Factorise
x^2 - x

Thank you! ​

The number of ways to select a subset of 1515 for a short list is,

⇒ ⁶⁶C₁₅

We have to give that,

A search committee is formed to find a new software engineer.

And, there are 66 applicants who applied for the position.

Hence, a number of ways to select a subset of 15 for a short list is,

⇒ ⁶⁶C₁₅

Simplify by using a combination formula,

⇒ 66! / 15! (66 - 15)!

⇒ 66! / 15! 51!

Therefore, The number of ways to select a subset of 1515 for a shortlist

⇒ ⁶⁶C₁₅

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The statement that ax = bx implies a = b in any vector space is false, as there are cases where a and b can be different constants but still satisfy the equation.

In a vector space, the equation ax = bx does not necessarily imply that a = b. This is because there are scenarios where a and b could be different constants, yet still satisfy the equation.

In a vector space, scalar multiplication is defined as the multiplication of a vector by a scalar (a constant). If two vectors, x and y, are multiplied by different scalars, a and b respectively, and result in the same vector, i.e., ax = bx, it does not necessarily mean that a and b are equal. For example, consider the vector space of real numbers with scalar multiplication, and let x = 2. If a = 3 and b = 6, then ax = 3×2 = 6 = bx, even though a and b are not equal.

Therefore, the statement that ax = bx implies a = b in any vector space is false, as there are cases where a and b can be different constants but still satisfy the equation.

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Answer: 480

Step-by-step explanation:

20(12)(2) = 480

The rate of return in perpetuity on an asset is equal to the asset's cash flow divided by the share price. By dividing the cash flow by the share price,  we are calculating the proportion of the investment amount that is returned to the investor as income.

Let's assume you invest in a stock with an annual cash flow (dividend) of $10 and a share price of $100. To calculate the rate of return in perpetuity, you divide the cash flow by the share price: $10 / $100 = 0.1 or 10%. This means that for every dollar you invest, you receive a return of 10 cents annually. It represents the annual return on your investment as a percentage.

The rate of return in perpetuity is 10% because the cash flow is 10% of the investment amount. The reason the rate of return is equal to the cash flow divided by the share price is because it captures the income generated by the asset relative to the investment made in it.

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The fraction 5/20 can be simplified to 1/4 .

To enter the fraction 5/20, we have to follow these steps:

1. Write the numerator (the number on top) first, which is 5.

2. Use a forward slash (/) to separate the numerator and the denominator (the number on the bottom).

3. Write the denominator next, which is 20.

So, you will enter the fraction as 5/20.

However, it is important to reduce the fraction to its simplest form if possible. In this case, both the numerator and denominator can be divided by 5, which gives you the reduced fraction 1/4.

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Answer:

∠D'A'B'

Step-by-step explanation:

Answer:

Chris = $25

Maria = $35

Justin = $75

Step-by-step explanation:

Chris's amount is x.

x + 3x + (x + 10) = 135

x = 25

Substitute 25 for x.

25 + 3(25) + (25 + 10) = 135

135 = 135

True

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

To solve the system of equations using the weighted least squares method, we need to minimize the sum of the squared weighted residuals. Let's solve the problem using both the algebraic approach and matrices.

Algebraic Approach:

We have the following equations:

A + 2B = 10.50 + V1 ... (1)

2A - 3B = 5.55 + V2 ... (2)

2A - B = -10.50 + V3 ... (3)

To minimize the sum of squared weighted residuals, we square each equation and multiply them by their respective weights:

\(2^2 * (A + 2B - 10.50 - V1)^2\)

\(3^2 * (2A - 3B - 5.55 - V2)^2\\1^2 * (2A - B + 10.50 + V3)^2\)

Expanding and simplifying these equations, we get:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1)\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2)\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\\\)

Now, let's sum up these equations:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1) +\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2) +\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\int\limits^a_b {x} \, dx\)

Simplifying further, we obtain:

\(14A^2 + 31B^2 + 1113 + 14V1^2 + 33V2^2 + 14V3^2 + 14AB - 231A - 246B + 21V1 - 11.1V2 + 21V3 = 0\)

Now, we have a single equation with two unknowns, A and B. We can use various methods, such as substitution or elimination, to solve for A and B. Once the values of A and B are determined, we can substitute them back into the original equations to find the most probable values of A and B.

