A city administrator with a $100,000 annual budget is trying to decide between fixing potholes or directing traffic at several busy intersections after school. Studies have shown that 15 cars hit potholes every week, causing average damages of $200. Collisions at the intersections are less frequent, averaging one per month at an average cost of $6,000, although none have ever caused injuries or deaths. Use this information to answer the following questions.

1. What are the annual costs from the pothole damage?

2. What are the annual costs due to damage from
collisions?

3. Given the size of the annual budget, make your
recommendation as to which project should be
undertaken. Explain you answer in terms of dollar
benefits per dollar spent.

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 bottle of grapefruit juice at store A is $6.63 less than the store B.

According to the question,

We have the following information:

The equation y = 1.75x represents what Lamonte would pay in dollars and cents, y, for a bottles of grapefruit juice at store A.

Cost of 17 bottles of grapefruit juice at store B = $36.38

Now, we will find the cost of 17 bottles at store A.

y = 1.75*17

y = $29.75

Now, the difference in their price = 36.38-29.75

Difference = $6.63

Hence, the bottle of grapefruit juice at store A is $6.63 less than the store B.

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Answer: 0.39

Step-by-step explanation:

Store A

y= 1.75x

A bottle of grapefruit juice costs 1.75 at store A

Store B

36.38$/17 bottles = 2.14$ per bottle

A bottle of grapefruit juice costs 2.14$ at store B

Store B - Store A= 2.14$ - 1.75$

=0.39

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:

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:

Step-by-step explanation:

percentage increase = (final - initial)/initial

increase = (672 - 480)/480

               = 192/480

               = 0.4 * 100 = 40% increase

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

Answer:

Page 1 of 3

1. twenty  

2. 16,49  

3. option3  

4.32  

5. 40 tickets     show your work--10= 1.00 40=4.00

Page 2 of 3

7, 14, 21, 28, 35, 42, 49, 56, 63

Page 3 of 3 (left to right)

56, 0, 21, 63, 42, 35, 14, 28, 7, 77, 84, 56, 14, 49, 63, 28, 70, 42, 21, 35, 84, 7, 77, 0, 70

Step-by-step explanation:

learn your times tables

it will help you in high school and college

Answer:

Step-by-step explanation:

1. Convert words to math

3/4/1/8=

3/4*8/1=

24/4=

6

3. Answer: 6

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

Check step-by-step explanation.

In order to form the table, we must take several values of x (any values you want to evaluate) and find it's correspondent y value. This is how you  do it:

[tex]y=3x+12[/tex]

[tex]x=0, \\y=3(0)+12\\y=12[/tex]

As you may notice, we are just substituting the x value for the x variable into the equation and calculating y. Do this with several values and form a table (check attached image 1).

[tex]x=1, \\y=3(1)+12\\y=15[/tex]

[tex]x=2, \\y=3(2)+12\\y=18[/tex]

Using the calculated points, draw them in the cartesian plane. Remember that "x" means how many spaces you move horizontally, and "y" means vertical spaces.

Check attached image 2.

Let's take point (2, 18) as an example. This point is generated when you substitute the x value of 2, meaning 2 hotdogs and the souvenir hat. Then, the functions gives a result of 18, which would be the cost of those 2 hotdogs in addition to the souvenir hat. Point (0, 12), on the other hand, means that you didn't buy any hotdogs but you still have to pay $12 for the souvenir hat.

Answer: (3x^2)(y^3√y)

Step-by-step explanation:

1. To simplify the radical

> break the radicand (the number under the radical sign) into a product (the result of two numbers being multiplied together) of known factors.

2. Assume all numbers are real.

The speed of the humming bird when converted to miles per minute is; 0.67 miles per minute

In scientific problems, sometimes, it is necessary to change units from one to another as specifically needed.

The procedure for unit conversion is;

1. Identify the unit you have.

2. Identify the unit you desire or require.

3. Identify appropriate unit conversion factor(s).

4. Cancel units and carry out the math calculations.

5. Evaluate the result.

We are given the speed as 40 miles per hour. Now, the unit of conversion factor from mph to miles per minute is;

1 mile per hour = 1/60 miles per minute

Thus;

40 miles per hour = 40 * 1/60 = 0.67 miles per minute

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Answer: Down there,

Step-by-step explanation:

Row 1 = 29

Row 2 = 5

Row 3 = -1

Row 4 = -7

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:.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: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: 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:

  (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:

s = 14m + 458

Step-by-step explanation:

current amount = 458

14 per month

s = 14m + 458

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

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 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:

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.

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 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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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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a perfect square trinomial, namely   [tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2[/tex]

where the middle-term is just a product of "2 times the square root of the terms on both sides".

so let's start by grouping the terms with a variable, and then adding the last term for the trinomial, keeping in mind the middle-term is just that product.

[tex]x^2+6x+5\implies (x^2+6x) ~~ +5\implies (x^2+6x+\square^2) ~~ +5 \\\\\\ \stackrel{middle-term}{6x}=2(\sqrt{x^2})(\sqrt{\square^2})\implies 6x=2x\square\implies \cfrac{6x}{2x}=\square\implies 3=\square[/tex]

ahhhaaa!!! so our missing term from our group is 3, meaning we need to use 3², however, let's remember, all we're doing is borrowing from our very  good friend Mr Zero, 0, so if we add 3², we also have to also subtract 3²

[tex](x^2+6x+3^2-3^2) ~~ +5\implies (x^2+6x+3^2)-3^2 +5\implies {\Large \begin{array}{llll} (x+3)^2-4 \end{array}}[/tex]