Factor the following complex matrices into unitary times upper triangular:
(i) i 1 , (ii) 1+i 2-1 , (iii) i 1 0 , -1 2i 1-i -1 1 i 1
0 1 i
(iv) 1 1 -i
1-i 0 1+i
-1 2+3i 1

The amount of element left after the decay is found as 43 grams.

Decay rate is given as:

N = N₀(1 - r)ˣ

x - is the time in minutes

N₀ - initial mass (570 grams)

r - rate of decay (18%)

Put the values:

N = 570(1 - 0.18)¹³

N = 570*0.0757

N = 43

Thus, the amount of element left after the decay is found as 43 grams.

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Answer:

Step-by-step explanation:

16 is diameter so r= 16/2= 8

area of circle = 3.14*r^2

therefore 3.14*8^2

which is 3.14*64=200.96cm sq

Enjoy :)

a. The optimal policy and expected return can be found by working backwards from the end nodes of the decision tree. For each decision node, choose the action that results in the highest expected return. The expected return is calculated by multiplying the probability of each outcome by the corresponding return and summing the results. The optimal policy is to choose A if X is high, and B if X is low.

The expected return is 0.7*30 + 0.3*10 = 24.

b. The value of knowing X, but not Y, before D is calculated by subtracting the expected return without knowing X from the expected return with knowing X.

The expected return without knowing X is 0.5*24 + 0.5*24 = 24.

The expected return with knowing X is 0.7*30 + 0.3*10 = 24.

Therefore, the value of knowing X is 24 - 24 = 0.

c. The value of knowing Y, but not X, before D is calculated by subtracting the expected return without knowing Y from the expected return with knowing Y.

The expected return without knowing Y is 0.5*24 + 0.5*24 = 24.

The expected return with knowing Y is 0.8*30 + 0.2*10 = 26.

Therefore, the value of knowing Y is 26 - 24 = 2.

d. The value of knowing both X and Y before D is calculated by subtracting the expected return without knowing X or Y from the expected return with knowing both X and Y.

The expected return without knowing X or Y is 0.5*24 + 0.5*24 = 24.

The expected return with knowing both X and Y is 0.7*0.8*30 + 0.7*0.2*10 + 0.3*0.8*10 + 0.3*0.2*30 = 25.2.

Therefore, the value of knowing both X and Y is 25.2 - 24 = 1.2.

e. The influence diagram that corresponds to this decision tree is shown below:

X -> D -> Y -> R
   -> A -> R
   -> B -> R

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The population function is N(t) = 850(0.96)^t.

The base of the exponential function is (0.96), which is less than 1. This means that the function is decreasing over time.

Therefore, the correct answer is:

A. The population is decreasing by 4% per year.

Answer:

x would be 8 and y is 10

so (8,10)

Step-by-step explanation:

hope it helps

The volume of the earth dug out from a pit = 23.4 m³

Let us assume that l represents the length of the pit, 'w' represents the width and 'h' be the height of the pit.

Here, the length of the pit(l) = 6.5 m

the width of the pit (w) = 2.4 m

height of the pit(h) = 1.5 m

We need to find the volume of earth dug out from a pit.

We know that pit is of the cuboid shape.

Using the formula of volume of cuboid,

V = l × w × h

V = 6.5 × 2.4 × 1.5

V = 23.4 m³

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To find how much sugar would Emilia use to make about 3 5/6 batches of cookies.

1 1/8 cups of sugar

Next, we need to convert the mixed number to an improper fraction:

1 1/8 = (8 + 1) / 8 = 9/8

So, the amount of sugar needed for one batch of cookies is:

9/8 cups of sugar

To find the total amount of sugar needed for 3 5/6 batches, we can multiply the amount of sugar per batch by the number of batches:

(9/8 cups of sugar) x (23/6 batches) = 69/48 cups of sugar

thus, Emilia would need 69/48 cups of sugar to make 3 5/6 batches of cookies.

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Answer: C.

Step-by-step explanation:

The final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $5386.42.

Interest is the amount a lender or financial institution receives for lending money. Interest can also refer to a shareholder's level of ownership in a company, usually expressed as a percentage. 