Matrix Approach:

We can rewrite the system of equations in matrix form as follows:

| 1 2 | | A | | 10.50 + V1 |

| 2 -3 | | B | = | 5.55 + V2 |

| 2 -1 | | -10.50 + V3 |

Let's denote the coefficient matrix as X, the variable matrix as Y, and the constant matrix as Z. Then the equation becomes:

X * Y = Z

To solve for Y, we can multiply both sides of the equation by the inverse of X:

X^(-1) * (X * Y) = X^(-1) * Z

Y = X^(-1) * Z

By calculating the inverse of X and multiplying it by Z, we can find the values of A and B.

Comparing Results:

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

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Answer: 119 billion

Step-by-step explanation:

Alright, so the rate of change is the same thing as the slope, so we can find this by using the slope formula (which I took a picture of because it's super messy to type it out like this)

Now that we know the slope formula, we need to find the x values and the y values to plug into the equation. We'll say that the years are our x values and the money spent (in billions) are our y values. Now that we've set up an axis, we can create points! Our points would be (2000, 1243) and (2005, 1838)

Now we can plug our points into our equations! On the top of our equation, we'll put (1838-1243), and on the bottom we'll put (2005-2000). When we simplify that, we end up with 595/5, which simplifies to 119. Now we know that the rate of change for the credit cards was 119 billion!

Step-by-step explanation:

Alright, so the rate of change is the same thing as the slope, so we can find this by using the slope formula (which I took a picture of because it's super messy to type it out like this)

Now that we know the slope formula, we need to find the x values and the y values to plug into the equation. We'll say that the years are our x values and the money spent (in billions) are our y values. Now that we've set up an axis, we can create points! Our points would be (2000, 1243) and (2005, 1838)

Now we can plug our points into our equations! On the top of our equation, we'll put (1838-1243), and on the bottom we'll put (2005-2000). When we simplify that, we end up with 595/5, which simplifies to 119. Now we know that the rate of change for the credit cards was 119 billion!  ANWSER (y2-y,)

                                                                                                           (x2-x1)

a) ACME's total money flow over the interval from t=0 years to t=20 years is $14,000. b) this integral, we need to use techniques like integration by parts. c) The cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

(a) To find ACME's total money flow over the interval from t=0 years to t=20 years, we need to calculate the definite integral of the income flow function f(t) from t=0 to t=20:

Total money flow = ∫(500+40t) dt (from 0 to 20)

To evaluate this integral, we can apply the power rule of integration:

Total money flow = [500t + 20t^2/2] (from 0 to 20)

               = [500(20) + 20(20^2)/2] - [500(0) + 20(0^2)/2]

               = [10000 + 4000] - [0 + 0]

               = 14000

Therefore, ACME's total money flow over the interval from t=0 years to t=20 years is $14,000.

(b) To find the present value of ACME's money flow over the same interval, we need to discount the future cash flows by an appropriate discount rate. Let's assume the discount rate is r%.

Present value = ∫(500+40t)e^(-rt) dt (from 0 to 20)

To evaluate this integral, we need to use techniques like integration by parts or substitution, depending on the value of r. Please provide the value of r so that we can proceed with the calculation.

(c) The accumulated amount of ACME's money flow over the same interval represents the sum of all the money flows received at each point in time. It can be calculated as the definite integral of the income flow function from t=0 to t=20:

Accumulated amount = ∫(500+40t) dt (from 0 to 20)

Using the same integration technique as in part (a), we find:

Accumulated amount = [500t + 20t^2/2] (from 0 to 20)

                  = 14000

Therefore, the accumulated amount of ACME's money flow over the interval from t=0 years to t=20 years is $14,000.

(d) To find the present value of ACME's money flow assuming the money flows forever, we need to consider the concept of perpetuity. A perpetuity represents a constant cash flow received indefinitely into the future.

