AOB is a sector of a circle, centre O and radius 12 cm. The length of arc AB is 15 cm. Find the area of the sector.​

Answer:

hey

Step-by-step explanation:

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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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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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

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:

slope = -3

Step-by-step explanation:

⭐ What is the equation of a line in slope intercept form?

The given line of best fit is written in slope-intercept form. All we have to do is identify which term is the slope.

[tex]y = -3x + 5[/tex]

-3 is the coefficient of x. Therefore, -3 is the slope.

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.

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: 5

Step-by-step explanation:

x=7-2

x=5

Answer:

x=5

Step-by-step explanation:

5+2=7  or 7-2=5

Answer:

Anna needs 801 boxes.

Step-by-step explanation:

You need to know how many groups of 9 are in 7209.

Use division to find this answer.

7209 ÷ 9 = 801

Anna needs 801 boxes.

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.

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:

Angle e = Angle a, as they are alternate angles.

Angle f = Angle c, as they are alternate angles.

Angles a, b, and c add up to 180°, as they are on a straight line.

Therefore, angles e, f and b also add up to 180°.

Answer:

10/3 mile

Step-by-step explanation:

perimeter = 4 × side

perimeter = 4 × 5/6 mile

perimeter = 20/6 mile

perimeter = 10/3 mile

Answer: 20

Step-by-step explanation:

x = 2

6(2)+8 = 20

Answer: 20

Step-by-step explanation:

f(2)= 6(2)+8

=20

 plug in x with 2

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

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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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

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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no 48 es un numero irracional

Cualquier número real que no se puede escribir como el cociente de dos números enteros, p/q, donde p y q son ambos números enteros, se denomina número irracional. Por ejemplo, la raíz cuadrada de 2 no se puede expresar como un número entero o una fracción.

Explicación detallada:

48 se puede expresar como [tex]\frac{48}{1}[/tex] aquí se puede ver que la forma p/q está presente. Entonces es un número racional.

no 48 es un numero irracional.

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48 is not an irrational number

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is called an irrational number. For example, the square root of 2 cannot be expressed as a whole number or a fraction.

48 can be expressed as  [tex]\frac{48}{1}[/tex] here you can see that the p/q form is present. So it is a rational number.

48 is not an irrational number.

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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

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:

7

Step-by-step explanation:

g(3)=4(3)-5

g(3)=12-5

g(3)=7

Answer:

g(3) = 7

Step-by-step explanation:

Given function:

[tex]g(x)=4x-5[/tex]

To find g(x3) substitute x = 3 into the function:

[tex]\begin{aligned}x=3 \implies g(3)&=4(3)-5\\&=12-5\\&=7\end{aligned}[/tex]

Therefore:

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.

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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The percentage of higher risk is unaffected by exposure as relative risk in unity.

In order to determine the strength of the relationship between exposures (treatments or risk factors) and outcomes, relative risk is employed in the statistical analysis of data from ecological, cohort, medical, and intervention studies. For instance, in a study looking at how the drug apixaban affected the occurrence of thromboembolism, 8.8% of patients receiving a placebo developed the condition, whereas only 1.7% of patients receiving the medication did. This means that the relative risk is.19 (1.7/8.8), meaning that patients receiving apixaban had 19% the disease risk of patients receiving a placebo. [4] In this instance, apixaban lowers the probability of disease, making it a protective rather than a risk factor.

Values of relative risk can be understood as long as the relationship between the exposure and the result is assumed to be causal.

RR = 1 denotes that the outcome is unaffected by exposure.

When the risk of the outcome is less than 1, this is referred to as a "protective factor."

RR > 1 indicates that the exposure, a "risk factor," has an effect on the outcome's risk.

Therefore, the percentage of higher risk is unaffected by exposure as relative risk in unity.

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1. The solution to the quadratic equation, x² - 14x + 49 = 40, is x = 13.32 and x = 0.68

2. The solution to the quadratic equation, x² - x = 12, is x = -3 and x = 4

3. i. The factors of 2x² - 15x - 8 = 0 are (2x +1) and (x - 8)

ii. The x-intercepts of 2x² - 15x - 8 = 0 are x = -1/2 and x = 8

From the question, we are to solve the given quadratic equation by completing the square.

The given equation is

x² - 14x + 49 = 40

Solving the equation

x² - 14x + 49 = 40

x² - 14x = 40 - 49

x² - 14x = -9

Multiply the coefficient of x by 1/2 square and add to both sides

x² - 14x + (-7)² = -9 + (-7)²

(x - 7)² = -9 + 49

(x - 7)² = 40

x - 7 = ±√40

x = 7 ± √40

x = 7 ± 6.32

x = 7 + 6.32 OR 7 - 6.32

x = 13.32 OR 0.68

Solving x² - x = 12 by factoring

x² - x = 12

x² - x - 12 = 0

x² -4x + 3x - 12 = 0

x(x - 4) + 3(x - 4) = 0

(x + 3)(x - 4) = 0

x + 3 = 0 OR x - 4 = 0

x = -3 OR x = 4

Determining the factors of 2x² - 15x - 8 = 0

2x² - 15x - 8 = 0

2x² - 16x + x - 8 = 0

2x(x - 8) + 1(x - 8) = 0

(2x + 1)(x - 8) = 0

The factors are (2x +1) and (x - 8)

Determining the x-intercepts

(2x + 1)(x - 8) = 0

2x + 1 = 0 and x - 8 = 0

2x = -1 and x = 8

x = -1/2 and x = 8

Hence, the x-intercepts are -1/2 and 8

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Volume of solid generated by revolving the region bounded by the graph is 3817.53 unit

A volume is created while a plane figure rotating about an axis or around any straight line situated on the same plane.

We apply definite integration to calculate the required volume.

we are given the equation y = 5x² and y =0, x= 3

volume is calculated by using the formula, V = ∫π y² dx

                                                                      V = ∫₀³π (5x²) ² dx

On the y-axis x = 0 so upper limit x = 3 and lower limit x= 0

                                                          V= π × 25/5 [x⁵] ³₀

                                                        V = 15.71 [3⁵- 0]

  hence, the volume of solid = 3817.53 unit

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