Interest rate indicates the cost of borrowing, or the reward for saving. So if you are a borrower, the interest rate is the amount charged to borrow money, expressed as a percentage of the total loan amount. 

Solution according to the information given in the question :

Given, Principal(P) = $5,000

          Compounding frequency(n) = 4

          Time(in years)(T) = 5  

           Interest rate = 6%

Amount = P× (1 + r/n)^t

             = 5,000 × (1 + 6/4×100)⁵

             = 5,000 × (1 + 0.015)⁵

             = 5,000 × (1.015)⁵

             = 5000 ×1.077

             = $5286.42

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The opposite sides of the quadrilateral should be parallel and the diagonals should be equal. [For a rectangle]

First, let's find the slope of AB and its perpendicular slope.

Slope of AB = (y2 - y1)/(x2 - x1) = (12 - (-3))/(1 - (-2)) = 5

Perpendicular slope of AB = -1/5

The midpoint of AB is ((-2+1)/2, (-3+12)/2) = (-0.5, 4.5)

Let D be the point on line segment AC such that AD is perpendicular to AC. Since AB is parallel to DC, the slope of DC is also 5.

Slope of AC = (-4 - (-3))/(3 - (-2)) = -1/5

The equation of line AC is y = (-1/5)x - (13/5)

The equation of line DC passing through (3,-4) with slope 5 is y - (-4) = 5(x - 3)

Solving these two equations, we get D(2,-14/5).

Therefore, the coordinates of point D are (2, -14/5).

We can plot the points on the coordinate axes and verify that A, B, C, and D indeed form a rectangle.

Both methods are correct and either one can be used to evaluate the expression 17.

Both Kode and Elijah are using the distributive property to evaluate the expression 17(4+15).

The distributive property states that a(b+c) = ab + ac.

Kode's method:

17(4+15) = (17*4) + (17*15) = 68 + 255 = 323

Elijah's method:

17(4+15) = 17*19 = 323

Both students get the same answer of 323.

Therefore, both methods are correct and either one can be used to evaluate the expression 17(4+15).

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Answer:

Total time = (length of one song) x (number of songs)

Length of one song = 3/8 minutes

Number of songs = 12

Total time = (3/8) x 12

Total time = 36/8

Simplifying the fraction, we get:

Total time = 4 and 4/8 minutes

Total time = 4 and 1/2 minutes

Therefore, Michael sang for a total of 4 and 1/2 minutes.

The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are: horizontal shift, vertical shift, and vertical stretch.

The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are:

- Horizontal shift: The parent function has been shifted to the right by 3 units. This is indicated by the subtraction of 3 from x in the equation.
- Vertical shift: The parent function has been shifted downward by 5 units. This is indicated by the subtraction of 5 from the entire equation.
- Vertical stretch: The parent function has been stretched vertically by a factor of (1)/(2). This is indicated by the multiplication of the entire equation by (1)/(2).

Therefore, the correct answers are horizontal shift, vertical shift, and vertical stretch.

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The mean selling price of new homes was $114,000. The population standard deviation was $5,000. A random sample of 100 new home sales was taken without doing the calculations, ranges the sample mean selling price is most likely to lie between C) $113,000 - $115,000.

The sample mean selling price is most likely to lie in the range of $113,000 to $115,000 because this range is within one standard deviation (i.e., $5,000) of the population mean of $114,000, and therefore it contains approximately 68% of the sample mean values. The other ranges are outside one standard deviation from the mean, and therefore, the probability of the sample mean being in those ranges is lower. However, it is important to note that the actual sample mean could fall outside this range as it is still subject to random variation.

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airplane A

To compare the rate of speed of Airplane A and Airplane B, we need to calculate the speed of Airplane B first.

The formula to calculate distance is:

distance = rate x time

For Airplane A, we know:

distance = 1662 miles

time = 6 hours

So, we can rearrange the formula to solve for the rate:

rate = distance / time = 1662 / 6 = 277 miles per hour

For Airplane B, we know:

y = 922/3

x = rate of speed over 6 hours

We can use the formula to solve for x:

distance = rate x time

922/3 = x * 6

x = (922/3) / 6 = 153.67 miles per hour

Comparing the rates of the two airplanes, we can see that Airplane A traveled at a faster rate with 277 miles per hour compared to Airplane B's rate of 153.67 miles per hour. Therefore, Airplane A traveled at a faster rate.

