrees.

The sum of all the interior angles is equal to 360 degrees.

4.The diagonals bisect each other.

Both the diagonals have the same length.

Some of these properties are also for square. The difference between a square and a rectangle is that the sides of are all equal but only the opposite sides of a rectangle are equal. Both angles in square and rectangle are congruent, they are all 90°.

Therefore the converse of the statement "If a polygon has four congruenet

angles, then it is a rectangle." is not always true because both rectangle and square as these properties

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The matrix of the system is [tex]\left[\begin{array}{cc}11&3\\1&-2\end{array}\right] \left[\begin{array}{c}20&5\end{array}\right][/tex]

The complete question is added as an attachment

From the question, we have the following system of equations that can be used in our computation:

11x + 3y = 20

x - 2y = 5

Remove the variables

So, we have the following representation

x    y

11   3   20

1     -2   5

Next, we input the numbers in a matrix

This gives

[tex]\left[\begin{array}{cc}11&3\\1&-2\end{array}\right] \left[\begin{array}{c}20&5\end{array}\right][/tex]

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Answer:

B 49/3

Explanation:

I did the work, unlike your lazy ahh! :)

The chance that the third number is bigger than twice the first number is equal to the number of combinations where the first number is between 1 and 5 (inclusive) and the third number is between 2 * first number + 1 and 10 (inclusive).

Here's the calculation:

Therefore, the answer is:

= 21/1000

= 21/10^3

= 0.021

which is closest to choice B, so the answer is B.

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The fractions are 15/24 < 16/24, 6/36 < 8/36, and 14/24 < 20/24. This can be found using LCM.

Finding the smallest common multiple between any two or more integers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.

The given fractions are:

A:

5/8 and 2/3

Using the least common multiple take a common denominator:

Here LCM = (8)(3) =24

5/8 multiply the numerator and denominator by 3.

5/8 = 15/24

Similarly, 2/3 multiply the numerator and denominator by 8.

2/3 = 16/24

15/24 < 16/24

B: Using LCM:

1/6 and 2/9

6/36 and 8/26

6/36 < 8/36

C: 7/12 and 5/8

Using LCM:

14/24 < 20/24

Hence, the fractions are 15/24 < 16/24, 6/36 < 8/36, and 14/24 < 20/24. This can be found using LCM.

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Answer:

The linear equation giving the demand x in terms of the rent p can be written as x = 40 - 0.042p, where x is the number of occupied units and p is the monthly rent.

Answer:

4x² + 5x - 6  = 0

Step-by-step explanation:

Quadratic equation:

             [tex]\boxed{x^2-(sum \ of \ roots)x+product \ of \ roots=0}[/tex]

    [tex]Sum \ of \ roots = -2 + \dfrac{3}{4}[/tex]

                           [tex]= \dfrac{-2*4}{1*4}+\dfrac{3}{4}\\\\=\dfrac{-8}{4}+\dfrac{3}{4}\\\\=\dfrac{-5}{4}\\\\[/tex]

[tex]\sf product \ of \ roots =-2 *\dfrac{3}{4}[/tex]

                         [tex]=\dfrac{-6}{4}[/tex]

Quadratic equation:

      [tex]x^2 - \left(\dfrac{-5}{4}\right)x+\left(\dfrac{-6}{4}\right)=0[/tex]

Multiply the entire equation by 4,

        4x² - (-5)x + (-6) = 0

         4x² + 5x - 6  = 0

Answer:

10 gallons is still in the tank.

Step-by-step explanation:

We have to calculate 5/8 of 16.

(5/8)*16 = 10.

Answer:To calculate the total interest paid on a mortgage, you can use the following formula:

Total Interest = (Interest Rate/12) * (Total Number of Payments) * (Loan Amount)

In this case, the loan amount is the total cost of the mortgage, which is not specified in the question. However, we know that the payments are made for 15 years or 15*12 = 180 months.

We can use the formula above to find the total interest:

Total Interest = (0.04/12) * (2000 * 180) = 53,333.33 dollars

So, you paid $53,333.33 in interest over the life of the mortgage.

Step-by-step explanation:

Answer:

Utilities: $315 (7% of $4500)

Labor: $1350 (30% of $4500)

Supplies: $1125 (25% of $4500)

Rent: $1575 (35% of $4500)

Advertising: $135 (3% of $4500)

Z = x + yi times its conjugate x – yi is the square of its absolute value |z|²

A complex number z = x + yi times its conjugate x – yi is simply verified to be the square of its absolute value |z|². As a result, 1/z equals z divided by the square of its absolute value |z|². A complex number z is one that can be represented as x+iy, where x and y are real integers and I is an imaginary unit, i²=1. In this equation, x represents the complex number’s real portion and y represents its imaginary part.

The discriminant, b 2 4 a c, demonstrates the different forms of quadratic equation solutions. If the discriminant is equal to zero, the equation has one genuine solution.

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Yes, that's correct. The Pareto Chart also called bar charts, named after Vilfredo Pareto, is a graphical tool used in quality control and continuous improvement methodologies such as Six Sigma to help identify the most significant causes of problems.

