Explain your method for determining the efficient route of a network.

The explicit formula for the given sequence is a(n) =  -5 + (-1)(n - 1).

What is termed as recursive definition?

A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.

The recursive formula for an arithmetic sequence is as follows.

a(1) = -5 and a(n) = a(n-1) -1

Remember that this formula provides us with two types of data.

Let's look for a formal formula again for sequence.

1) Remember that we can use the standard explicit form to represent a sequence in which the first term is A & common difference is B:  

A + B(n - 1)

2) As a result, the sequence's explicit formula is a(n) = -5 + (-1)(n - 1).

Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) =  -5 + (-1)(n - 1).

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The amount of Rs8550 will be equal to 60 pounds.

The rate at which one currency will be exchanged for another is known as the exchange rate in the world of finance. The most frequent types of currencies are national currencies.

Given that $5 = 4 pounds and Rs 342 = $3, the amount RS 8550 will be calculated as below:-

$5 = 4 pounds

$1 = 4 / 5 pounds  .............................( 1 )

Rs 342 = $3

$1 =  342 / 3 RS  ..............................( 2 )

From the two equations:-

342 / 3 RS = 4 / 5 pounds

1 RS = ( 3 / 342 ) x  ( 4 / 5 )

8550 RS = ( 8550 x 3 x 4 ) / ( 342 x 5 )

8550 RS = 60 pounds

Therefore, the amount of Rs8550 will be equal to 60 pounds.

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Given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]  in decreasing order are as follows:

[tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .

As given in the question,

Given numbers are as follow : [tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]

Approximate value of all given numbers

[tex]\sqrt{14} =3.74\\\\\sqrt{5/2}= 1.58\\ \\\sqrt{9 /16} = 0.75\\ \\1 =1.00\\\\11=11.00[/tex]

Arrange the given numbers in decreasing order :

11 > 3.74 > 1.58 > 1 > 0.75

[tex]\implies 11 > \sqrt{14} > \sqrt{5/2} > 1 > \sqrt{9/16}[/tex]

Therefore, given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]  in decreasing order are as follows:  [tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .

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By substitution, the solution of the system of equations, x - 2y + z = -4, -4x + y -2z = 1 and 2x + 2y - z = 10, is (x , y , z) = (2 , 1 , -4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given three equations in x, y, and z,

x - 2y + z = -4     (equation 1)

-4x + y -2z = 1     (equation 2)

2x + 2y - z = 10     (equation 3)

Using the equation 1, find the value of one variable, lets say x, in terms of the other variables.

x - 2y + z = -4     (equation 1)

x = 2y - z - 4     (equation 4)

Substitute the equation 4 to equation 2 and 3 and find the value of another variable, lets say y, in terms of the other variable.

-4x + y -2z = 1     (equation 2)

-4(2y - z - 4) + y -2z = 1

-8y + 4z + 16 + y -2z = 1

-8y + y = 2z - 4z + 1 - 16

-7y = -2z - 15

y = -(2z + 15)/-7

y = (2z + 15)/7     (equation 5)

2x + 2y - z = 10     (equation 3)

2(2y - z - 4) + 2y - z = 10

4y - 2z - 8 + 2y - z = 10

4y + 2y = 2z + z + 10 + 8

6y = 3z + 18

y = (1/2)z + 3     (equation 6)

Substitute the value of y from equation 5 to equation 6 and solve for z.

y = (1/2)z + 3     (equation 6)

(2z + 15)/7 = (1/2)z + 3

2z + 15 = 7[(1/2)z + 3]

2z + 15 = (7/2)z + 21

2z - (7/2)z = 21 - 15

(-3/2)z = 6

z = -4

Substitute the value of z in either equation 5 or 6.

y = (1/2)z + 3     (equation 6)

y = (1/2)(-4) + 3

y = -2 + 3

y = 1

Finally, substitute the value of y and z to equation 4 and solve for x.

x = 2y - z - 4     (equation 4)

x = 2(1) - (-4) - 4

x = 2 + 4 -4

x = 2

Hence, the solution of the given system of equations is (x , y , z) = (2 , 1 , -4).

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The exponential function is y=2000(4/5)ˣ. 0.8 is the decay factor and 0.2 is the decay rate.

Given that,

The exponential function is y=2000(4/5)ˣ.

Parts of exponential function.

The general equation for an exponential growth function is :

y=a(b)ˣ

a is the initial value.

1. If b>1, growth. Then b is growth factor. r is the growth rate is b=1+r.

2. If 0<b<1, decay. Then b is decay factor. r is the decay rate is b=1-r.

Now, from the given y=2000(4/5)ˣ.

2000 is the initial value.

4/5=0.8 which is 0<0.8<1

So, 0.8 is the decay factor.

Decay rate r is

b=1-r

r=1-b

r=1-0.8

r=0.2

Therefore, 0.8 is the decay factor and 0.2 is the decay rate.

