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Fill in the blanks to solve the system of equations. Enter only 1 term in each blank.

The dimensions of the vegetable patch with the largest area we can enclose are

length = 12 feet and breadth = 6 feet.

Given, a rectangular vegetable patch.

The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot.

We have a budget of $96 for the project.

Let the length of the rectangle be, l

and breadth of the rectangle be, b

according to the ques,

4l + 8b = 96

l + 2b = 24

l = 24 - 2b

Now, area of the rectangle be,

Area = length×breadth

Area = l×b

A = (24 - 2b)b

A = 24b - 2b²

On differentiating both sides, we get

A' = 24 - 4b

b = 6

l = 24 - 12 = 12

So, the dimensions of the vegetable patch with the largest area we can enclose are

length = 12 feet and breadth = 6 feet.

Hence, The dimensions of the vegetable patch with the largest area we can enclose are

length = 12 feet and breadth = 6 feet.

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Answer:

They took 3 vans and 3 buses.

Step-by-step explanation:

Given:

To find:

The number of vans and the number of buses they took.

Explanation:

Let the number of vans = v

Let the number of buses = b

The total number of vans and buses is 6:

[tex]v+b=6[/tex]

⇒[tex]v=6-b....[/tex]Equation(1)

Each van holds 6 students and each bus hold 50 students.

The number of students on the trip is 168.

[tex]6v+50b=168[/tex]....Equation(2)

Substitute equation (1) into equation (2):

[tex]6v+50b=168[/tex]

[tex]6(6-b)+50b=168[/tex]

Then solve the equation for b:

[tex]36-6b+50b=168[/tex]

[tex]44b=168-36[/tex]

[tex]44b=132[/tex]

[tex]\frac{44b}{44}=\frac{132}{44}[/tex]

[tex]b=3[/tex]

Then, solve for v:

[tex]v=6-b=6-3=3[/tex]

Answer:

They took 3 vans and 3 buses.

Answer:

Slope: 1

__________

y-intercept: (0,0)

Step-by-step explanation:

Answer: At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident.

Step-by-step explanation:

{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Linear function is a function whose graph is a straight line

Slope of a line tells us how steep the line is . Slope of a line is same at all the points.

For option A:

m=1+2/3-1=3/2

m=3/2

m=7-4/8-5=3/3=1

Slopes are not same

For option B:

m=3-6/-3+6=-3/3=-1

m=0-3/0+3=-1

m=-4/3

Slopes are not same

For option C:

m=6-8/-1+2=-2

m=4-6/1=-2

m=-3/2

Slopes are not same

For option D:

m=3-6/-4+8=-3/4

m=-3/4

m=-3/4

Slopes are same at every point, so this set of ordered pairs could represent a  linear function

Hence, {(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function

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Answer:

6

Explanation:

x = 3 /cos(60) = 6

Answer: (2,0)

Step-by-step explanation:

The total number of pizzas were made in 4 hour in pizza shop is 24.

For the stated question-

For one pizza-

Ounce of cheese required = 5.

Ounces of sauce required = 3.

Total requirement = 8 ounces.

After 4 hours,

Total ounces combined of sauce and cheese used = 192.

Thus,

Number of pizza = 192 / 8

Number of pizza = 24

Thus, the total number of pizzas were made in 4 hour in pizza shop is 24.

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Answer:

56

Step-by-step explanation:

The angle of elevation of the sun is [tex]tan^{-1}[/tex](106/ 135).

The angle of elevation:

The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.

Here we have to find the angle of elevation of the sun.

Data given:

length of the tower = 106 feet

shadow form by the tower = 135 feet

The formula for the angle of elevation = height/base

tanФ = height/base

        = 106/ 135

Ф = [tex]tan^{-1}[/tex](106/135)

Therefore the angle of elevation is [tex]tan^{-1}[/tex]( 106/ 135).

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The expression in terms of x that represents the total amount that Zoe paid is 1.2075x.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.

The expression will be:

= x + (5% × x) + (15% × 1.05x)

= x + 0.05x + 0.1575x

= 1.2075x

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a) Probability model

P(40) = 1/6

P(0) = 5/36

P(-10) = 25/36

b)  E(X) = -5/18

standard deviation  = 18.331

c) standard deviation  = 91.65

d) Probability = 0.560

From the question, we have

a) X = -10, 0 or 40 for your winnings (or losses). The corresponding probabilities are:

P(40) = 1/6

P(0) = (5/6)(1/6) = 5/36

P(-10) = 1 - 1/6 - 5/36 = 25/36

b) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18

E(X^2) = (100)(25/36) + 1600(1/6) = 3025 / 9

Var(X) = E(X^2) - [E(X)]^2 = 3025 / 9 - (-5/18)^2 = 108875 / 324

standard deviation = sqrt [Var X] = 119043 / 6494 =18.331

c) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18

5 * E(X)  =  - 25/18

standard deviation = 5 * 18.331 = 91.65

d) Probability :

P(X < 0) = P{ z < [0 - (-5/18)] / [(119043 / 6494) / sqrt 100] } = P(z < 0.1515) = 0.560

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

Complete question:

From the Data at Hand to the World at Large 4. New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What's the probability the person running the game makes a profit?

