A cube with each face a different colour will fit exactly into a box in which it is packaged. In how many ways can the cube be placed in the box?

The compound interval for the given interval is (-∞, ∞).

A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".

The given intervals are (-∞, -2] or [-3, ∞).

Now, the compound interval is (-∞, ∞)

Thus, the interval notation is -∞<x<∞

Therefore, the compound interval for the given interval is (-∞, ∞).

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the 10 th term for the sequence 1,3,5,7..... is 19

Step-by-step explanation:

n = 1; 1st = 2*1–1=1;

n= 2; 2nd =2*2–1=3;

n =3; 3rd =2*3–1=5;

n=4; 4th =2*4–1=7;

n=5; 5th =2*5–1=9;

n=6; 6th =2*6–1=11;

n=7; 7th = 2*7-1= 13

n= 8; 8th = 2*8-1 =15

n = 9; 9th = 2*9-1 = 17

n= 10; 10th = 2*10-1 =19

To maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

To maximize the seating area, we need to determine the dimensions of the rectangular auditorium that will give us the largest possible area while using the given length of light strips.

Let the length of the rectangular auditorium be L, and its width be W.

The seating area consists of the rectangular portion minus the semicircular stage. So, the seating area's length is L - 2r (subtracting the semicircle's diameter) and the seating area's width is W - 2r.

The perimeter of the seating area is the sum of the lengths of its four sides, excluding the semicircular stage. The perimeter is given as 45π + 60 meters.

Perimeter = 2(L - 2r) + 2(W - 2r) + πr = 45π + 60

Simplifying: 2L + 2W - 8r + πr = 45π + 60

Rearranging: 2L + 2W = 8r + 44π + 60

The area of the seating area is given by A = (L - 2r)(W - 2r).

We want to maximize A, so we need to express it in terms of a single variable. Since we have an equation with two variables (L and W), we can rewrite one of the variables in terms of the other.

Rearranging the perimeter equation: 2L + 2W = 8r + 44π + 60

Solving for L: L = (8r + 44π + 60 - 2W) / 2

Substituting L in terms of W into the area equation: A = [(8r + 44π + 60 - 2W) / 2 - 2r] (W - 2r)

Simplifying: A = (4r + 22π + 30 - W) (W - 2r)

Now we have the area equation in terms of a single variable, W. To maximize A, we can take the derivative of A with respect to W, set it equal to zero, and solve for W.

dA/dW = 2(4r + 22π + 30 - W) - (W - 2r) = 0

Solving for W: 8r + 44π + 60 - W = W - 2r

Simplifying: 10r + 44π + 60 = 2W

W = 5r + 22π + 30

Now that we have W in terms of r, we can substitute this expression back into the area equation to get the area in terms of r only.

A = (4r + 22π + 30 - (5r + 22π + 30)) ((5r + 22π + 30) - 2r)

Simplifying: A = (r - 22π) (3r + 22π + 30)

Expanding: A = 3r² + 8rπ + 30r - 66πr - 660π

Now, to find the maximum area, we can take the derivative of A with respect to r, set it equal to zero, and solve for r.

dA/dr = 6r + 8π + 30 - 66π = 0

Simplifying: 6r - 58π + 30 = 0

6r = 58π - 30

r = (58π - 30) / 6

r ≈ 29π/3 - 5

Therefore, to maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

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Answer:

Step-by-step explanation:

The solution of this systems of equations is the intersection of both graphs

Let's kick start with a:

a)

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

From the first attached diagram by using graph:

the solution is the set {(-5, 8), (3, 0)}

b)

\(y-15=x^3+4x \\ \\ x-y =1\)

Using the graph tool from the last diagram below;

the solution is the set⇒( there is no solution)

c)

\(y+5 =x^2-3x \\ \\ 2x+y =1\)

From the second attached diagram by using graph:

the solution is the set {(-2, 5), (3, -5)}

d)

\(y-6=x^2-3x \\ \\ x+2y =2\)

the solution is the set ⇒ there is no solution (shown in the last diagram  below)

e)

\(y-17=x^2-9x \\ \\ -x+y =1\)

the solution is the set {(2, 3), (8, 9)} as shown in the third diagram

f) Lastly:

\(y-15=-x^2+4x \\ \\ x+y =1\)

Using the graph tool from the fourth diagram below;

the solution is the set  {(-2, 3), (7, -6)}

The solution to the system of equations are the truth values of the system of equations

\(\mathbf{(a)\ y + 12 = x^2 + x,\ x + 3 = y}\)

The graphs of the equations intersect at (-5,8) and (3,0).

