Which expression is equivalent to ?

Answer:

1.  $76,000

2. $58,000 + $2,000 * t

Step-by-step explanation:

2. Now, you might be questioning why we are going with the second question first, but this will be useful as it sets up our equation to make the first question easier. So, we will start with Luke's base salary of $58,000. Then, we will add $2,000 for every year he works at the company. If he works for t years and gains $2,000 on his salary per year, our equation will look like this:

$58,000 + $2,000 * t

That is the equation.

1. Now, using our previous equation, $58,000 + $2,000 * t, we will substitute 9 in for t. We get:

$58,000 + $2,000 * 9

Then, we simplify, giving us:

$58,000 + $18,000 = $76,000

Answer:

49.5

Step-by-step explanation:

i looked it up lol just kidding i put it in the calculator

Part A: By comparing B and L, L has greater rate of change.

Part B: By comparing B and L, B has greater y-intercept.

This can be solved using the concept of equation of function.

Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.

Part B:

Let, the equation of function B is,

Y = mx+c

Where m is slope and C is intercept

At (-3,-7)

-7 = -3m+c

C = 3m-7

At (-1,-1)

-1 = -m+3m-7

-1 = 2m -7

2m = 6

m = 3

C = 3m-7

C = 3×3 - 7

C =2

So, equation of line B is

Y = mx+c

Y = 3x+2

Where intercept is 2, note y intercept can also be found by putting x = 0, slope = 3

Part A:

Rate of change is slope for B can also be found by -1-(-7)/-1-(-3)=6/2=3

For equation L.

Y=6x+4

Slope=6, intercept =4

For L: when x=0, y=4,x=1,y=10

Rate of change=slope=(10 - 4)/ (1 - 0)=6

Line            Equation              Rate of change(slope(m)      Y intercept (c)

B                    y = 3x+2                      3                                         2

L                     y = 6x- 4                     6                                         - 4

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Answer: 14

Step-by-step explanation:

10.5 / 3 = 3.5

4 x 3.5 = 14

Answer:

We can form an isosceles triangle by using the given measures.

Step-by-step explanation:

Hope this helps!! :)

Answer:

the population variance is 2 and the population standard deviation is approximately 1.41.

Step-by-step explanation:

To calculate the variance and standard deviation of a population, you can use the following formulas:

Population variance = (Σ(x - μ)²) / N

Population standard deviation = √(Σ(x - μ)² / N)

Where:

Σ is the sum of

x is each individual score in the population

μ is the population mean

N is the number of scores in the population

To begin, we need to find the population mean (μ):

μ = (6 + 2 + 3 + 0 + 4) / 5 = 3

Next, we can calculate the variance:

Population variance = ((6-3)² + (2-3)² + (3-3)² + (0-3)² + (4-3)²) / 5

Population variance = (9 + 1 + 0 + 9 + 1) / 5

Population variance = 2

Finally, we can calculate the standard deviation:

Population standard deviation = √((6-3)² + (2-3)² + (3-3)² + (0-3)² + (4-3)²) / 5

Population standard deviation = √(9 + 1 + 0 + 9 + 1) / 5

Population standard deviation = √2

Therefore, the population variance is 2 and the population standard deviation is approximately 1.41.

The variance of the given set of scores is 4 and the standard deviation is 2. Both are measures of how spread out the data is in statistics. The variance is calculated by acquiring the average squared deviation from the mean, while the standard deviation is the square root of the variance.

This is a question about the notions of variance and standard deviation in statistics. Variance is a measure of how spread out the numbers in a data set are. Standard deviation, on the other hand, is the square root of the variance, indicating the amount of deviation (or variation) you can expect in your data.

Here are the steps for calculating variance and standard deviation for given set of scores: 6, 2, 3, 0, 4

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To show that if an integer k is an eigenvalue of A, then k divides the determinant of A, we can use the fact that the determinant of a matrix is equal to the product of its eigenvalues.

Let λ be an eigenvalue of A corresponding to the eigenvector x. Then we have Ax = λx. Taking the determinant of both sides, we get det(Ax) = det(λx). Since det(cX) = c^n * det(X) for any scalar c and an n x n matrix X, we have λ^n * det(x) = λ^n * det(x). Since λ is an eigenvalue, λ^n = det(A). Therefore, det(A) is divisible by λ, which implies that if k is an eigenvalue of A, then k divides the determinant of A.

