the volume of a rectangle prism is 8cm height 4 width.​

Therefore the the length =21 and width =42 of the plot that will maximise the area is 882 [tex]ft^{2}[/tex] .

A region's size on a planar or curved surface can be expressed mathematically as its area. The term "surface area" refers to the area of a surface or the border of a three-dimensional object, whereas the term "plane area" refers to the area of a shape or planar lamina.

Here,

Here, take note that the shape is still a rectangle and the fencing is still 84 feet long.

As a result, the area is equal to xy and the sum of the sides NOT along the river is 84.

Thus, 2x + y = 84 and A = xy are the two equations.

We must find A as a function of x or y to determine the area with the largest value. My recommendation is to solve the first equation for y and substitute that value into the second equation.

A(x) = x and y = 84 - 2x (84-2x)

Currently, we must maximize A(x) = 84x - 2.

Recall that if we determine the vertex's x value by substituting, x = -b/(2a), we may find the vertex's y value.

Therefore, x = -84/(-4) = 21 ft because a = -2 and b = 84. If x = 21, y = 84 - 2(21) = 42

Thus, the dimensions are 21 by 42, and the maximum size is 21 by 42, or 882 square feet.

Therefore the the length =21 and width =42 of the plot that will maximise the area is 882 [tex]ft^{2}[/tex] .

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A fraction of the bicycles which are silver is 3/4.

You should shade three (3) sections on the pie chart to show the number of bicycles that are silver.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.

Based on the information provided, we can logically deduce the following parameters;

Number of silver bicycles = 3 silver bicycles.

Number of green bicycles = 1 green bicycles.

Therefore, the total number of bicycles is equal to 4 bicycles.

For the fraction of silver bicycles, we have;

Fraction = 3/4 bicycles.

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Answer:

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

One full circle is:

Three times the same distance:

Answer:

Distance travelled = 565.2 m

Step-by-step explanation:

Formula of circumference,

→ C = 2πr = π × d

The circumference of circle is,

→ π × d

→ (22/7) × 60

→ 1320/7

→ 188.4

Distance traveled after 3 rounds,

→ C × 3

→ 188.4 × 3

→ 565.2 m

Hence, Andi covered 565.2 m.

The number of belts produced must be positive: X1, X2, X3 >= 0

The shadow price of a constraint can be understand as the change in the objective function value for a unit change in the right-hand side (RHS) value of the constraint, with all other variables held constant.

A constraint is a condition of an optimization problem that should be satisfied the condition.

Here we can formulate this problem as a linear programming model (LPM):

Consider X1 be the number of belt A produced per day

Let X2 be the number of belt B produced per day

Let X3 be the number of belt C produced per day

The objective function is to maximize the profit, that is;

3X1 + 5X2 + 4X3.

The constraints are as follows:

The time spent on machine M1 must be less than or equal to 8 hours per day then;

2X1 + 3X2 <= 8

The time spent on machine M2 must be less than or equal to 10 hours per day then;

3X1 + 2X2 + 5X3 <= 10

The time spent on machine M3 must be less than or equal to 15 hours per day then we have

2X1 + 2X2 + 4X3 <= 15

Thus number of belts produced must be positive:

X1, X2, X3 >= 0

To solve this LPM using the simplex algorithm, you can follow these steps:

w In standard form, the objective function is to minimize the cost, and all constraints are in the form of "less than or equal to" a certain value.

The pivot row is the row that corresponds to the smallest positive ratio between the right-hand side (RHS) value and the corresponding pivot column element the constraint 2X1 + 3X2 ≤ 8.

Now Interpret the shadow prices.

The shadow price of a constraint can be understand as the change in the objective function value for a unit change in the right-hand side (RHS) value of the constraint, with all other variables held constant.

It can help to understand the value of the constraints in the LPM and how they contribute to the optimal solution.

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Answer:

48s + 48

Step-by-step explanation:

The store manager purchases 7 pens which can be determined by the concept of equations.

According to question store manager purchased a total of 15 pens and markers. So, let us assume the total number of pens =x and the total number of markers = y

The above statement gives us the equation as follows:

x + y=15

The statement each pen cost $3.50, and each marker cost $1.75 and the manager spent a total of $38.50 gives us the equation as follows:

3.50x +1.75 y=38.50

By solving both the equation on multiplying first eq by 3.50 gives

3.50x+3.50y=52.5

Subtracting the above two equations gives

1.75y=14

y=8

Putting value of y in first equation gives x=7

As we had assumed that the total number of pens = x

Hence, the total number of pens =7

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Answer:

Yes, it is proportional because it is a line that goes through (0, 0).

Step-by-step explanation:

Answer:

Yes, it is proportional because it is a line that goes through (0, 0).