So, the solution set is {(-5,8), (3,0)}

\(\mathbf{(b)\ y - 15 = x^3 + 4x,\ x - y = 1}\)

The graphs of the equations do not intersect

So, the system has no solution

\(\mathbf{(c)\ y + 5 = x^2 - 3x,\ 2x + y = 1}\)

The graphs of the equations intersect at (-2,5) and (3, -5).

So, the solution set is {(-2, 5), (3, -5)}

\(\mathbf{(d)\ y - 6 = x^2 - 3x,\ x + 2y = 2}\)

The graphs of the equations do not intersect

So, the system has no solution

\(\mathbf{(e)\ y - 17 = x^2 - 9x,\ -x + y = 1}\)

The graphs of the equations intersect at (2,3) and (8,9).

So, the solution set is {(2, 3), (8, 9)}

\(\mathbf{(f)\ y - 15 = -x^2 + 4x,\ x + y = 1}\)

The graphs of the equations intersect at (-2,3) and (7,-6).

So, the solution set is {(-2, 3), (7, -6)}

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Answer:

C(coner) J(Jackson)

Step-by-step explanation:

Jx3=C age

Answer:

Step-by-step explanation:

find the semiperiter (1/2 perimeter or L+W)

80 : 2 = 40

now we know that 4z + 2 + 3z + 3 = 40

we solve for z with an equation

4z + 2 + 3z + 3 = 40

7z = 40 - 2 - 3

7z = 35

z = 35 : 7

z = 5

now we find CD

3z + 3 =      (z=5)

3 * 5 + 3 =

15 + 3 =

18

-------------------------------

check (remember pemdas)

4z + 2 + 3z + 3 = 40

4*5+2+3*5+3 = 40

20+2+15+3=40

40 = 40

the answer is good

Considering the definition of a line, the equation of the line that passes through the point (0, -4) and has a slope of  is y=3x -4.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know:

Substituting the value of the slope and the value of the point, the value of the ordinate to the origin b can be obtained:

-4= 3×0 + b

-4= 0 + b

-4= b

-4= b

Finally, the equation of the line is y= 3x -4.

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Liliana's next step is to find the area of each of the two trapezoids.

From the question, we have the following parameters that can be used in our computation:

Given that she has broken the polygon into two trapezoids, the next step ti so calculate the area of each trapezoid

This is done using

Area = 1/2 * (sum of parallel sides) * height

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Complete question

Area of Trapezoids and Other Figures quick check

Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids. What is Liliana's next step?

a) Definition of Limit: Let f(x) be defined on an open interval containing c, except possibly at c itself.

We say that the limit of f(x) as x approaches c is L and write: 

\(limx→cf(x)=L\)

if for every number ε>0 there exists a corresponding number δ>0 such that |f(x)-L|<ε whenever 0<|x-c|<δ.

Let's prove that f(x) = 2x³ - 1 is continuous at the point x = 2; that is, \(lim-2 2x³ - 1\)= 15.

Let \(limx→2(2x³-1)\)= L than for ε > 0, there exists δ > 0 such that0 < |x - 2| < δ implies

|(2x³ - 1) - 15| < ε

|2x³ - 16| < ε

|2(x³ - 8)| < ε

|x - 2||x² + 2x + 4| < ε

(|x - 2|)(x² + 2x + 4) < ε

It can be proved that δ can be made equal to the minimum of 1 and ε/13.

Then for

0 < |x - 2| < δ

|x² + 2x + 4| < 13

|x - 2| < ε

Thus, \(limx→2(2x³-1)\)= 15.

b) (i) Definition of Contractions: Let f: [a, b] → [a, b] be a function.

We say f is a contraction if there exists a constant 0 ≤ k < 1 such that for any x, y ∈ [a, b],

|f(x) - f(y)| ≤ k |x - y| and |k|< 1.

(ii) We need to prove that h(x) = cos(sin x) is continuous at every point x = x0; that is, \(limx→x0\) | cos(sin x)| = | cos(sin(x0)).

First, we prove that cos(x) is a contraction function on the interval [0, π].

Let f(x) = cos(x) be defined on the interval [0, π].

Since cos(x) is continuous and differentiable on the interval, its derivative -sin(x) is continuous on the interval.

Using the Mean Value Theorem, for all x, y ∈ [0, π], we have cos (x) - cos(y) = -sin(c) (x - y),

where c is between x and y.