Now, let's consider the matrix A with each row sum equal to k. We can write A as A = kI - B, where B is the matrix obtained by subtracting k from each entry of A and I is the identity matrix. It is clear that the sum of each row of B is zero, meaning that the matrix B has a zero eigenvalue. Therefore, the eigenvalues of A are given by λ = k - λ', where λ' are the eigenvalues of B. Using the result from Part A, we know that each λ' divides the determinant of B. Therefore, each k - λ' divides the determinant of A. Since k is an integer and the determinant of A is also an integer, it follows that k must divide the determinant of A.

In conclusion, if each row of a square matrix A has a sum of k, then k divides the determinant of A. This result is derived from the fact that the eigenvalues of A are given by k minus the eigenvalues of a matrix obtained by subtracting k from each entry of A. The divisibility of k by the eigenvalues implies the divisibility of k by the determinant of A.

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Step-by-step explanation:

Aight, so the same intercept

\( - 2y = - 4 - x = = = > \\ y = \frac{1}{2} x + 2\)

m=½

\(y = \frac{1}{2} x + b = = = > \\ now \: let \: us \: replace \: the \: point \\ 1 = \frac{1}{2} ( - 3) + b = = = > \\ \frac{5}{2} = b\)

soooo

\(y = \frac{1}{2} x + \frac{5}{2} \)

First subtract the difference of the points from total points:

56-36 = 20

Now divide 20 points by 2 teams:

20/2 = 10

Now add 36 to 10: 36 + 10 = 46

The final score was 46 to 10

Chicago got 46 points New England got 10 points.

Answer:

Dilate by a scale factor of 0.5 with the origin as the center of dilation.

Rotate 90° clockwise about the origin

Step-by-step explanation:

Polygon ABCD:

Dilate by a scale factor of 0.5 with the origin as the center of dilation (pink polygon on attached diagram).

This means multiply the x and y values of the points by 0.5:

A → (-1, 2)

B → (-4, 1)

C → (-2, 4)

D → (-1, 3)

Rotate 90° clockwise about the origin: (x, y) → (-y, x)

A' = (-2, 1)

B' = (-1, 4)

C' = (-4, 2)

D' = (-3, 1)

So the transformations are:

Answer:

B: 72

Step-by-step explanation:

Here, we want to find the measure of arc AC

Mathematically, we will use an angle arc relationship here

The angle arc relationship to use here is that the arc AC is twice the measure of angle ABC

Thus, we have the arc AC as 2 * 36 = 72 degrees

Answer:

Step-by-step explanation:

Slope is expressed as shown;

m = y2-y1/x2-x1

Given

m = 1/3

Coordinates A(x,6) B(2,4)

Substitute and get x

1/3 = 4-6/2-x

1/3 = -2/2-x

Cross multiply

2-x = 3(-2)

2-x = -6

-x = -6-2

-x = -8

x = 8

Hence the value of x is 8

Longest Path Problem in Ordered, Unweighted, Directed Graphs.

The longest path problem in ordered, unweighted, directed graphs aims to find the longest path in an ordered, unweighted, directed graph. The length of the path is measured by the number of vertices that it contains. Developing an O(n2) algorithm for solving the longest path problem in ordered, unweighted, directed graphs entails determining the longest path in a directed acyclic graph (DAG).

The algorithm is as follows:

Step 1: Find the indegrees of all vertices in the graph. A queue will also be created, which will contain all vertices with zero indegrees.

Step 2: While the queue is not empty, remove the first vertex, add it to the topological order, and decrease the indegrees of its neighbors by one.

Step 3: If the indegree of a neighbor reaches zero as a result of the previous step, it is added to the queue.

Step 4: The algorithm maintains an array d[], where d[v] represents the longest path that ends at vertex v.

Initialize all values in d[] to 0. Also, initialize a variable maxPath to 0.

Step 5: For each vertex u in the topological order, iterate over each of its neighbors v. If d[v] + 1 > d[u], update d[u] to d[v] + 1.

Step 6: If d[u] > maxPath, update maxPath to d[u].

Step 7: The length of the longest path will be stored in maxPath when the algorithm terminates. The longest path can be retrieved using d[] and the topological order.

In conclusion, the above algorithm has an O(n2) time complexity, and it solves the longest path problem in ordered, unweighted, directed graphs.