Step-by-step explanation:

Answer: A. x^3 +x^2-8x+4 B. 10

Step-by-step explanation: (f•g)(x) is the same as f(x) • g(x)

A. (x^2+3x-2) • (x-2) = (x^3+3x^2-2x) -(2x^2+6x-4) -> x^3 +x^2-8x+4

B. plug in -3 for x -> (-3)^3 + (-3)^2 -8(-3) + 4 -> 10

Answer:89

Step-by-step explanation:math

Answer:89

Step-by-step explanation:7p+5

This means 7 *p+5

Where we see the p we put in 12

We get 7*12+5=89

(a) 4x + 6y ≥ 500 , (b) The graph of this inequality is a line with a slope of 4/6 and a y-intercept of 500/6.

(a) The inequality expresses the total hours of community service that must be given, which is at least 500 hours. The 4x term represents the hours given by the full members, and the 6y term represents the hours given by the pledges. The ≥ symbol means that the sum of these two terms must be greater than or equal to 500.

(b) To graph the inequality, you first need to find the y-intercept, which is 500/6. Then you need to find the slope, which is 4/6. This means that the line has a positive slope and passes through the point (0, 500/6). The graph of the inequality is a line that passes through this point and has a positive slope of 4/6.

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Answer:

282.6in^2

Step-by-step explanation:

Surface area of a cylinder = 2πrh+2πr^2

plugging in r=5 and h=4 gives

2π20+2π25

40π+50π = 90π

90*3.14=282.6in^2

10.9 years long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.

Given that,

We have to find how long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.

We know that,

P = $1000

r = 6.35% = 0.635

n=12

A = $2000

A = P(1+r/n[tex])^{nt}[/tex]

2000 = 1000(1+0.635/12[tex])^{12t}[/tex]

2= (1+0.635/12[tex])^{12t}[/tex]

log2= log(1+0.635/12[tex])^{12t}[/tex]

log2= 12t×log(1+0.635/12)

t=log2/12×log(1+0.635/12)

t≈10.9 years.

Therefore, 10.9 years long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.

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Answer:

The result is 0.074 ÷ 1000 = 0.00074, which means that 10□ = 1000, so the value of the missing exponent is 3.

Step-by-step explanation:

Step-by-step explanation:

since I don't see the options, I can only tell you what it is supposed to be and you need to pick the best fitting option :

the score of the test is simply

the number of correctly answered questions times 3 (as every correctly answered question is with 3 points).

the equation is therefore

y = R(x) = 3x

the independent variable x represents the number of correctly answered questions,

and the dependent variable is y, the test score, because the test score depends on the number of correctly answered questions.

so,

R(25) = 3×25 = 75, meaning 25 correctly answered questions × 3 results in the score of 75.

Step-by-step explanation:

To find the number of years it will take for Enola's investment to triple in value, we can use the formula for simple interest:

I = P * r * t

where I is the total interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the number of years.

Since the investment will triple in value, the total interest earned will be equal to two times the initial investment, or 2 * $8,600.00 = $17,200.00. Substituting these values into the formula and solving for t, we get:

$17,200.00 = $8,600.00 * 5.1% * t

t = $17,200.00 / ($8,600.00 * 5.1%) = 3.28 years

Rounding this value to the nearest tenth of a year, we get t = 3.3 years. Therefore, it will take approximately 3.3 years for Enola's investment to triple in value.

Equation of option (d) is having different value of x than other 3 equations.

So, option (d) is correct option.

Solving equations

(a) (-7/8)x-(3/4)=20

adding 3/4  on both sides, we get

(-7/8)x = 20+(3/4)

multiplying (-8/7) on both sides, we get

x = -23.71

(b)  (7/8)x+(3/4)=-20

subtracting 3/4  on both sides, we get

(7/8)x = -20-(3/4)

multiplying (8/7) on both sides, we get

x = -23.71

(c) 7(-1/8)x-(3/4)=20

adding 3/4 on both sides, we get

(-7/8)x = +20+(3/4)

multiplying (-8/7) on both sides, we get

x = -23.71

(d) (-7/8)×(-8/7)x-(3/4)=20×(-8/7)

⇒ x-(3/4) = -22.85

adding 3/4 on both sides, we get

x = -22.85+(3/4)

x = -22.10

So equation in option (d) has different value of x than all other equation.

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By using a Venn diagram, we can conclude that:

a. 10 businesses have a drive-up window and no outside seating

b. 4 Businesses have a drive-up window and outside seating, but no pay telephone

c. 20 businesses have no pay telephone

d. 9 businesses have only a drive-up window

e. 8 businesses have outside seating or a pay telephone

A Venn diagram is a diagram consisting of overlapping circles to illustrate the logical relationship between two or more sets of items.