Then,

|cos(x) - cos(y)| = |sin(c)|

|x - y| ≤ 1 |x - y|.

Therefore, cos(x) is a contraction on the interval [0, π].

Now, we need to show that h(x) = cos(sin x) is also a contraction function.

Since sin x takes values between -1 and 1, we have -1 ≤ sin(x) ≤ 1.

On the interval [-1, 1], cos(x) is a contraction, with a contraction constant of k = 1.

Therefore, h(x) = cos(sin x) is also a contraction function on the interval [0, π].

Hence, by the Contraction Mapping Theorem, h(x) = cos(sin x) is continuous at every point x = x0; that is,

\(limx→x0 | cos(sin x)| = | cos(sin(x0)).\)

(c) (i) Given a common deviation bound of 0.00025 for both x - 2 and y - 2, we need to prove that x + y is accurate to +2 by 3 decimal places.

Let x - 2 = δ and y - 2 = ε.

Then,

x + y - 4 = δ + ε.

So,

|x + y - 4| ≤ |δ| + |ε|

≤ 0.00025 + 0.00025

= 0.0005.

Therefore, x + y is accurate to +2 by 3 decimal places.(ii) The mapping diagram is shown below:

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Answer:

6.71

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2

6^2+3^2=c^2

36+9=c^2

45=c^2

6.71=c

Answer:

3 square fhfhfjshxfjkzkdjzhx h2jxfjwjznnznzn

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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The maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

To determine the maximum price Matthew can pay for the car, we need to consider his repayment capability and the terms of the loan.

Matthew can make annual repayments of $35,000. Since the loan term is six years, the total amount he can repay over the loan period is $35,000 multiplied by six, which equals $210,000.

To calculate the maximum price of the car, we need to account for the interest rate of 9.25%. The interest rate represents the cost of borrowing and is applied to the loan amount.

Let's assume the loan amount is denoted by P.

The formula to calculate the future value of a loan with interest is:

FV = P(1 + r)^n

Where:

FV = Future value (total amount repaid)

P = Principal amount (maximum price of the car)

r = Interest rate per period (9.25% or 0.0925)

n = Number of periods (six years)

Since Matthew can repay a total of $210,000 over the loan period, we can set up the equation:

$210,000 = P(1 + 0.0925)^6

Now we can solve for P:

P = $210,000 / (1 + 0.0925)^6

Evaluating this expression, we find:

P ≈ $126,318.29

Therefore, the maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

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If there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use

Given,

The conditions

We know

In multiple regression method the dependent variables are predicted by using the known independent variables. This method is usually used to analyze the relationship between multiple independent variables and one independent variables,

So here multiple regression method is using.

Hence, if there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use

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Answer:

x= y/e (or the last answer choice on your screen)

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

21/3

7*2

With an interest rate of 3% compounded continuously and an initial deposit of $15,000, the amount of money in the account after 20 years would be approximately $27,322.80.

Using the formula for continuous compound interest:

A = P * e^(rt)

Where:

A = the amount of money in the account after the given time period

P = the initial deposit amount

e = the mathematical constant approximately equal to 2.71828

r = the interest rate (expressed as a decimal)

t = the time period (in years)

Let's assume an interest rate of 3% (0.03) compounded continuously and an initial deposit of $15,000. We can calculate the amount of money in the account after 20 years:

A = $15,000 * e^(0.03 * 20)

Using a calculator, we can evaluate the expression:

A ≈ $15,000 * e^(0.6)

A ≈ $15,000 * 1.82212

A ≈ $27,322.80

Therefore, with an interest rate of 3% compounded continuously and an initial deposit of $15,000, the amount of money in the account after 20 years would be approximately $27,322.80.

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a) Activity that should be crashed first to reduce the project duration by 1 day is B.

b) Activity that should be crashed next to reduce the project duration by one additional day is C.

c) Total cost of crashing the project by 2 days = $10,000.

To determine the activities that should be crashed first and next, we need to consider the critical path method (CPM). The critical path is the longest sequence of activities that determines the total project duration. Crashing activities on the critical path will reduce the project duration.

