A camp counselor and four campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the fourth and a camper who has a tendency to engage in food fights must sit to the​ counselor's immediate ​?

Objective function is a maximum at (3,2),     Z = 3x+y = 3(3) + 1(2) = 9 + 2 = 11

Given,

Maximize: z = 3x +y

Subject to:

x-y≤9

3x + 5y ≤45

x≥0, y≥0​

For the purpose of representing and resolving the linear programming optimization issues, objective functions are frequently used. The choice variables x and y are used in the objective function, which has the form Z = axe + by. The best answer can be obtained by maximizing or minimizing the function Z = ax + by

Plot the constraints and the objective function Z, or z = 3x +y

Push the objective function to the limit permitted by the feasible region to find the maximum.

Objective function is a maximum at (3,2),

Z = 3x+y = 3(3) + 1(2) = 9 + 2 = 11

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Answer:

Step-by-step explanation:

a)  x2 to x4   and  x6 to x7

b)  x1 to x2  ,  x3 to x5   ,  x6 to x7

c)  x2, x3, x5, x6, x7

d)  x2.5  , x4 , x5.5 ,  x6.5

Check the picture below, so the ellipse looks more or less like so

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-4\\ k=10\\ a=8 \end{cases}\implies \cfrac{(x- (-4))^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1\implies \cfrac{(x+4)^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1 \\\\\\ \stackrel{\textit{we know that c = 6}}{6=\sqrt{8^2 - b^2}}\implies 6^2=8^2-b^2\implies b^2=8^2-6^2\implies \underline{b^2=28} \\\\\\ \cfrac{(x+4)^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1\implies {\Large \begin{array}{llll} \cfrac{(x+4)^2}{ 64}+\cfrac{(y- 10)^2}{ 28}=1 \end{array}}[/tex]

Answer:

Step-by-step explanation:

percentage increase = (final - initial)/initial

increase = (672 - 480)/480

               = 192/480

               = 0.4 * 100 = 40% increase

Answer:

Step-by-step explanation:

1. Convert words to math

3/4/1/8=

3/4*8/1=

24/4=

6

3. Answer: 6

The missing statements/ reasons are:

     Statement                                         Reason

LN bisects ∠MLO                                    Given

LM ≅ LO                                                  Given

∠MLN ≅ ∠NLO                                  Def of angle bisector

LN ≅ LN                                                 Common side

ΔLMN ≅ ΔLON                         SAS postulate of triangle congruence

In this question, we have been given some information about triangles LMN and LON.

We need to prove ΔLMN ≅ ΔLON

LN bisects ∠MLO                    ....................(Given)

LM ≅ LO                                   ...................(Given)

∠MLN ≅ ∠NLO                         ...................(Def of angle bisector)

LN ≅ LN                                    ....................(Common side)

ΔLMN ≅ ΔLON                         ...................(SAS congruence postulate)

Therefore, the missing statements/ reasons are:

     Statement                                         Reason

LN bisects ∠MLO                                    Given

LM ≅ LO                                                  Given

∠MLN ≅ ∠NLO                                  Def of angle bisector

LN ≅ LN                                                 Common side

ΔLMN ≅ ΔLON                         SAS postulate of triangle congruence

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Answer:you have 2 lines that cross.

the left angle formed is equal to 3x + 8

the right angle formed is equal to 5x - 20.

the bottom angle formed is equal to 5x + 4y

since the lines are crossed, the opposite angles to each other are equal.

this means that:

3x + 8 = 5x - 20

solve for x to get x = 14 degrees.

the angle on the left side will be equal to 3(14) + 8 = 50 degrees.

the angle on the right side will be equal to 5(14) - 20 = 50 degrees.

this is at it should be since the angles are equal to each other.

since the sum of the 4 angles formed is equal to 360 degrees, the sum of the remaining 2 angles is equal to 260 degrees.

since those 2 angles are equal, then each one must be equal to 130 degrees.

one of those angles is equal to 5x + 4y.

you get 5x + 4y = 130

since x was already found to be 14, replace x with 14 to get:

5(14) + 4y = 130

solve for y to get y = (130 - 5(14)) / 4 which is equal to 15 degrees.

when x = 14 and y = 15, 5x + 4y = 5(14) + 4(15) = 70 + 60 = 130 which confirms the value of 15 for y is good.

your answers are:

x = 14 degrees

y = 15 degrees

2 of the angles measure 50 degrees each.

2 of the angles measure 130 degrees each.