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Answer:

The dimensional analysis method uses equivalences written in fractional form. Because the numerator and denominator of the fraction are equivalent, the value of the fraction is 1. Multiplying by 1 does not change the quantity, but using an equivalence will change the units (or label). In order for units to cancel they must be in the numerator and the denominator of the fraction

Step-by-step explanation:

Dimensional analysis is a method of problem solving that takes into consideration the identity property of multiplication whereby the product of a number and 1 will always give the same number, that is 1 × n = n whereby the value "n" remains the same after the multiplication

Therefore, a fraction of two equivalent measurements but different units has a value of 1, and multiplying the equivalent fraction with another measurement with the same unit as the denominator of the fraction with a value of 1 changes the unit to that of the unit of the numerator

Answer:

The answer is (-sin(cos^4a(x)))^4a

The 1st two methods can improve the quality of its service,the 3rd method may also be an option ,depending on the type of business and customer preferences

A business that experiences service delivery gaps can use the following methods to improve the quality of its service:

Empower employees to work in the customers' best interest - Provide incentives and support for service problems

Both of these methods can help motivate employees to provide better customer service and address any delivery gaps that may exist.

Implement self-service technologies may also be an option, depending on the type of business and customer preferences.

However, this alone may not necessarily address delivery gaps, as it does not involve direct interaction with customers.

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Answer:

1.2x10^-1 seconds

Step-by-step explanation:

Answer:

0.12 seconds

Step-by-step explanation:

just think - how long does it take you to travel for example 30 km, if you are going 60 km/h ?

you have to divide 30 by 60 and get 0.5 or 1/2. meaning it takes you (logically) 30 minutes or half an hour to do so.

it is the same principle for all these kinds of questions.

we only need to keep an eye on the dimension of what we are talking about. is it hours or seconds ? meters or kilometers ? and do in

we need here to focus on seconds and to calculate

3.6×10⁷ / 3×10⁸ = 3.6 / 3×10¹ = 1.2 / 10 = 0.12 seconds

or

\(1.2 \times {10}^{ - 1} \)

seconds

Answer:

280%

Step-by-step explanation:

67,500 divided by 2,025 is 280.25

Answer:

if the tip is 20% and 7%, it means that the meal MUST cost less than 32.85.

the reason behind this is that if we have $45 to spend it means that each 1% is 0.45 and 0.45x27=12.15 meaning that if we subtract this from $45 we get 32.85.

Now we have already spent $14 on our drink and appetizer so 32.85-14=18.85 we can only spend 18.85 on our meal

Answer:

1. 10 x 12 = 120      2. 4 (48/12)

An invertible matrix P and a diagonal matrix D such that A = PDP⁻¹ is shown below.

To find an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹:

Let \(\lambda\) be an eigenvalue of A. Then:

\(\begin{aligned}0 &=|A-\lambda I| \\&=\left|\begin{array}{ccc}-11-\lambda & 3 & -9 \\0 & -5-\lambda & 0 \\6 & -3 & 4-\lambda\end{array}\right| \\&=-(0)\left|\begin{array}{cc}3 & -9 \\-3 & 4-\lambda\end{array}\right|+(-5-\lambda)\left|\begin{array}{cc}-11-\lambda & -9 \\6 & 4-\lambda\end{array}\right|-(0)\left|\begin{array}{cc}-11-\lambda & 3 \\6 & -3\end{array}\right| \\&=(-5-\lambda)[(-11-\lambda)(4-\lambda)+54] \\&=-(5+\lambda)^{2}(2+\lambda)\end{aligned}\)

Therefore, \(\lambda = -2\) or \(\lambda = -5\).

Let \(\mathbf{v}=\left[\begin{array}{l}a \\b \\c\end{array}\right]\) be an eigenvector associated with the eigenvalue \(\lambda\).\(\lambda = -2\): From \((A+2 I) \mathbf{v}=\mathbf{0}\) we obtain:

\(\left[\begin{array}{ccc}-9 & 3 & -9 \\0 & -3 & 0 \\6 & -3 & 6\end{array}\right]\left[\begin{array}{l}a \\b \\c\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]\)

Applying elementary row operations to find the reduced echelon form of the coefficient matrix, we obtain:

\(\left[\begin{array}{ccc}-9 & 3 & -9 \\0 & -3 & 0 \\6 & -3 & 6\end{array}\right] \stackrel{\left(-\frac{1}{9}\right) R_{1} \rightarrow R_{1}}{\longrightarrow}\left[\begin{array}{rrr}1 & -\frac{1}{3} & 1 \\0 & -3 & 0 \\6 & -3 & 6\end{array}\right] \stackrel{(-6) R_{1}+R_{3} \rightarrow R_{3}}{\longrightarrow}\left[\begin{array}{rrr}1 & -\frac{1}{3} & 1 \\0 & -2 & 0 \\0 & -1 & 0\end{array}\right] \stackrel{\left(-\frac{1}{2}\right) R_{2} \rightarrow R_{2}}{\longrightarrow}\)