In a Pareto Chart, the bars are arranged in descending order of height, with the most frequently occurring cause appearing first on the left. This allows you to quickly see which issues are the most pressing and require the most attention. By focusing on the most impactful causes, organizations can achieve the greatest improvement in their processes.

A bar chart gives a visual representation of the information.

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Mean of the sampling distribution of sample means is 5.9 years.

A normal distribution in statistics is defined as the type of continuous probability distribution where the data are arranged in a symmetrical bell shaped graph.

Population mean, μ = 5.9 years

Population standard deviation, σ = 0.8 years

If the sample size is at least 30, we can use the normal approximation of sampling distribution of sample means.

Here, sample size for the sampling distribution, n = 68 > 30.

For a sample which is drawn from a normally distributed population, mean of the sampling distribution of sample means is equal to the population mean and standard deviation = σ / √n.

Mean of the sampling distribution of sample means = μ = 5.9 years.

Hence mean is same as the population mean.

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a) The probability that an employee does not know C/C++ = 0.4

(b) The probability that an employee knows either C/C++ or R = 0.8

(c) The probability that an employee knows R and does not know C/C++ =  0.2

(d) The probability that an employee knows at least one of the languages = 0.8

Let us assume that an event A:  employee knows C/C++ languages

here, 60% know C/C++

So, P(A) = 0.6

event B:  employee knows R

here, 50% know R

This means, P(B) = 0.5

30% know both languages

This means, P(A ∩ B) = 0.3

Also, 20% know neither language.

⇒  P(A ∪ B)c = 0.2

a.  the probability that an employee does not know C/C++ would be,

1 - P(A)

= 1 - 0.6

= 0.4

b. the probability that an employee knows either C/C++ or R

We know that the formula, P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 0.6 + 0.5 - 0.3

P(A∪B) = 0.8

c.  the probability that an employee knows R and does not know C/C++

P(B) - P(A∩B)

= 0.5 - 0.3

= 0.2

d.  the probability that an employee knows at least one of the languages

1 - P(A ∪ B)c

= 1 - 0.2

= 0.8

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The function has a minimum of y = -2 at x = -4

The function is increasing on interval:

(-4 , ∞)

The function is decreasing on interval:

(-∞ , -4)

A function is a process or a relation that associates each element 'a' of a set A , to a single element 'b' of another set B.

Given function graph,

Function is increasing when, 4 < x < ∞

Function is decreasing when -∞ < x < -4

Function is minimum at (-4 , -2)

Hence,

On interval (-4 , ∞) function increases.

On interval (-∞ , -4) function decreases.

Function has minimum of y = -2 at x = -4.

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Answer:

Exercise 37:

In this exercise, the question is to find the x-coordinate of the point of inflection of the graph of the function f(x).

The point of inflection of the graph of the function f(x) is at the x-coordinate of 1.

Answer:

$20584

Step-by-step explanation:

using of proportion

if $20,750 = 2000

than ? = 1984

=1984/2000 × 20750

=4116,8000/2000

=$20584

The statement states that the rectangular garden has the following measurements: length = -4 and width = -2.

Sums with terms of something like the form kxn, where k has been any variable & n is a real number, make up polynomials. For instance, the polynomial 3x+2x-5. a description of radicals. The concepts degrees, standard form, monomial, binomial, and trinomial are all covered in this video.

A rectangle's area is represented by the polynomial [tex]x2 + 6x + 8,[/tex] which may be solved in (x + a)(x + b), in which a and b are indeed the rectangle's length and breadth.

So,[tex]x^2 + 6x + 8 = (x + a)(x + b).[/tex]

Solving for a and b, we find that a = -4 and b = -2, so the dimensions of the rectangular garden are length = -4 and width = -2.

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This type of data can be analyzed using a two-way analysis of variance (ANOVA) to determine the effect of both the day of the week (weekday or weekend) and the shift (morning or evening) on chair production. The manager can use this information to make predictions about future production based on the day of the week and shift.

The manager can start by creating a table to show the average number of chairs produced on each day of the week and shift. Then, a two-way ANOVA can be performed to determine if there is a significant difference in the mean number of chairs produced between weekdays and weekends, and between morning and evening shifts.

If the results of the ANOVA show that there is a significant effect of the day of the week and/or the shift on chair production, the manager can use this information to make more accurate predictions about future chair production. For example, if the results show that chair production is higher on weekdays compared to weekends, the manager can make predictions based on this information and allocate resources accordingly.

It is important to note that other factors such as the availability of materials, number of workers, and machine downtime can also impact chair production and should be considered when making predictions.

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The total charge on the shell is 678.24 nC, The electric field at the following radial distances from the long axis of the cylinder is (b) 1.524 x 10¹⁶ N/C, (c) 1.75 x 10¹⁵ N/C, (d) 1.63 x 10¹⁵ N/C, and (e) 6.097 x 10¹⁴ N/C.

