Micah withdrew $4.50 from his bank account. Write a rational number to represent this situation

Answer:

x=31/14

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−4x+1=−9x−16+9x+16

−4x+1=−9x+−16+9x+16

−4x+1=(−9x+9x)+(−16+16)(Combine Like Terms)

−4x+1=0

−4x+1=0

Step 2: Subtract 1 from both sides.

−4x+1−1=0−1

−4x=−1

Step 3: Divide both sides by -4.

−4x−4=−1/-4

x=1/4

All of the points from Table D which shows a proportional relationship has been plotted in the graph shown in the image attached below.

Generally speaking, the graph of any proportional relationship is represented by a straight line with the data points passing through the origin (0, 0). In Mathematics, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in table D as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 1/2 = 3/6 = 4/8 = 2/10

Constant of proportionality, k = 1/2 or 0.5.

In conclusion, a linear equation for this proportional relationship can be correctly written and plotted using an online graphing calculator as follows:

y = kx

y = 0.5x

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Answer: b. 2

Step-by-step explanation:  3√64= 4 simplified is 2

Answer:

[See Below]

Step-by-step explanation:

____________________________________

✦ Solve for \(\sqrt[3]{64}\):

✦ Now divide:

____________________________________

So the answer would be D, \(8\).

~Hope this helps Mate. If you need anything feel free to message me.

\(-Your~ Friendly~ Answerer,~Shane\) ☺

To find the magnitude of r prime of quantity pi over 3 end quantity, we first need to take the derivative of r of t. r prime of t = a vector with two components, sec^2(t) and 2csc(2t) .Then, we can evaluate r prime of pi/3 using these components: r prime of pi/3 = a vector with two components, sec^2(pi/3) and 2csc(2(pi/3)).
Using the fact that sec^2(pi/3) = 4 and csc(2(pi/3)) = -2sqrt(3)/3, we can simplify the vector to: r prime of pi/3 = a vector with two components, 4 and -4sqrt(3)/3
Now, we can find the magnitude of this vector using the formula:

magnitude of a vector = square root of (sum of squares of its components)

magnitude of r prime of pi/3 = square root of (4^2 + (-4sqrt(3)/3)^2)

= square root of (16 + 16/3)

= square root of (64/3)

= 4/square root of 3

Multiplying this by the given constants (1/3 square root of thirty four, 1/2 square root of nineteen, 2 square root of thirteen over three, 4/3 square root of ten), we get the final answer:

magnitude of r prime of quantity pi over 3 end quantity = (4/square root of 3) * (1/3 square root of thirty four) * (1/2 square root of nineteen) * (2 square root of thirteen over three) * (4/3 square root of ten)

= 16/square root of (3 * 34 * 19 * 13 * 10/9)

= 16/square root of 2,583.49

= 16/50.83

= 0.3147 (rounded to four decimal point)

To find the magnitude of r'(π/3), we need to take the square root of the sum of the squared components:

Magnitude of r'(π/3) = √[sec^4(π/3) + (2*cot(2(π/3))*csc^2(2(π/3)))^2]

Once you evaluate the trigonometric functions at π/3 and simplify the expression, you will have the magnitude of r'(π/3).

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The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model. The optimal number of notebooks to make in each order is 590 units. The annual ordering cost (AOC) is approximately $892.20. The Annual Holding Cost (AHC) is $3540. The annual product cost (APC) is $233,460. The annual total cost of managing inventory (ATC) is approximately $237,892.20. The total number of orders in the year (N) is 33. The estimated time between each order (T) is approximately 7.58 days. The daily demand is approximately 77.82 units. The reorder point (ROP) is approximately 311 units.

The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model.

To find the optimal number of notebooks to make in each order, we can use the EOQ formula:

EOQ = √[(2 * Demand * Ordering Cost) / Holding Cost]

EOQ = √[(2 * 19455 * 27) / 6]

EOQ ≈ 589.96

Since the number of notebooks must be a whole number, the optimal number to order would be 590 notebooks.