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The given statement that a trinomial is always a higher degree than a monomial is false because greater number of terms does not means higher degree.

A monomial is an algebraic expression with only one term. Or we can say that the representation of a single concept is a monomial.

An example of an unary expression is: 12

A trinomial is an algebraic expression containing three terms. An example of a ternary is: x + y + 7

A trinomial is always of higher degree than a monomial is false statement .

A counterexample can be used to explain why this is wrong. Suppose we have a monomial, 8⁵ and then a trinomial x² + 2x + 3 . This is just a random example. This monomial has a higher degree because 5 is greater than 2. So basically it doesn't matter what the monomial is, if the degree is higher it is just a term than the maximum degree of the trinomial. Just because this has three terms does not mean that the highest degree term is greater than his one term in the monomial.

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Answer:

[tex]\huge\boxed{\sf v = 81}[/tex]

Step-by-step explanation:

Let Vidya's age be v.

v - 15 = 66

Add 15 to both sides

v = 66 + 15

[tex]\rule[225]{225}{2}[/tex]

a) Considering the scale factor, the height that she should build the model is of: 22.1 inches.

b) Essence has enough information to build the accurate scale model, as she needs only the scale and either the actual or the drawn model.

An scale is defined as the relation between the actual length of a segment and the length of drawn segment, as follows:

Scale = Actual length/drawn length

The scale for this problem is given as follows:

Scale factor = 300 ft/1 in.

Which means that each inch on the drawing represents an actual height of 300 ft.

The height of the Clingman Dome is given as follows:

6,643 feet.

Considering the scale factor of 300 ft/1 in, the height of the drawing is obtained as follows:

6643/300 = 22.1 inches.

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Answer:

x = - 25

Step-by-step explanation:

the absolute value function always gives a positive value , however , the expression inside the bars can be positive or negative, that is

| - a | = | a | =a

given

| x + 10 | = 15 , then

x + 10 = 15 ( subtract 10 from both sides )

x = 5

OR

-(x + 10) = 15

- x - 10 = 15 ( add 10 to both sides )

- x = 25 ( multiply both sides by - 1 )

x = - 25

solutions are x = 5 , x = - 25

Answer: -25

Step-by-step explanation:

The time taken for Bob take to run one lap of the track is 69 seconds

Akira is running around a circular track. Akira runs counterclockwise.

It takes him 95 seconds to run one complete lap

Bob starts running at the same time as Akira

Bob and Akira pass each other for the first time after 26 seconds

It takes him 95 seconds to run one complete lap

In 26 seconds he covers 26/95 laps

In this time Bob must have covered 69/95 laps

An inverse relationship

c/95 = 69/95

c = (69/95) x 95

c = 69

Therefore, time taken for Bob take to run one lap of the track is 69 seconds.

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The value of x in the given function, f(x) = 3/2x - 4 when f(x) = 5, is x = 6

From the question, we are to determine the value of x in the given function for the given value of f(x).

The given function is

f(x) = 3/2x - 4

and

f(x) = 5

Now, to determine the value of x, put f(x) = 5 in the given function

f(x) = 3/2x - 4

5 = 3/2x - 4

Add 4 to both sides of the equation

5 + 4 = 3/2x - 4 + 4

9 = 3/2x

Multiply both sides by 2

2 × 9 = 2 × 3/2x

18 = 3x

Divide both sides by 3

18/3 = 3x/3

6 = x

Therefore,

x = 6

Hence, the value of x is 6

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At 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.

What is the quadratic equation?

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 45 ft, the distance from the anchor point to the right pole is 45 - x

The wire length from the top of the left pole to the anchor point is

[tex]L^{2} _l = 30^{2} + x^{2}[/tex]

= x² + 900

Similarly for the 2nd part of the wire

[tex]L^{2} _r = 15^{2} + (45-x)^{2}[/tex]

= 256 + 2025 - 45x + x²

= x² + 2281 - 45x

We want to minimize the length of the wires, or [tex]L_l + L_r[/tex]

√x² + 900 + √ x² + 2281 - 45x

we can take the first derivative of this and set it to 0

[tex]\frac{x}{\sqrt{ x^2 + 900} } + \frac{45 - x}{\sqrt{x^2 + 2281 - 45x} } = 0[/tex]

x = 30

Hence, at 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.