\(\left[\begin{array}{ccc}1 & -\frac{1}{3} & 1 \\0 & 1 & 0 \\0 & -1 & 0\end{array}\right] \stackrel{\left(\frac{1}{3}\right) R_{2}+R_{1} \rightarrow R_{1}}{\stackrel{R_{2}+R_{3} \rightarrow R_{3}}{\longrightarrow}}\left[\begin{array}{ccc}1 & 0 & 1 \\0 & 1 & 0 \\0 & -1 & 0\end{array}\right] \stackrel{R_{2}+R_{3} \rightarrow R_{3}}{\longrightarrow}\left[\begin{array}{ccc}1 & 0 & 1 \\0 & 1 & 0 \\0 & 0 & 0\end{array}\right]\)

Hence, we have a + c = 0 and b = 0. Let c = -1 and a = 1.So, \(\left[\begin{array}{c}1 \\0 \\-1\end{array}\right]\) is an eigenvector associated with \(\lambda = -2\).

\(\lambda = -5\): From \((A+5 I) \mathbf{v}=\mathbf{0}\) we obtain:

\(\left[\begin{array}{ccc}-6 & 3 & -9 \\0 & 0 & 0 \\6 & -3 & 9\end{array}\right]\left[\begin{array}{l}a \\b \\c\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]\)

Applying elementary row operations to find the reduced echelon form of the coefficient matrix, we obtain:

\(\left[\begin{array}{ccc}-6 & 3 & -9 \\0 & 0 & 0 \\6 & -3 & 9\end{array}\right] \stackrel{\left(-\frac{1}{6}\right) R_{1} \rightarrow R_{1}}{\longrightarrow}\left[\begin{array}{ccc}1 & -\frac{1}{2} & \frac{3}{2} \\0 & 0 & 0 \\6 & -3 & 9\end{array}\right] \stackrel{(-6) R_{1}+R_{3} \rightarrow R_{3}}{\longrightarrow}\left[\begin{array}{ccc}1 & -\frac{1}{2} & \frac{3}{2} \\0 & 0 & 0 \\0 & 0 & 0\end{array}\right]\)

Hence, we have a - 1/2b + 3/2c = 0. Let b = 2 and c = 0.Then a = 1. Let b = 0 and c = -2. Then a = 3. Therefore,

\(\left[\begin{array}{l}1 \\2 \\0\end{array}\right],\left[\begin{array}{c}3 \\0 \\-2\end{array}\right]\)

are two linearly independent vectors associated with \(\lambda = -5\)

Matrices P and D: Let

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

be the matrix whose columns are the eigenvectors obtained in the previous step. Set

\(Q=\left[\begin{array}{ccc}-2 & 0 & 0 \\0 & -5 & 0 \\0 & 0 & -5\end{array}\right]\)

to be the diagonal matrix whose diagonal entries are the eigenvalues.

Thus we have, A = PDP⁻¹.

Therefore an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹ is shown.

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The correct question is given below:

Diagonalize matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹.

\(A=\left[\begin{array}{ccc}-11 & 3 & -9 \\0 & -5 & 0 \\6 & -3 & 4\end{array}\right]\)

The relative frequency for La'vonn rolling a 3 is 0.15 or 15%.

Relative frequency is a measure of how often an event occurs in relation to the total number of events. It is usually expressed as a decimal or percentage.

To find the relative frequency, you take the number of times a certain event occurs (in this case, rolling a 3) and divide it by the total number of events (rolling the die 100 times). This gives you the proportion of times the event occurred out of the total number of events.

relative frequency = 15/100 = 0.15 = 15%

Hence, the relative frequency for La'vonn rolling a 3 is 15/100 = 0.15 or 15%.

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Answer:

there's no grid provided

Answer:

2x+6

Step-by-step explanation:

Simplify the expression

I'm so sorry if I'm wrong.

Your cars average acceleration in that time is 12.21m/s^2

The given parameters are

Initial velocity, u = 8.9 m/s

Final velocity, v = 35.76 m/s

Time, t - 2.2 seconds

The average acceleration is calculated using

v = u + at

So, we have

35.76 = 8.9 + 2.2a

Evaluate the like terms

26.86 = 2.2a

Divide by 2.2

a = 12.21

Hence, your cars average acceleration in that time is 12.21m/s^2

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Answer:

sorry i still didn't learn those equestion