The annual ordering cost (AOC) can be calculated by dividing the annual demand by the EOQ and multiplying it by the ordering cost:

AOC = (Demand / EOQ) * Ordering Cost

AOC = (19455 / 590) * 27

AOC ≈ $892.20

The Annual Holding Cost (AHC) is calculated by multiplying the EOQ by the holding cost per unit:

AHC = EOQ * Holding Cost

AHC = 590 * 6

AHC = $3540

The annual product cost (APC) is calculated by multiplying the annual demand by the cost per unit:

APC = Demand * Cost per unit

APC = 19455 * 12

APC = $233,460

The annual total cost of managing inventory (ATC) is the sum of the annual ordering cost, annual holding cost, and annual product cost:

ATC = AOC + AHC + APC

ATC = 892.20 + 3540 + 233460

ATC ≈ $237,892.20

The total number of orders in the year (N) can be calculated by dividing the annual demand by the EOQ:

N = Demand / EOQ

N = 19455 / 590

N ≈ 33

The estimated time between each order (T) can be calculated by dividing the number of working days in a year by the total number of orders:

T = Number of working days / N

T = 250 / 33

T ≈ 7.58 days

The daily demand is calculated by dividing the annual demand by the number of working days in a year:

Daily Demand = Demand / Number of working days

Daily Demand = 19455 / 250

Daily Demand ≈ 77.82 units/day

The reorder point (ROP) is the number of units at which a new order should be placed. It can be calculated by multiplying the daily demand by the lead time (time taken for the supplier to deliver the order):

ROP = Daily Demand * Lead Time

ROP = 77.82 * 4

ROP ≈ 311.28 units

Therefore, the reorder point would be approximately 311 units.

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Answer:140 i believe

I can't see the answer choices clearly but to find the median, you would cross off from least to greatest and the choice in the middle would be the answer.

Answer:A

Step-by-step explanation: I can't see the full thing but i believe it's a. I believe that because when you find median, you add up all of the numbers. Then you divide by how many numbers you have. You have 11 numbers, 22,32,24,28,25,27,23,27,27,22,29.

D) 144(π) cm2

See the image I have shared

If the incenter, circumcenter, centroid, and orthocenter are always inside the triangle, the correct answer is an acute triangle (option B).

In an acute triangle, all three angles are less than 90 degrees. The incenter, which is the center of the inscribed circle, lies inside the triangle. The circumcenter, which is the center of the circumscribed circle, also lies inside the triangle.

The centroid, which is the point of intersection of the medians, is located inside the triangle as well. Finally, the orthocenter, which is the point of intersection of the altitudes, is inside the triangle in an acute triangle.

In contrast, a right triangle has one angle measuring 90 degrees, an obtuse triangle has one angle greater than 90 degrees, and an isosceles triangle has two equal side lengths. These types of triangles may have some of the points (incenter, circumcenter, centroid, orthocenter) located outside the triangle.

Therefore, the correct answer is option B, acute triangle.

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The vector equation of the line is r(t) = t<2, 0, -1>, and the corresponding parametric equations are x = 2t, y = 0, z = -t.

To find the vector equation and parametric equations of the line passing through the point (0, 0, 0) and perpendicular to both u = <1, 0, 2> and w = <1, -1, 0>, we can use the cross product of u and w.

The cross product of two vectors u and w gives us a vector that is perpendicular to both u and w. So, by finding the cross product, we can determine the direction vector of the line.

First, we calculate the cross product of u and w:

u x w = <1, 0, 2> x <1, -1, 0>

Using the determinant rule for the cross product, we have:

u x w = <0(0) - 2(-1), 2(0) - 1(0), 1(-1) - 0(1)>

= <2, 0, -1>

The resulting vector <2, 0, -1> is the direction vector of the line.