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Six candies would cost $1.44.

Answer:

$1.44

Step-by-step explanation:

We need to figure out how much one piece of candy costs. So you do .96/4, which is going to equal 0.24.

1 piece of candy = $0.24

So we do 0.24*6= 1.44

I hope this helps!!!

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Answer: x=4

Step-by-step explanation:

6x + 10 = 5x + 14

x + 10 = 14

x = 4

The amount of sales Terry must make is $1667

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

Commission = 18% of sales

Commission = $300

These parameters mean that

Commission = 18% of sales

Substitute the known values in the above equation, so, we have the following representation

18% of sales = 300

Divide both sides by 18%

Sales = 1667

Hence, the amount is $1667

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Answer:

Below

Step-by-step explanation:

Total pages read = 40 + 60 +43  = 143 pages read

  Total pages of all of the books  = 70 + 85 + x  

       percentage READ =   (143) / ( 70 + 85 + x)  * 100% =  ???  

            percentage NOT read = 100 - ???

              (since 'x' was not given in the question post)

Read pages:

40+60+43=143

All pages:

70+85+43=198

198-143=55

55/198=0,2778

0,2778×100%=27.78%

The average rate of change of the function f(x)=2(3)x from x = 2 to x = 4   =  72

The term "function" refers to the relationship between a collection of inputs and outputs with one each. Simply described, a function is an association of inputs where each input is coupled with exactly one output. Every function has an associated domain, codomain, or range. The most common way to represent a function is as f(x), where x represents the input.

To calculate the average rate of change, use the slope formula:

y2−y1/x2−x1=m

f(4)−f(2)/4−2=m

Finding the values of f(4) and f(2) will help us to simplify this.

f(4)=2(3)4=2(81)=162

f(2)=2(3)2=2(9)=18

m=162−18/2

m=144/2

m=72

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Answer:

You could divide 5 in half and then add that to the five to find the amount of flour to use in a triple recipe. Hope this helps.

Step-by-step explanation:

Answer and explanation in one:

(4+9)/(-2-1) = 13/-3 = -13/3

y=-13x/3 + b

4=26/3 + b

b = 4-26/3 = (12-26)/3 = -14/3

y=-13x/3 -14/3 is the line through the two given points

find the line perpendicular and through (14,-6)

y=3x/13 + b, plug in the point to find b

-6 = 3(14)/13 + b

b = -6 -42/13 = -78/13 - 42/13 = -120/3

y= 3x/13 - 120/13

find the intersection point of the two lines, set them equal

3x/13 -120/13 = -13x/3 - 14/3

multiply by 39

9x - 360 = -169x - 182

178x = 360-182 = 178

x = 1

y= -27/3=-9

the point is (1,-9)

calculate the distance from (1,-9) to (14,-6)

d^2 = 9+169 = 178

d = sqr178 = about 13.34

29.78% of customers will most likely probability be waiting between 4 and 9 minutes.

The formula for the z score is-

z = (x - μ)/σ

In which,

μ =  mean of 10. 3 minutes

σ = standard deviation of 2. 7 minutes.

z score for the x = 4 minutes.

z = (4 - 10.3)/2.7

z = -2.33

z score for the x = 9 minutes.

z = (9 - 10.3)/2.7

z = -0.48

Thus,

Probability that the customer will have to wait between 4 and 9 minutes.

P(4 < x < 9) = P(-0.48 < z <  -2.33)

Use z score table-

P(4 < x < 9) =  0.3085 - 0.0107

P(4 < x < 9) = 0.2978

P(4 < x < 9) = 29.78%

Thus, 29.78% of customers will most likely be waiting between 4 and 9 minutes.

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Using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Compound interest works by periodically adding collected interest to your main, which is the sum you first deposited into the savings account so that interest can then be earned on both.

In essence, your interest begins to generate interest of its own.

Compound interest formula: [tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]

Now, calculate the amount Danni will have after 4 years:

[tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]

A = 5700(1+0.021)⁴

A = 5700(1.0210⁴

A = $6,194.09

Therefore, using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.

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Answer:

A=6199.48

Step-by-step explanation:

Use the formula for calculating compound interest A=P0ert where A is the unknown, P0=5700, r=0.021, and t=4. Substitute the values into the formula and simplify.

A=5700e0.021⋅4

A=5700e0.084

A=5700(1.0876...)

A=6199.48

The amount in the account after four years is A≈6199, to the nearest dollar.