(a) The total charge of the shell can be found by multiplying the surface charge density by the surface area of the cylinder:

Q = σ × 2π × r × L

where

σ = 9.00 nC/m² (surface charge density)

r = 0.06 m (radius)

L = 200 m (length)

Q = 9.00 nC/m² × 2 × π × 0.06 m × 200 m

Q = 678.24 nC

(b) To find the electric field at a radial distance of 2cm from the long axis of the cylinder, we use the formula:

E = k × Q / r²

where

k = 8.99 x 10⁹ Nm^2/C² (Coulomb's constant)

Q = 678.24 nC (total charge)

r = 0.02 m (radial distance)

E = 8.99 x 10⁹ Nm^2/C² × 678.24 nC/(0.02 m)²

E = 1.524 x 10¹⁶ N/C

(c) To find the electric field at a radial distance of 5.9cm from the long axis of the cylinder, we use the formula:

E = k × Q / r²

where

k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)

Q = 678.24 nC (total charge)

r = 0.059 m (radial distance)

E = 8.99 x 10⁹ Nm²/C² × 678.24 nC/(0.059 m)²

E = 1.75 x 10¹⁵ N/C

(d) To find the electric field at a radial distance of 6.1cm from the long axis of the cylinder, we use the formula:

E = k × Q / r⁷

where

k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)

Q = 678.24 nC (total charge)

r = 0.061 m (radial distance)

E = 8.99 x 10⁹ Nm²/C² × 678.24 nC / (0.061 m)²

E = 1.63 x 10¹⁵ N/C

(e) To find the electric field at a radial distance of 10cm from the long axis of the cylinder, we use the formula:

E = k × Q / r²

where

k = 8.99 x 10⁹ Nm²/C² (Coulomb's constant)

Q = 678.24 nC (total charge)

r = 0.10 m (radial distance)

E = 8.99 x 10⁹ Nm²/C² × 678.24 nC / (0.10 m)²

E = 6.097 x 10¹⁴ N/C

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Answer:

23cm

Step-by-step explanation:

The value of x is 3 and value of y is 2 in 4x + 5y = 22 and 2x + 3y = 12

Two or more expressions with an Equal sign is called as Equation.

The given system of equations are  4x + 5y = 22 and 2x + 3y = 12

Multiply equation 2 with 2

4x+6y=24

Subtract the above equation from equation 1

4x + 5y -4x-6y= 22-24

-y=-2

y=2

Now plug in y value in equation  2x + 3y = 12

2x+6=12

2x=6

Divide both sides by 2

x=3

Hence, the value of x is 3 and value of y is 2 in 4x + 5y = 22 and 2x + 3y = 12

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Answer:

below

Step-by-step explanation:

2 * 27    + 2*22    + 2*22  + 2 * 98 = 338 in

Answer:

84 tables are available

Step-by-step explanation:

30% = 30 ÷ 100

120 x (30 ÷ 100) = 36

36 tables are reserved hence

120-36 = 84

84 tables are available

The cost of each ranch chicken sandwich before tax is, $14.99

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

3 Coffee 5.85

1 Diet Bev. – lg. 3.38

1 Sparkling Water 2.50

3 Ranch Chicken Sandwich 44.97

1 Classic Burger 12.95

1 Thai Stir-fry Special 11.50

2 Club Sandwich 22.98

Subtotal 104.13

Tax (13%) 13.54

Total 117.67

The cost of each ranch chicken sandwich before tax.= ?

Total Amount = 44.97

⇒  For 1 ranch chicken sandwich = 44.97/3                                                             =  14.99

Therefore, the cost for 1 ranch chicken sandwich is $44.97/3

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Answer:

C

Step-by-step explanation:

The standard form of a circle is

(x-a)^2 + (y-b)^2 = r^2

Where (a, b) is the centre and r is the radius

Multiplication's characteristics. Commutative and associative properties of multiplication, respectively.

Multiplication's characteristics. Commutative and associative properties of multiplication, respectively.

Multiplication's "Distributive Property"

Multiplication's identity property.

The Japanese technique of multiplication is only a graphic representation of the four stages. Two integers are multiplied by each of the four smaller products represented by each cluster of intersections.

6666652222 - 12

6666652210 * 2 / 78 = 175438216.05

6666652210 * 6 / 78 = 512819400.76

6666652210 * 8 /78 = 701752864.21

6666652210 * 9 / 78 = 789471972.23

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In a right triangle, the length of the hypotenuse is the square root of the sum of the squares of the other two legs. Therefore, we can use the Pythagorean theorem to find the length of the legs of a right triangle given the length of the hypotenuse.

Pythagorean theorem: c^2 = a^2 + b^2

where c is the hypotenuse and a and b are the legs of the right triangle.

If the length of the longer leg is x, then the length of the other leg is 2x.

Using the Pythagorean theorem:

25^2 = x^2 + (2x)^2

625 = x^2 + 4x^2

625 = 5x^2

x = √(625/5) = √125 = 5

So, the length of the longer leg is 5 units.