The present value of a perpetuity can be calculated using the formula:

Present value = Cash flow / Discount rate

In this case, the cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

Present value = (500 + 40t) / r

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The question is:

ACME Exploding Faucets' income flows at the rate f(t) = 500 + 40t

(a) (2 pts) Find ACME's total money flow over the interval from t = 0 years to t = 20 (b) (2 pts) Find the present value of ACME's money flow over the same interval. (c) (1pt) Find the accumulated amount of ACME's money flow over the same interval. (d) (2 pts) Find the present value of ACME's money flow, assuming that the money flows forever. years.

For full (or any) credit, show your work and explain your reasoning, briefly

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

The midpoint formular used in finding the midpoint of a segment is expressed as;

( [x₁+x₂]/2 , [y₁+y₂]/2 )

Given the data in the question;

Point V(-2,5)

Point Z(3,-17)

Plug these values into the equation above.

( [x₁+x₂]/2 , [y₁+y₂]/2 )

( [(-2) + 3]/2 , [5 + (-17)]/2 )

( 1/2 , -12/2 )

( 1/2, -6 )

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

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The correct option is D. 120.

Given,

The number of sausages in a packet is 10

The number of rolls in a packet is 12

We have to find the smallest number of each we have to buy to have the same number of sausages and rolls.

The smallest number of sausages and rolls will be a common multiple of 10 and 12LCM(10,12) = 60

So, the smallest number of each we have to buy to have the same number of sausages and rolls is 60/10 = 6 sausages and 60/12 = 5 rolls.

If we want to have the same number of sausages and rolls,

we will have to buy in multiples of LCM of 10 and 12.

Therefore, the smallest number of each we have to buy to have the same number of sausages and rolls is: 5 × 12 = 60 sausages and 5 × 10 = 50 rolls.

Let us verify,The total number of sausages we will have = 5 × 10 = 50

The total number of rolls we will have = 5 × 12 = 60

Therefore, the answer is 50 and 60 respectively. The correct option is D. 120.

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To determine how long it will take the Baxter boys to prepare 131 papers, we can use the concept of rate and proportion.

It will take approximately 11 minutes and 14 seconds (to the nearest minute) for the Baxter boys to prepare 131 papers. Given that the Baxter boys can prepare 35 papers in 3 minutes, we can set up a proportion to solve for the time it will take to prepare 131 papers.
First, let's set up the proportion using the information given about the rate of working:
35 papers / 3 minutes = 131 papers / x minutes
To solve for x, we can cross-multiply and then divide:
35 * x = 3 * 131
35x = 393
x = 393 / 35
x ≈ 11.229
Therefore, it will take approximately 11 minutes and 14 seconds (to the nearest minute) for the Baxter boys to prepare 131 papers.

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A curvilinear term in mathematics is "Consisting of, bounded by, or characterized by a curved line." However, the definition of a quadratic is a second-order polynomial equation in a single variable \(0= ax^{2}+bx+c\) with

\(a\neq 0\). A quadratic is a curvilinear term according to my definition, but a function like \($x^{4}$\) would also fit the definition of curvilinear. So, your answer is

False, a quadratic and a curvilinear term are not the same.

False, a curvilinear term is more broad, but quadratics have specific restrictions.

Answer:

..........................

Step-by-step explanation:

soh,cah,toa

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

\(Answer:\large\boxed{y=\frac{2}{3} x+6}\)

Step-by-step explanation:

First let's convert 2x - 3y = 12 into \(y = mx + b\)  form.

In order to do this, solve for y.

\(2x-3y=12\)

\(-3y=-2x+12\)

\(y=\frac{2}{3} x-4\)

This shows us that the slope is   \(\boxed{\frac{2}{3}}\)

Now we use the point-slope formula:

\((y-y1)=m(x-x1)\)

where m is the slope and y1 and x1 are the point the line passes through

Using the point (-6,2) and slope, 2/3, we can find the equation:

\((y-2)=\frac{2}{3} (x-(-6))\)

\((y-2)=\frac{2}{3} (x+6)\)

\((y-2)=\frac{2}{3} x+4\)

\(\large\boxed{y=\frac{2}{3} x+6}\)

Given the integral,- √√5cos(3(Y + X))J11710-sin(5)dA where R is the trapezoidal region with vertices (5, 0), (8, 0), (0, 8), and (0,5)Let R is the trapezoidal region with vertices (5, 0), (8, 0), (0, 8), and (0,5). Thus, √5 and J11710-sin(5) are constants.