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Answer: It is irrelevant if multiplying or dividing decimal numbers. For addition and subtraction it is not sufficient: you need to line up the decimal points as well as the digits according to their place values. If you intend to simply align the decimal points then you may as well not bother.

Step-by-step explanation:

x = 29 is the value of x.

To find the value of x:

So,

Now, rounding to the nearest tenths gives x = 29.

Therefore, x = 29 is the value of x.

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According to the arithmetic progression, explicit formula for this sequence can.be depicted by:

aⁿ =  a + ( n -1 ) d.

This sequence is in arithmetic progression, and an explicit formula for this sequence is

aⁿ =  a + ( n -1 ) d

where n is the number of terms,  d = the difference between two-term, and a is the first term of this sequence.

For example, We have to determine the 8th term of this sequence, so n = 8, and the difference between two correspondent numbers, ( 7 - 4 = 3 )

a⁸ = 1 + ( 8 - 1 ) 3 = 1 + 21 = 22.

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Answer:

No solution is what I got if you solve for x

Step-by-step explanation:

Hope this helps!!

The number of batches of muffins and bread to be made in order to maximize the profits is 16 and 2.

Considering the x to be the number of batches of bread and y be the number of batches of muffins.

In the problem, it is mentioned that the preparation of both the bread and muffin takes 4 hours and 0.5 hours since the maximum preparation time is 16 altogether

The inequality equation for it will be  [tex]4x+0.5y\leq 16[/tex]

For baking the bread and  muffin it takes 1 hour and 0.5 hours, the maximum baking  time all together is  10

The inequality equation for it will be  [tex]x+0.5y\leq 10[/tex]

The profit  got from one batch of bread if  35 $ and from one batch of muffins is 10$

 f(x,y)= 35x+ 10y

for f(0,0)= 0, f(0,20)= 200, f(2,16)= 230 , f(4,0) =140

So it requires 2 batches of bread and  16 batches of muffins.

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A bakery is making whole-wheat bread and apple bran muffins. For each batch of break they make $35 profit. For each batch of muffins, they make $10 profit. The break takes 4 hours to prepare and 1 hour to back. The muffins take 0.5 hours to prepare and 0.5 hours to bake. The maximum preparation time available is 16 hours. The maximum bake time available is 10 hours. Let x = # of the batches of bread and y = # of batches of muffins. What constraints can be used to find the number of batches of bread and muffins that should be made to maximize profits?

The sum of the annual salary and the annual contribution toward health insurance from the employer is $36,420.

Given,

Imagine that an employer purchases a health insurance plan that costs $365 per month, but requires that the employee pay $35 per month toward the cost of the plan.

The employee's salary is $36,000 per year.

We need to find what is the sum of the annual salary and the annual contribution toward health insurance from the employer.

We divide the total value by the number of items.

Example:

$120 = 5 items

1 items = 120 / 5 = $24

We have,

Health insurance plan costs = $365

Employee pay = $35 per month.

The employee's salary = $36,000 per year.

The sum of the annual salary and the annual contribution toward health insurance from the employer;

=  $36,000 + $35 x 12 months

= $36,000 + $420

= $36,420

Thus the sum of the annual salary and the annual contribution toward health insurance from the employer is $36,420.

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Using an inequality, Plan 1 is more economical than Plan 2 given that the number of monthly phone calls is greater than 200.

If Plan 1 charges 31$ per month for unlimited calls, then the total cost per month of using Plan 1 is also 31$.

Plan 1 = 31$

If Plan 2 charges 13$ per month plus 0.09$ per call, we can express the total cost per month of using Plan 2 as:

Plan 2 = 13 + 0.09x

where x is the number of monthly phone calls

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

If Plan 1 is more economical than Plan 2 then the monthly cost of Plan 1 is less than the monthly cost of Plan 2.

Plan 1 < Plan 2

31 < 13 + 0.09x

Solving for x.

31 - 13 < 13 + 0.09x - 13

18 < 0.09x

200 < x

x > 200

the number of monthly phone calls > 200

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The triangles are congruent by SSS.

What exactly do you mean by congruent?

Given:

First Label the Diagram:

AB ≅ CD

AD ≅ BC

To Prove:

Δ ABC ≅ Δ CDA

Proof:

In  Δ ABC and Δ CDA

AB ≅ CD     ....……….{Given}

BC ≅ DA     …………..{Given}

AC ≅ AC     ……….{Reflexive Property}

Δ ABC ≅ Δ CDA  ….{ By Side-Side-Side test}

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The number of students that did major in the north is 300 and the number of student that do major in the south is 700.

At the north campus of a performing arts school, 30% of the students are music majors.