Next, we can write the vector equation of the line:

r(t) = <x₀, y₀, z₀> + t<2, 0, -1>

Since the line passes through the point (0, 0, 0), the equation simplifies to:

r(t) = t<2, 0, -1>

This equation represents the line in vector form.

To obtain the parametric equations, we can express each component separately:

x = 2t

y = 0

z = -t

These equations represent the line parameterized by the variable t, where t = 0 corresponds to the given point (0, 0, 0).

In summary, the vector equation of the line is r(t) = t<2, 0, -1>, and the corresponding parametric equations are x = 2t, y = 0, z = -t.

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A 90% confidence interval for the proportion of adults who are worried about having enough money for retirement is (0.5031, 0.5396).

To construct a 90% confidence interval for the proportion of adults who are worried about having enough money for retirement, follow these steps:

1. Determine the sample proportion (p- hat):
p- hat = number of adults worried / total number surveyed
p- hat = 569 / 1094
p- hat ≈ 0.5199

2. Determine the confidence level (90%) and find the corresponding z-score using a z-table or calculator. For a 90% confidence interval, the z-score is approximately 1.645.

3. Calculate the standard error (SE):
SE = sqrt((p- hat * (1 - p- hat)) / n)
SE = sqrt((0.5199 * (1 - 0.5199)) / 1094)
SE ≈ 0.0156

4. Construct the confidence interval using the sample proportion, z-score, and standard error:
Lower limit: p- hat - (z-score * SE)
Lower limit: 0.5199 - (1.645 * 0.0156)
Lower limit ≈ 0.4938

Upper limit: p- hat + (z-score * SE)
Upper limit: 0.5199 + (1.645 * 0.0156)
Upper limit ≈ 0.5460

A 90% confidence interval for the proportion of adults who are worried about having enough money for retirement is (0.4938, 0.5460).

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Answer:

1 17/22

14 5/11 can my converted to

14 10/22 - 13 = 1 10/22

then add 1 10/22 and 7/22

to equal

1 17/22

The function for the model that gives the future value of the investment in dollars after t years is: f(t) = 2000.e⁰·°⁴²t

Give, a lump sum of $2000 is invested at 4.2% compounded continuously.

Hence we have:

P = $2000

rate of interest = 4.2%

years = t

we know that A = Pe^rt

Substitute the above values in the formula.

Amount = f(t)

f(t) = 2000.e⁰·°⁴²t

hence we get the function for the model that gives the future value of the investment is f(t) = 2000.e⁰·°⁴²t

Therefore we get the required function.

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Answer:

Retrial, Guilty, and Innocent

Step-by-step explanation:

Khan Academy

Answer:

what the question

Step-by-step explanation:

a. The ordering of these states from smallest to largest populations is of:

Washington, Virginia, Pennsylvania, Texas.

b. The z-score formula was used to find the populations of Texas and Pennsylvania, and then they were compared to Virginia and Washington.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for this problem are given as follows:

\(\mu = 141.51, \sigma = 87.49\)

Then the population of Texas, which has Z = 1.52, is calculated as follows:

1.52 = (X - 141.51)/87.49

X - 141.51 = 1.52 x 87.49

X = 274.5 million. -> greatest population among these states.

The population of Pennsylvania, which has Z = -0.15, is calculated as follows:

-0.15 = (X - 141.51)/87.49

X - 141.51 = -0.15 x 87.49

X = 128. 4million. -> second greatest population among these states.

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The rank of the standard matrix for T is 2, which is determined by the number of linearly independent columns in the matrix.

To find the rank of the standard matrix for the linear transformation T: R^5 → R^3, we need to determine the number of linearly independent columns in the matrix.

The standard matrix for T can be obtained by applying the transformation T to the standard basis vectors of R^5.

The standard basis vectors for R^5 are:

e1 = (1, 0, 0, 0, 0),

e2 = (0, 1, 0, 0, 0),

e3 = (0, 0, 1, 0, 0),

e4 = (0, 0, 0, 1, 0),

e5 = (0, 0, 0, 0, 1).