In the question, there are 3 sets of criteria that describe the condition of the fast-food businesses in Valley Mills Drive: whether or not there is a drive-up window, outside seating, or a pay telephone.

Let d denotes the number of businesses that have the three criteria.

If a denotes the number of businesses that have drive-up window and outside seating only, then:

drive-up window and outside seating = a + d

                                                           12 = a + 4

                                                             a = 8

If b denotes the number of businesses that have outside seating and a pay telephone only, then:

outside seating and a pay telephone = b + d

                                                           6 = b + 4

                                                            b = 2

If c denotes the number of businesses that have drive-up window and a pay telephone only, then:

drive-up window and a pay telephone = c + d

                                                             5 = c + 4

                                                              c = 1

If x denotes the number of businesses that have drive-up window only, then:

have a drive-up window = a + c + d + x

                                    18 = 4 + 1 + 4 + x

                                    18 = 9 + x

                                      x = 9

If y denotes the number of businesses that have outside seating only, then:

have outside seating = a + b + d + y

                                17 = 4 + 2 + 4 + y

                                17 = 10 + y

                                  y = 7

If z denotes the number of businesses that have pay telephone only, then:

Have pay telephone = b + c + d + z

                               8 = 2 + 1 + 4 + z

                               8 = 7 + z

                                z = 1

Then we can draw a Venn diagram to illustrate those numbers to get a better illustration in answering the questions.

a. a drive-up window and no outside seating = c + x = 1 + 9 = 10

b. a drive-up window and outside seating, but no pay telephone = a = 4

c. no pay telephone = x + y + a = 9 + 7 + 4 = 20

d. only a drive-up window = x = 9

e. outside seating or a pay telephone = y + z = 7 + 1 = 8

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2.5 price hikes are often required to optimize profit.

How do you calculate the cost per unit?

To get the unit price of an item, we divide the price of a specific number of units by the number of units. If 12 ounces of soup cost $2.40, for instance, divide $2.40 by 12 ounces to get the unit price of soup, which is $0.20 per ounce.

x = the number of price hikes

y = Earnings

Additionally from the query, we have

starts at (0, 50)

expands to (2.5, 81.25)

Reduce through (6.531, 0)

It follows that

the most is (2.5, 81.25)

Remember that

x = the number of price hikes

Thus, we have

x = 2.5

Hence, the number of price increases is 2.5

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Answer:

The following equations are true when 3.27 is used:

÷ 1,000 = 0.0327

÷ 10 = 0.327

÷ 100 = 3.27

Note that the equations ÷ 102 and ÷ 1 are not true when 3.27 is used. The equation ÷ 102 is not true because 102 is not a multiple of 1,000, so dividing 3.27 by 102 will not result in a value that is close to 0. The equation ÷ 1 is not true because it is simply stating that 3.27 divided by 1 is equal to 3.27, which is true but not very interesting or useful.

The solution type to the system is one solution or consistent system

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

f(x) = [x + y = 4

        [y = 2x - 1

Substitute y = 2x - 1 in the equation x + y= 4

So, we have the following representation

x + 2x - 1 = 4

Evaluate the like terms

3x = 5

So, we have

x = 5/3

Substitute x = 5/3 in y = 2x - 1

So, we have the following representation

y = 2 * 5/3 - 1

Evaluate

y = 2.33

Because x and y have real values

Then, the solution type is a consistent system

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y=5/2x+24

Step-by-step explanation:

use the formula y-y1=m(x-x1)

5/2 symbolizes m

put in 4 for y1 and put in -8 for x1

y-(4)=(5/2)(x-(-8)

y-4=5/2(x+8)

y-4=5/2x+20

y=5/2x+24

Answer:

  y = 5/2x -18

Step-by-step explanation:

You want the slope-intercept equation for the line with slope 5/2 through point (4, -8).

It can work well to start with the point-slope equation and rearrange it to the desired form.

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y -(-8) = 5/2(x -4) . . . . . line with slope 5/2 through point (4, -8)

Add -8 and eliminate parentheses

  y = 5/2x -10 -8

  y = 5/2x -18 . . . . . . . . simplify

The desired equation is y = 5/2x -18.

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The gross pay of Adrian Ortega for assembling 70 units of electronics in a week is $425

Gross pay refers to the total payment earned over a period of time.

Adrian Ortega assembled 70 units in one week

Pay for 1–20 units = $4.50 × 20

= $90

Pay for 21 - 30 units = $5.50 × 10

= $55

Pay for 30 - 70 = $7 × 40

= $280

Gross pay = $90 + $55+ $280

= $425

Therefore, Adrian Ortega is paid $425 in a week for assembling 70 electronics.