Let's calculate the project duration and costs for each activity:

Activity A:

Normal Time: 7 days

Crash Time: 6 days

Normal Cost: $5000

Total Cost with Crashing: $5600

Activity B:

Normal Time: 4 days

Crash Time: 2 days

Normal Cost: $1500

Total Cost with Crashing: $3400

Immediate Predecessor(s): A

Activity C:

Normal Time: 11 days

Crash Time: 9 days

Normal Cost: $4200

Total Cost with Crashing: $6600

Immediate Predecessor(s): B

To find the critical path, we add the normal times of each activity:

Critical Path: A -> B -> C

a) Activity that should be crashed first to reduce the project duration by 1 day:

Since the critical path includes activities A, B, and C, we need to identify which activity's crash time can reduce the project duration by 1 day. The activity that can achieve this is B since its crash time is 2 days compared to activity A's crash time of 6 days. Therefore, activity B should be crashed first.

b) Activity that should be crashed next to reduce the project duration by one additional day:

After crashing activity B, the project duration will be reduced by 1 day. To further reduce the duration by an additional day, we need to determine which activity's crash time can achieve this. The activity that can achieve this is C since its crash time is 9 days compared to activity A's crash time of 6 days. Therefore, activity C should be crashed next.

c) Total cost of crashing the project by 2 days:

The total cost of crashing the project by 2 days is the sum of the total costs for the crashed activities:

Total cost of crashing = Total cost of crashing activity B + Total cost of crashing activity C

                   = $3400 + $6600

                   = $10,000

Therefore, the total cost of crashing the project by 2 days is $10,000.

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Complete Question:

Three activities are candidates for crashing on a project network for a large computer installation (all are, of course, critical). Activity details are in the following table.

a) Activity that should be crashed first to reduce the project duration by 1 day is

b) Activity that should be crashed next to reduce the project duration by one additional day is

c) Total cost of crashing the project by 2 days =

Answer:

The answer is "1.5".

Step-by-step explanation:

Given value:

\(p= 60 \% = \frac{60}{100}= 0.60\\\\\sigma_p = 0.10 \\\\\hat{p} =0.75\)

testing the statistics:

\(Z= \frac{\hat{p} -p}{\sigma_p}\\\\\)

  \(=\frac{0.75-0.60}{0.10}\\\\=\frac{0.15}{0.10}\\\\=1.5\)

The total number of people at the stadium is 11000.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

At a football stadium, 2% of the fans in attendance were teenagers.

If there were 220 teenagers at the football stadium.

the total number of people at the stadium= 220*100/2

                                                                     =1100

Hence, the total number of people at the stadium is 11000.

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All of the points on the graph could represent rational numbers. (-1, 0, 1, 4.5)

Answer:

B

Step-by-step explanation:

A: false, point C isn't a rational number

B: True, Every negative integer is a negative rational number, like point A

C: false, point D is a fraction, therefore, point D is a rational number

D: false, like said in A, point C isn't a rational number

Answer:

i think its 12%

Step-by-step explanation:

Answer:

38 cards

Step-by-step explanation:

Assuming that you replaced all your baseball cards that were ruined, that would mean that you started with 38, because we know that 19 is half of all the baseball cards that were lost so 19*2=38

There are 5 adults and 15 children in the group.

Let's solve the system of equations to determine the number of adults and children in the group.

From the first equation, we have a + c = 20. We can rearrange it to a = 20 - c.

Substituting this value of a into the second equation, we have 40(20 - c) + 20c = 500.

Simplifying this equation, we get 800 - 40c + 20c = 500.

Combining like terms, we have -20c = -300.

Dividing both sides by -20, we get c = 15.

Substituting this value of c back into the first equation, we have a + 15 = 20, which gives us a = 5.

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Answer:

$30000at 8%compound interest

Answer:

the answer is blue because -3 to 0 takes 1 step right and 3 steps up

Answer:

Step-by-step explanation:

5x - 3 = 2(x +2)^2

Don't try this. It is a double ugly equation. But you can see that you use the power property. You use the distributive property. You use addition and subtraction and division and multiplication to solve it.

Based on the given information, the x-intercept is 2 and the y-intercept is 3.

The x-intercept is the point where the line crosses the x-axis. At this point, the value of y is zero. To find the x-intercept, we set y to zero and solve for x and the y-intercept is the point where the line crosses the y-axis. At this point, the value of x is zero. To find the y-intercept, we set x to zero and solve for y.

To find the x-intercept, we set y to zero and solve for x:

3x + 2y = 6

3x + 2(0) = 6

3x = 6

x = 2

Therefore, the x-intercept is 2.

To find the y-intercept, we set x to zero and solve for y:

3x + 2y = 6

3(0) + 2y = 6

2y = 6

y = 3

Therefore, the y-intercept is 3.

So the x-intercept is 2 and the y-intercept is 3.

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