At the south campus, 80% of the students are music majors.

let

x = number of student at the north campus before the merger

Therefore,

1000 - x = number of students at the south campus before the merger

Hence, the equation for the music majors in the merger is as follows:

0.3x + 0.8(1000 - x) = 0.65(1000)

0.3x + 800 - 0.8x = 650

-0.5x = 650 - 800

-0.5x = -150

divide both sides by -0.5

x = -150 / -0.5

x = 300

Therefore, the number of students that did major in the north is 300 and the number of student that do major in the south is 700.

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Answer:

1 dollar and 6 cents

Step-by-step explanation:

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as

D = b² - 4ac

The type of roots will be given below.

The equation is given below.

x² + 4x + 5 = 0

The discriminant of the given equation will be

D = 4² - 4 x 1 x 5

D = 16 - 20

D = - 4

D < 0

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

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According to the question, to calculate the probability of the event which states that to draw a card from the standard deck but the condition is getting either ace or heart.

The total number of the playing cards are [tex]52[/tex]

And total number of heart cards are [tex]13[/tex]

And total number of ace cards are [tex]4[/tex]

Therefore, the total number of favorable outcomes in which either heart or ace can be drawn: [tex]4+13[/tex]

As per question, the probability can be written as:

P(h or a) = P(a) + P(h) - P( a and h)

[tex]= \frac{4}{52} +\frac{13}{52} -\frac{1}{52} = \frac{16}{52} = \frac{4}{13} = 30.8%[/tex]

Hence, the probability of getting either an ace or heart card is [tex]\frac{4}{13}[/tex].

The given event is not mutually exclusive because it has [tex]30.8[/tex] percent which is not close to tenth of a percent.

What are mutually exclusive events?

Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.

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Using elimination method, the solution of the given system of equations is (-3, -23/4)

A system of equations can be solved using:

The given system of equations is:

5c - 4t = 8   ...... (1)

14 + 4t = 3c  ...... (2)

Re-arrange equation (2) to

-3c + 4t = -14  ........ (3)

To eliminate variable t, add equation (1) to equation (3):

5c  - 4t = 8

-3c + 4t = -14 +

2c         = -6

 c         = -3

Substitute c = -3 into equation (1)

5c  - 4t = 8

5 . (-3) - 4t = 8

-15 - 4t = 8

Add 15 to both sides:

-4t = 23

   t = -23/4

Hence, the solution is (-3, -23/4)

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When there qre 240scoops and that there are 12 gumdrops per scoop, the number of gumdrop is 20 per scoop.

From the information, it was stated that there are 240scoops and that there are 12 gumdrops per scoop.

Therefore, the number in each scoop will be

= Total scoops /Number of gumdrop

= 240 / 13

= 20

Therefore, there are 20 gumdrops.

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There are 240scoops. If there are 12 gumdrops per scoop how much is each scoop

Answer:57

Step-by-step explanation:180-123 I hope i have helped u have a wonderful day or night!

Answer:

So C

Step-by-step explanation:

Average = all values added up/ how many numbers there are

(400.5+560.35+628.29)/3=Average

Average = 529.71

Mr. Wong paid 63.75 for the car rental.

The cost of rental car will be added one time to the total rent. The cost of trip will be calculated based on the distance covered.

So, forming the equation -

Total cost = 30 + 45 × 0.75

Performing multiplication on Right Hand Side of the equation to find the cost of business trip based on miles distance traveled

Total cost = 30 + 33.75

Performing addition on Right Hand Side of the equation to find the total cost based on one time rent of car and distance traveled

Total cost = 63.75

Hence, the total cost of car rental on business trip is 63.75.

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We can conclude that ΔMSP ≅ ΔRQP under SAS conditions.

So,

Given: MS ≅ RQ, MS || RQ

To Prove: ΔMSP ≅ ΔRQP

ΔMSP ≅ ΔRQP is proved.

Therefore, ΔMSP ≅ ΔRQP under SAS condition.

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The equation of the circle with radius 4.5 and center at (2 , 3) is (x - 2)^2 + (y - 3)^2 = 20.25.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (2 , 3)

r = 4.5

(x - 2)^2 + (y - 3)^2 = 4.5^2

(x - 2)^2 + (y - 3)^2 = 20.25

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The two-column proof are:

The angle WXV is congruent to angle YXZ

Triangle WXV congruent triangle YXZ

In this question, we are given;

X as the midpoint of line segment WY and line segment VZ

Therefore, it is correct for us to conclude that;

segment XZ is congruent to segment XV, segment XW is congruent to segment XY

Thus, angle WXV is congruent to angle YXZ

Triangle WXV congruent triangle YXZ

We then conclude that;

VW = ZY

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By elimination, the system of equations, 4x - 6y = -26 and -2x + 3y = 13, has infinite solutions.

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

First, simplify the first equation by dividing it by -2.

4x - 6y = -26 ⇒ -2x + 3y = 13     (equation 1)

-2x + 3y = 13     (equation 2)

Since the simplified equation of the first equation is the same as the second equation, then the two lines are exactly the same or overlapping.

Hence, the system of equations has infinite solutions.

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