Applying the transformation T to these vectors, we get:

T(e1) = (1 + 0, 0 + 0 + 0, 0 + 0) = (1, 0, 0),

T(e2) = (0 + 1, 1 + 0 + 0, 0 + 0) = (1, 1, 0),

T(e3) = (0 + 0, 0 + 1 + 0, 0 + 0) = (0, 1, 0),

T(e4) = (0 + 0, 0 + 0 + 1, 1 + 0) = (0, 1, 1),

T(e5) = (0 + 0, 0 + 0 + 0, 0 + 1) = (0, 0, 1).

The standard matrix for T is then:

[1 0 0 0 0]

[1 1 0 1 0]

[0 1 0 1 1]

To find the rank of this matrix, we can perform row reduction or use the concept of linearly independent columns. By observing the columns, we see that the second column is a linear combination of the first and fourth columns. Hence, the rank of the matrix is 2.

Therefore, the rank of the standard matrix for T is 2.

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COMPLETE QUESTION - Let T: R5-+ R3 be the linear transformation defined by the formula T(x1, x2, x3, x4, x5) = (x1 + x2, x2 + x3 + x4, x4 + x5). (a) Find the rank of the standard matrix for T.

The only perfect squares between 150 and 250 that satisfy this condition are 169, 196, and 225, as we found earlier. Therefore, these are the only possible Square numbers that Lara could have chosen.

Lara rounds her chosen square number to the nearest hundred, and the result is 200. This means that her chosen square number must be greater than or equal to 150 and less than or equal to 250.

The first perfect square greater than or equal to 150 is 169, which is 13 squared. The next perfect square is 196, which is 14 squared. The last perfect square less than or equal to 250 is 225, which is 15 squared.

Therefore, Lara could have chosen any of the following three square numbers:

- 169

- 196

- 225

To verify that these are indeed the only possible square numbers that could have been rounded to 200, we can use the formula for rounding to the nearest hundred:

rounded number = 100 * (original number rounded to the nearest hundred)

If the original number is a perfect square, then we can write it as n^2, where n is a positive integer. Substituting this into the formula above, we get:

200 = 100 * (n^2 rounded to the nearest hundred)

Simplifying this expression, we get:

2 = (n^2 rounded to the nearest hundred) / 100

Since the right-hand side is an integer, it follows that n^2 rounded to the nearest hundred must be a multiple of 200. The only perfect squares between 150 and 250 that satisfy this condition are 169, 196, and 225, as we found earlier. Therefore, these are the only possible square numbers that Lara could have chosen.

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\(\\ \sf\longmapsto sin10°-cos10°\)

\(\\ \sf\longmapsto sin(90-10°)-cos10°\)

\(\\ \sf\longmapsto cos10-cos10\)

\(\\ \sf\longmapsto 0\)

To test if the graph is connected, we can use the adjacency matrix and check if there is a path between every pair of vertices. In this case, we can see that there is a path between every pair of vertices, so the graph is connected.

To find spanning trees using depth-first search (DFS), we can start at any vertex and traverse the graph, marking the edges we visit. As we visit edges, we can add them to a list to create a spanning tree. We can continue until we have visited all vertices. One possible spanning tree for this graph using DFS is:

X3--X6
|   |
X1--X4
|   |
X2--X7
  |
  X5

To find spanning trees using breadth-first search (BFS), we can also start at any vertex and traverse the graph, but using a queue instead of a stack. Again, we can mark the edges we visit and add them to a list to create a spanning tree. One possible spanning tree for this graph using BFS is:

X3--X6
|   |
X1--X4
|   |
X2--X7

Note that there can be many possible spanning trees for a graph, depending on the starting vertex and the traversal method used.

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The value of (f . g)' at x = 9 is 0.

Given function:

f(u) = + 20, u = g(x) = 1 x2 - 20, x = 9

To find: The value of (f . g)' at the given value of x.