The expression, h(x), in standard form that describes the length of the top surface of the rectangular boxes can be modelled by the function

[tex]h(x) = 6x + 66x^2 + 17[/tex].

A simplified way to write an expression is to use the expression in standard form. It entails expressing the expression in terms of its highest exponent, variables, and numerical coefficients. The use of standard form is intended to simplify the reading and comprehension of an expression. As opposed to writing an expression as, [tex]3x^2 + 4x +[/tex]7, it can be written in standard form as [tex]3x^2 + 4x + 7[/tex].

The two functions, f(x) and g(x), can be combined to form a single equation that expresses the length of the top surface of the rectangular boxes, which leads to the derivation of this expression.

The top surface's area is represented by the function f(x), which has the following form: [tex]f(x) = 66x^2 + 17x + 1[/tex]. With the formula g(x) = 6x + 1, the function g(x) denotes the width of the top surface. These two functions are combined to give us [tex]h(x) = 6x + 66x^2 + 17[/tex]. As a result, this expression describes how long the top surface of the rectangular boxes is.

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The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We are given that the line passes through the point (0,9) and has a slope of -3, so we can substitute these values into the equation to find the y-intercept:

y = mx + b

9 = (-3)(0) + b

b = 9

Now we know that the y-intercept is 9, so we can write the equation of the line:

y = -3x + 9

Therefore, the equation of the graph that passes through (0,9) and has a slope of -3 is y = -3x + 9.

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The zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4) are x = 1, x = -5, and x = 0. The smallest zero is x = -5 with multiplicity 2.

To find the zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4), we need to set the function equal to zero and solve for x:

0 = -8(x-1)^(3)(x+5)^(2)x^(4)

This equation will be true when any of the factors on the right-hand side are equal to zero. Therefore, we can find the zeros by setting each factor equal to zero and solving for x:

x-1 = 0 -> x = 1
x+5 = 0 -> x = -5
x^(4) = 0 -> x = 0

So, the zeros of the polynomial function are x = 1, x = -5, and x = 0.

The smallest zero is x = -5 with multiplicity 2, since it is the smallest value of x and the factor (x+5)^(2) has an exponent of 2.

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The equation that represents the amount of money Gilberto has after buying T-shirts for n sponsors at a cost of $4.75 per shirt can be written as nx - 4.75n = n² - 4.75n.

Assume count that Gilberto has n sponsors, and he plans to buy a t-shirt for each sponsor at a fee of $4.75 in step with a t-shirt. Assume also count on that every sponsor contributes x greenbacks to Gilberto's fundraising marketing campaign.

The overall amount of money Gilberto raises from all n sponsors is n instances x or nx. If Gilberto makes use of some of this cash to buy t-shirts, he may have nx - 4. 75n bucks left over.

Therefore, the equation that represents the quantity of cash Gilberto has after shopping for t-shirts is:

nx - 4. 75n = (n - 4. 75)n

simplifying this equation, we get:

nx - 4. 75n = n² - 4. 75n

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The probability of landing on a 6 is 1/6. The probability of rolling a 7 is zero.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.

If you roll a fair number cube, The probability of landing on a 6 is 1/6.

As, all the possible outcome is 6 and favourable outcome is 1 (6), Probability = 1/6 or 16.66%

The probability of rolling a 7 is zero as there is only 6 possible out come and 7 is the 7th outcome which is not possible, therefore 0.

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a) The critical value of t for this question at the .05 significance level is -2.11.

b) The calculated value of t for this question at the .05 significance level is -1.47, given a standard deviation of 0.63.

c) We can reject the null hypothesis because the calculated t-value (-1.47) is less than the critical t-value (-2.11). This indicates that games are less than 3.50 hours long.

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The vector form of the general solution of the given system of linear equations is given by:

{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}

where s and t are arbitrary constants.