Answer: Down there,

Step-by-step explanation:

Row 1 = 29

Row 2 = 5

Row 3 = -1

Row 4 = -7

The domain of the polynomic function f(x)=−2 · x · (x − 3) · (x − 6) is (- ∞, + ∞).

In this problem we find a polynomic function in factor form, whose definition is presented below:

f(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., n - 1, n}

Where:

The grade of the polynomial is equal to the number of roots. The statement shows a polynomial of grade 3 and, according to function theory, the domain of polynomic functions is the set of all real numbers, whose interval notation is (- ∞, + ∞).

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Answer: only 1

Step-by-step explanation:

Answer: One-fifth.

Step-by-step explanation:

2/5 is two-fifths, 3/5 is three-fifths, and so on.

1/10 is one-tenth, 2/10 is two-tenths, and so on.

Answer:

36mins

Step-by-step explanation:

So, the time of travel to cover 5 1/5 miles at a speed of 8 2/3 mph is 36 minutes.

Answer:

El otro extremo dista :

12.5 decímetros

Step-by-step explanation:

1 dm = 1 decímetro = 10 cm

1 m = 1 metros = 10 decímetros = 10 dm

3.5 metros = 3.5 * 10 = 35 decímetros

125 cm = 125/10 = 12.5 decímetros

Entonces:

35 dm - 12.5 dm = 22.5 dm

Answer:

Think its B.

Step-by-step explanation:

Answer:

[tex]4cd(6-9c)[/tex]

Step-by-step explanation:

Factor out what all terms have in common

9 feet is the same as = 2.74 m

Given

1 ft≈ 0.305 m

To find out 9 feet is the same as how many meters:

To convert a foot measurement to a meter measurement, multiply the length by the conversion ratio.

Since one foot is equal to 0.3048 meters, you can use this simple formula to convert:

meters = feet × 0.3048

= 9 * 0.3048

= 2.7432 m

The length in meters is equal to the feet multiplied by 0.3048.

Hence the answer is the 9 feet is the same as meters = 2.74m.

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The value of v is -12.5 when u = 15, t = 8, and s = 40.

According to the question,

We have the following expression:

s = (u+v)[tex]t^{2}[/tex]

We have the following values:

u = 15, t = 8, s = 40

Now, we can easily find the value of v by putting all these values in the given expression.

So, we have the following expression:

40 = (15+v)8*8

40 = (15+v)16

Multiplying 16 into the bracket:

40 = 15*16+16v

40 = 240+16v

Subtracting 240 from both sides:

40-240 = 16v

-200 = 16v

Dividing by 16 on both sides:

-200/16 = v

v = -12.5

Hence, the value of v is -12.5 when u = 15, t = 8, and s = 40.

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The equation of the function is: y = 11.5x.

The slope = 11.5 garbage bag per hour.

Y-intercept = 0 bag at 0 hour.

The domain: number of hours

Range of the function: number of garbage bags filled.

138 bags will be filled in 12 hours.

The equation of a function can be written as y = mx + b in slope-intercept form. Here, we have:

Given the graph with the points that represents the number of garbage bags filled as a function of time as:

(6, 69); (5, 57.5); (4, 46); (2, 23); (1, 11.5); (3, 34.5)

Use two points, (6, 69) and (4, 46) to find the slope of the function:

Slope (m) = change in y / change in x = (69 - 46)/(6 - 4)

Slope (m) = 23/2

Slope (m) = 11.5

To find the y-intercept (b), substitute m = 11.5 and (x, y) = (6, 69) into y = mx + b:

69 = 11.5(6) + b

69 = 69 + b

69 - 69 = b

b = 0

To write the equation of the function, substitute m = 11.5 and b = 0 into y = mx + b:

y = 11.5x + 0

y = 11.5x

The slope, 11.5, means 11.5 garbage bags were filled per hour.

Y-intercept is zero, which means no bag was filled at 0 hour.

The domain is the set of the number of hours, while the range of the function is the set of number of garbage bags filled.

To find the number of garbage bags that volunteers fill in 12 hours, substitute x = 12 into y = 11.5x:

y = 11.5(12)

y = 138 bags.