The function (f . g)' is defined as follows:

(f . g)' = f '(g(x)) g'(x)

First we need to find g'(x), which is the derivative of the function g(x).g(x) = 1 x² - 20

Using the power rule of differentiation, we have:

g'(x) = d/dx (x² - 20)= 2x

Hence, g'(9) = 2(9) = 18

Now we need to evaluate f '(g(x)) at g(9).

Since f(u) = 20, f '(u) = 0 (the derivative of a constant function is zero).

Therefore, f '(g(x)) = f '(g(9)) = 0

Finally, we can use the formula to find (f . g)' at x = 9:(f . g)' = f '(g(x)) g'(x)= f '(g(9)) g'(9)= 0 x 18= 0

Hence, the value of (f . g)' at x = 9 is 0.

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Answer:

\(18x^3y\)

Step-by-step explanation:

The area of a trapezium is \(\frac{a+b}{2}h\) (where \(a,b\) are the parallel sides and \(h\) is the perpendicular height)

Area of trapezoid \(= \frac{4xy+8xy}{2}3x^2\)

\(=6xy(3x^2)\)

\(=18x^3y\)

∴ The area of the trapezoid is \(18x^3y\)

Hope this helps :)

An antisymmetric tensor of rank 2 in n dimensions has n choose 2 (or n(n-1)/2) components since the indices must be distinct and the tensor is antisymmetric.

To find the number of independent components, we can use the fact that an antisymmetric tensor satisfies the condition that switching any two indices changes the sign of the tensor. This means that if we choose a set of n linearly independent vectors as a basis, we can construct the tensor by taking the exterior product (wedge product) of any two of them. Since the wedge product is antisymmetric, we only need to consider the set of distinct pairs of basis vectors. This set has n choose 2 elements, so the number of independent components of the antisymmetric tensor of rank 2 is also n choose 2.

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Answer:

0

Step-by-step explanation:

Answer:

Variable terms:

x and y

Constant terms:

7 and -9

Coefficient terms:

-5.6 and 24

Answer:

a- 6/20=3/10

b- 4/20= 1/5

c- 14/20=7/10

d- 10/20=1/2

e- 10/20=1/2

Answer:

x=-1

Step-by-step explanation:

5x-2x-7=-10

3x-7=-10

3x-7+7=-10+7

3x=-3

x=-1

\(\text{Hey \: there!}\)

\(\text{5x - 7 - 2x = 10}\)

\(\bf{(5x - 2x) \: which \: gives \: us \: 3x}\)

\(\text{3x - 7 + 7 = 10 + 7}\)

\(\bf{ - 7 + 7 \: because \: it \: gives \: you \: 0}\)

\(\bf{10 + 7 = 17}\)

\( \frac{3x}{3} = \frac{17}{3} \)

\(\text{we \: cant \: divide \: 17 \: from \: 3 \: because \: itll \: give \: us \: a \: decimal}\)

\(\boxed{\bf{thus \: your \: answer \: is \: \bf{ \frac{17}{3} }}}\)

~

\(\frak{loveyourselffirst:)}\)

Answer:

Step-by-step explanation:

boody boody

Using it's concept, it is found that the inequality represents the domain of the exponential piece is:

d) \(x \leq -2\).

The domain of a function is the set that contains all possible input values.

Researching this problem on the internet, we have that the function is divided as follows:

Hence, for the domain of the exponential piece, option d is correct.

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Based on the information, it can be inferred that this salesperson must make sales equivalent to $28,000 to obtain an equal profit with both options.

To find the amount of money that we must sell to have the same profit with both options we must carry out the following mathematical procedure.

1. We must calculate how much you would earn with option A in a week.

$28 * 40 = $1,120

2. We must make a rule of three to find a value of which 4% is equal to 1,120

Based on the above, the salesperson must sell $28,000 to make the same profit on both options in one week.

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