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Answer:

(a)  11 g

(b)  8.63 g

(c)  Attached

Step-by-step explanation:

Given function:

[tex]Q = 11 \left(\dfrac{1}{2}\right)^{\dfrac{t}{5715}}[/tex]

where:

Substitute t = 0 into the given function to determine the initial quantity:

[tex]\begin{aligned} t=0 \implies Q &= 11 \left(\dfrac{1}{2}\right)^{\dfrac{0}{5715}}\\\\&=11\left(\dfrac{1}{2}\right)^0\\\\&=11\left(1\right)\\\\&=11\; \rm g\end{aligned}[/tex]

Substitute t = 2000 into the given function to determine the quantity present after 2000 years:

[tex]\begin{aligned} t=2000 \implies Q &= 11 \left(\dfrac{1}{2}\right)^{\dfrac{2000}{5715}}\\\\&=11\left(0.784697887...\right)\\\\&=8.63\; \rm g\;\; \sf (2 \; d.p.)\end{aligned}[/tex]

[tex]\begin{aligned} t=10000 \implies Q &= 11 \left(\dfrac{1}{2}\right)^{\dfrac{10000}{5715}}\\\\&=11\left(0.297346855...\right)\\\\&=3.27\; \rm g\;\; \sf (2 \; d.p.)\end{aligned}[/tex]

The graph of the function over the interval t = 0 to t = 10000 is attached.

An inequality to explain the reason Heather is incorrect is t > $8.75.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

From the histogram, we can logically deduce the following information;

Miguel’s work record during Weekend 1 = 9 hours.

Miguel’s work record during Weekend 2 = 7 hours.

Therefore, the total number of hours which Miguel worked in two Weekends is given by;

Total hours = 9 hours + 7 hours

Total hours = 16 hours.

Next, we would calculate the amount of money that Miguel would earn per hour;

Amount = $140/16

Amount = $8.75 per hour.

Note: Let the variable t represent the total earnings.

In conclusion, the correct inequality is t > $8.75.

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Step-by-step explanation:

1.

10 ft in 2 hours = 10/2 / 1 hour = 5 ft/h

2.

165 miles in 3 hours = 165/3 / 1 hour = 55 m/h or mph

3.

48 bottles in 4 cases = 48/4 / 1 case = 12 bottles per case

4.

$3.60 for 12 oz = 3.6/12 / 1 oz = $0.30 per ounce

The km per liter based on the information that Sunil can drive is 19.33 km.

An 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.

In this case, Sunil drove 63.9823 km to visit his grandmother. When he reached his grandmother's house he noticed that the car had used up 3.31 litre of petrol.

Therefore, the km per liter will be:

= 63.9823 / 3.31

= 19.33 km per liters

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The initial state of a queuing system (for example, when a restaurant first opens), is referred to as the primary state.

1) Orderly queue, also known as FIFO (First In, First Out) or FCFS (First Come, First Serve).

2) Stack, also known as LCFS (Last Come First Serve), or LIFO (Last In First Out).

3) SIRO (Serve in Irregular Request).

Let P n(t) represent the probability of having n customers in the system at time t. This is the steady state of a queueing system, where the probability of the number of customers in the system is independent of t.

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Surface area of the given prism is 6 square cm .

How to Calculate the Surface Area of Prism?

The steps to determine the surface area of the prism are:

Step 1: Note down the given dimensions of the prism.

Step 2: Substitute the dimensions in the surface area of prism formula (2 × Base Area) + (Base perimeter × height).

Step 3: The value of the surface area of the prism is obtained and the unit of the surface area of the prism is placed in the end (in terms of square units).

The lateral area is the area of the vertical faces, in case a prism has its bases facing up and down. Thus, the lateral surface area of prism = base perimeter × height

The total surface area of a Prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area or (2 × Base Area) + (Base perimeter × height).

Area of triangular cross-section:

Area = 1/2 . b . h

Area = 1/2 . 4. 3

Area = 6 square cm

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There is no point of intersection between a line that is tangent to the function () = x²  + 4 at = −1 , and the function () = x²  − 4

To find the point of intersection between the line that is tangent to the function y = x²  + 4 at x = −1 and the function y = x²  − 4 , we can set the two equations equal to each other and solve for x. This will give us the x-coordinate of the point of intersection.

Setting the two equations equal to each other, we have:

x^2 + 4 = x² - 4

This simplifies to:

2 = -8

This equation has no solutions, so the two functions do not intersect. This means that the point of intersection does not exist.

Alternatively, we could see that the two functions have different slopes at the point x = −1 .

However, since the two functions have different y-intercepts, they cannot be tangent to each other at this point. Therefore, the point of intersection does not exist.

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