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Answer:

a = 70 degrees

b = 20 degrees

c = 20 degrees

Step-by-step explanation:

First, we can find "c":

angleBCA = 90

angleBCA = angleBCD + c

90 = 70 + c

90 - 70 = c

20 = c

Knowing "c", we can find "a".

angleADC = 90

triangleADC = 180

triangleADC = angleADC + c + a

180 = 90 + 20 + a

180 = 110 + a

180 - 110 = a

70 = a

Knowing "a", we can find "b".

angle BCA = 90

triangleACB = 180

triangleACB = angleBCA + a + b

180 = 90 + 70 + b

180 = 160 + b

180 - 60 = b

20 = b

Answer:

y = 5x/6 + 3/2

Step-by-step explanation:

First, find the slope (m):

m=(y2-y1)/(x2-x1)

m=(9-4)/(9-3)

m=5/6

y=mx+b ==> slope-intercept form equation

y = 5x/6 + b==> substitute the value of the slope for m

9 = 5(9)/6 + b ==> substitute a point (x, y) or (9, 9) into the equation

9 = 45/6 + b ==> simplify

(9 = 45/6 + b)*6 ==> multiply the equation by 6 to remove denominators

54 = 45 + 6b ==> simplify

54 - 45 = 45 - 45 + 6b ==> solve for b

9 = 6b

9/6 = 6b/6

b = 3/2

y = 5x/6 + 3/2 ==> plug in b for the slop-intercept equation

The numbers that opposite 1/15 and 1/16 are -1/15 and -1/16

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

Numbers = 1/15 and 1/16

The opposite of numbers is the negative equivalent of the number

Take for instance, we have a number x

The opposite of x is -x

Using the above as a guide, we have the following representation

Numbers = 1/15 and 1/16

This means that, the opposite numbers can be represented as

Opposite numbers = -1/15 and -1/16

Hence, the opposite numbers are -1/15 and -1/16

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The new annual output from the turbine is 1122kw to give a percentage of 87

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Data;

This can be represented mathematically as

87 / 100 = y - 600/ 600

We can solve for y

0.87 = y - 600 / 600

x = 1122kw

The new annual output from the turbine is 1122kw

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The probability that an individual man’s step length is less than 2.2 feet is 0.10 or 10%

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = (X - mean)/S.D

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 2.8 feet and a standard deviation of 0.5 feet.

Find the probability that an individual man’s step length is less than 2.2 feet.

This is the p-value of Z when X = 2.2. So

Z = (2.2 - 2.8)/0.5

Z = 0.6/0.5 = 1.2

Z = 1.2

has a p-value of 0.10

Therefore, the probability that an individual man’s step length is less than 2.2 feet is 0.10 or 10%

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Answer:

  (c)  50 units²

Step-by-step explanation:

You want to know the area of the rectangle with vertices (-5, 5), (-1, 7), (4, -3), and (0, -5).

The distance formula can be used to find the lengths of the sides. That formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

The distance between the first two points is ...

  d = √((-1 -(-5))² +(7 -5)²) = √(4² +2²) = √20

The distance between the next two points is ...

  d = √((4 -(-1))² +(-3 -7)²) = √(5² +(-10)²) = √125

The area is the product of two adjacent side lengths:

  A = LW

  A = (√125)·(√20) = √(125·20) = √2500 = 50 . . . . square units

The area of the rectangle is 50 units².

Answer:.15

Step-by-step explanation:

390/27= 130/9

130/9=14.444...

divide by 100

.1444... is approxomatly .15 so there is your answer

Answer:

14 or 15

u can do 3.90 divied by 0.27

Step-by-step explanation:

Answer:

s = 14m + 458

Step-by-step explanation:

current amount = 458

14 per month

s = 14m + 458

The expression has 3 terms, that are

1st term n²

2nd term 2k³

3rd term 3m²

Given that,

The expression is n²+2k³+3m².

We have to find how many terms are in the expression.

A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these. A single term or a collection of phrases can be used to create an algebraic expression. For instance, 4x and y are the two terms in the formula 4x + y.

Take the expression,

n²+2k³+3m²

There are 3 terms

1st term n²

2nd term 2k³

3rd term 3m²

Therefore, The expression has 3 terms, that are

1st term n²

2nd term 2k³

3rd term 3m²

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Answer:

3x

Step-by-step explanation:

When the equation is like this and they both are being multiplied by x you can just add the coefficients

x+2x

1x+2x

3x

Hopes this helps please mark brainliest

Hello..!

[tex] \sf{x + 2x = 3x}[/tex]

It is known that in similar terms "x" is an unknown quantity and that in this problem "x" is 1 and that we only have to add it to 2:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf2 + 1 = 3[/tex]

So the result is 3x

The inequality has a solution set of  {-∞, 13} in order to make it equal

In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions. An inequality shows the relationship between two values in an algebraic expression that are not equal.

In the given question

8(n - 3) < 4(n + 7)

Expand the bracket

8n - 24 < 4n + 28

8n - 4n < 28 + 24

n < 13

The solution set to make the inequality equal is {-∞, 13}

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