Let's find the Jacobian:

Jacobian(J) =

\($\frac{\partial(x,y)}{\partial(u,v)}$\)

If we take\($x = 3(y+x), y$\)

then the Jacobian is J = 2

Then the given integral can be written as,

\(√5/2 $\int^{5}_{0}$$\int^{8-3y}_{5-y/3}$-cos(u)Jdudv\\=√5/2$\int^{5}_{0}$ $\int^{5}_{0}$-cos(3(y+x))Jdxdy\)

∴

\(= √5/2$\int^{5}_{0}$ $\int^{5}_{0}$-cos(3(y+x))Jdxdy\)

Now, we will evaluate this integral.

Substitute x + y = u, y = v.

So we get,

\(\\$\frac{\partial(u,v)}{\partial(x,y)}$\\= $\begin{vmatrix} 1 & 1\\ 0 & 1\\ \end{vmatrix}$ = 1\)

Now the integral becomes,\(\\$\int^{8}_{5}$ $\int^{5}_{0}$ $\frac{-\sqrt{5}}{2}$cos(3u)Jdxdy\)

Here, u = x+y, v = y

Lower limit of u is 5 and the upper limit of u is 8.

Integrating with respect to x,

\(\\$\int^{5}_{0}$cos(3u)Jdx \\= $\frac{1}{3}$sin(3u)J|^{8}_{5} = $\frac{1}{3}$[sin(24) - sin(15)]J\)

Now the integral becomes,

\(\\$\int^{5}_{0}$ $\frac{-\sqrt{5}}{2}$ [$\frac{1}{3}$sin(24) - $\frac{1}{3}$sin(15)]Jdy\\= [$\frac{\sqrt{5}}{6}$sin(24) - $\frac{\sqrt{5}}{6}$sin(15)]J\)

\(= [$\frac{\sqrt{5}}{6}$sin(24) - $\frac{\sqrt{5}}{6}$sin(15)]J.\)

Therefore, the solution of the given integral is \([$\frac{\sqrt{5}}{6}$sin(24) - $\frac{\sqrt{5}}{6}$sin(15)]J.\)

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Answer:

7.92

Step-by-step explanation:

A two-sample t-test (independent samples) would be used to determine if there is a difference in the mean amount of time for each shift to process 100 pounds of coconuts.

A t-test is a statistical test that compares the means of two groups or samples. It allows you to determine if there is a significant difference between the means of two sets of data.The most basic type of t-test is a two-sample t-test.

This is used when you want to compare the means of two independent groups. In this case, we have the day shift and night shift, which are independent groups. Hence, we would use a two-sample t-test (independent samples) to determine if there is a difference in the mean amount of time for each shift to process 100 pounds of coconuts.

The one-way ANOVA is used when you have more than two independent groups to compare, randomized block ANOVA is used when the samples are paired, and the paired t-test is used when you have two dependent samples.

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Assume the sales price is $15 per unit, variable cost is $6 per unit, and fixed cost is $5,000. If the variable cost decreases to $3 per unit. The number of units is 250 units.

Using this formula to find the units sold

Number of units = [Fixed cost / ( Sales - variable cost)]  - [Fixed cost / ( Sales - decrease in variable cost)

Let plug in the formula

Number of units = [$9,000 / ($15- $6)] - ($9,000 / ($15-$3)

Number of units = ($9,000 /$9) - ($9,000 / $12)

Number of units = 1,000- 750

Number of units = 250 units

Note:

(Fixed cost + target profit = $5,000+$4,000 = $9,000)

Therefore 250 units was sold.

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Answer:

-1.86

Step-by-step explanation:

1.86 is half of 3.72, and when you divide a negative with a positive, you get a negative.