To find the vector form of the general solution, we need to find the null space of the coefficient matrix of the system of linear equations. The coefficient matrix of the system is:

A = [ 1 1 0 1; 1 2 0 4; 2 0 0 -4]

The null space of A is the set of all vectors x such that Ax = 0. We can find the null space of A by reducing A to its reduced row echelon form:

A = [ 1 0 0 -2; 0 1 0 1; 0 0 0 0]

From the reduced row echelon form of A, we can see that x1 and x2 are the leading variables and x4 is the free variable. Therefore, the general solution of the system of linear equations is given by:

x1 = -2x4
x2 = x4
x4 = x4

We can write the general solution in vector form as:

{x} = {x1, x2, x4} = x4 { -2, 1, 1}

Since x4 is an arbitrary constant, we can write the general solution in terms of two arbitrary constants s and t as:

{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}

Therefore, the vector form of the general solution of the given system of linear equations is:

{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}

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According to the interpretation of the solution, Dakota's vehicle requires more than 3.6 gallons of fuel to travel the 117 miles to his brother's home.

Dakota will use x gallons of gas to travel 117 miles to his brother's home.

The following inequalities can be used to determine how many gallons of fuel Dakota requires the most:

x ≥ 117/32.5

According to this inequality, x must be more than or equal to 117 miles, which is the required driving distance for Dakota, divided by 32.5 miles per gallon, the maximum fuel efficiency for his vehicle.

After finding x, we obtain:

x ≥ 3.6

Hence, in order to go 117 miles to his brother's home, Dakota would require at least 3.6 gallons of gasoline.

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The height of the ball is represented by the equation -1(-6x^(2)+4x+2), where x is time in seconds.

We can rewrite this equation by distributing the -1 and simplifying.

First, we distribute the -1 to each term inside the parentheses:
-1(-6x^(2)+4x+2) = 6x^(2) - 4x - 2

Now, we can simplify by combining like terms:
6x^(2) - 4x - 2 = 6x^(2) - 4x - 2

Therefore, the rewritten equation for the height of the ball is:
h = 6x^(2) - 4x - 2

This equation shows the relationship between the height of the ball (h) and the time in seconds (x). As time increases, the height of the ball changes according to the equation.

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1. The height of the pyramid is 3.7 inches.

2. The length of the crossbar is 2√2 feet.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

1. We know, The height, slant height, and half of the base length form a

right-angled triangle

Therefore, h² = 4² - (3/2)².

h² = 13.75

h = 3.7 inches.

2. We know, In a 45°, 45° and 90° triangle, It is an isosceles right-angled triangle, The hypotenuse is √2 times the two similar sides.

Therefore, From the given information, The length of the crossbar is

2√2 feet.

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On simplifying the given expression using simplification method BODMAS, we get the answer 10. Thus, in the calculator the calculation must be done from left to right.

Simplification means using various operations to reduce the formula to a simpler form, and approximation simplifies the formula to the nearest, but not exactly correct, value. 

BODMAS in simplification stands for Bracket, Ob, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction. 

Solution using BODMAS and simplifying it:

72÷12+9−5 = (72/12) + 9 - 5

                  =6 + 9 - 5

                  = 15 - 5

⇒72÷12+9−5 = 10

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The final solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.

To solve the inequality y>=-(7)/(6)x, we will first graph the boundary line and then shade the appropriate region.

1. Begin by graphing the boundary line y=-(7)/(6)x. This line has a slope of -(7)/(6) and passes through the origin (0,0).

2. Since the inequality includes the "greater than or equal to" symbol (>=), the boundary line should be solid to indicate that points on the line are included in the solution.

3. Next, we need to determine which region to shade. To do this, we can choose a test point that is not on the boundary line. A common test point is (0,1), which is above the boundary line.

4. Substitute the coordinates of the test point into the inequality to see if it is true or false: 1>=-(7)/(6)(0)

5. Since the inequality is true, the region that includes the test point is the solution. This means we should shade the region above the boundary line.

6. The final graph should have a solid boundary line with the region above it shaded.

The solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.

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The function distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).

Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

The right response is: The information is categorical and univariate.

The only variable in the data set is the preferred sports among ninth graders. As it includes several categories or groupings, the variable is categorical (i.e., baseball or softball, basketball, lacrosse, soccer, and field hockey). The distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).

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