Answer:

-1.86

Step-by-step explanation:

Answer:

48.72

Step-by-step explanation:

your old value =42

your new value = let it be x

your original percentage =100percent

your new percentage:100+16

=116percent

old. new

value. 42. x

percentage 100. 116

cross multiply :x multiply by 100=42 multiplyby 116

100x=42x116

x=42x116/100

x=48.72

So, your increased value is 48.72

Answer:

Step-by-step explanation:

u have to combine like terms

7.2+0.8w B

The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).

The difference of two expressions is determined by subtracting one from the other.

Find the difference of each of the expressions given to determine which will give us 5.

-3 - (-8)

= -3 + 8

= 5

-2 - 3 = -5 [this is not the same as 5]

1 - (-4)

= 1 + 4

= 5

7 - (-2)

= 7 + 2

= 9

-3 - (-8) and 1 - (-4) will give us a difference of 5.

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Answer:

4 Hats and 6 Scarves

For the function transformation form of f(x), \(g(x) = a f(\frac{1}{b} x - h) + k \), we are replacing variable a by 2, result will in the transformation displayed in the above graph. So, option(d) is right one.

A transformation is an another way to a parent function's graph. There are serval formulas for distinct rules of transformation. If consider transformation function of f(x) is g(x) = f(x - h) + k,

We have a function f(x) = 2cos(x), that is cosine function and g(x) is it's transform function. Here, \(g(x) = a f(\frac{1}{b} x - h) + k \), now see the graph carefully.

Thus, for g(x) in above graph, there are no horizontal and vertical translation. So, h = k = 0. Also, the graphs are not reflected on both axes. However, notice that the graph of g(x) is just the vertical stretched version of f(x). The values of g(x) are twice that of f(x). Therefore, the factor a must be twice, a = 2. Hence, we replace a by 2.

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Complete question:

The above graph of shows f(x) = 2cos(x) and transform g(x). For the transformation rule in the form , g(x) = a f( 1/b x - h) + k

replacing which variable with what number will result in the transformation displayed in the graph?

a) b is replacing by 1/2

b) k is replacing by -1/2

c) h is replacing by -2

d) a is replacing by 2

The Laplace transform can be used to solve the initial-value problem y'' + 10y' + 9y = 0, y(0) = 1, y'(0) = 0. The solution is given by \(y(t) = \frac{1}{3} e^{-t} - \frac{1}{3}e^{-9t}\)

The Laplace transform of the differential equation y'' + 10y' + 9y = 0 is given by L(y'') + 10L(y') + 9L(y) = 0, where L denotes the Laplace transform. Using the property of the Laplace transform that \(L(y') = sY(s) - y(0)\), where Y(s) is the Laplace transform of y(t), and \(L(y'') = s^{2}Y(s) - sy(0) - y'(0)\), we can rewrite the transformed equation as \(s^{2}Y(s) - s + 10sY(s) - 10 + 9Y(s) = 0\)

Solving for Y(s), we get \(Y(s) = \frac{1}{(s^{2} + 10s + 9)}\).

To find the inverse Laplace transform of Y(s), we factor the denominator of Y(s) as (s+1)(s+9) and use partial fractions to write Y(s) as \(Y(s) = \frac{1}{((s+1)(s+9))} = \frac{(1/8)}{(s+1)} - \frac{(1/8)} {(s+9)}\).

Taking the inverse Laplace transform of each term, we get \(y(t) = \frac{1}{8}}e^{-t} - \frac{1}{8} e^{-9t}}\).

Using the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the constants in the solution.

We have \(y(0) = \frac{1}{8}(1 - 1) = 0\), which is not equal to 1.

To fix this, we add the term \(\frac{1}{3} e^{-t}\), which has a derivative of \(-\frac{1}{3}e^{-t}\) and thus does not affect the value of y'(0).

Therefore, the solution to the initial-value problem is \(y(t) = \frac{1}{3} e^{-t} - \frac{1}{3}e^{-9t}\).

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Answer: try B

Step-by-step explanation: