Find the area of the figure. Use 3.14 for pie​

Exponents, terms in parenthesis, multiplication, division, addition, and finally subtraction. You can use PEMDAS as a helpful acronym to help you remember this.

[tex]$\frac{4 x^2+12 x-16}{\frac{2 x+10}{\frac{6 x+24}{x^2+9 x+20}}}$[/tex]

Here we have two fractions top and bottom

[tex]$\frac{4 x^2+12 x-16}{2 x+10}$ divide by $\frac{6 x+24}{x^2+9 x+20}$[/tex]

We have division in between . we reverse the second fraction and multiply it with first fraction.

[tex]$\frac{4 x^2+12 x-16}{2 x+10} * \frac{x^2+9 x+20}{6 x+24}$[/tex]

Now we factor both numerator and denominator

[tex]$\begin{aligned} & 4 x^{\wedge} 2+12 x-16=4(x+4)(x-1) \\ & 2 x+10=2(x+5) \\ & x^{\wedge} 2+9 x+20=(x+5)(x+4) \\ & 6 x+24=6(x+4)\end{aligned}$[/tex]

Replace the factors,

[tex]$\frac{4(x+4)(x-1)}{2(x+5)} * \frac{(x+5)(x+4)}{6(x+4)}$[/tex]

We cancel out same factors at the top and bottom

So it becomes ,[tex]$\frac{(x-1)(x+4)}{3}$[/tex]

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The force is 80,000 Dynes.

We know that when we talk about the joint variation then we have a lot of variables that are being altered at the same time and this is what we are going to work on in the questions that we have here.

We are told that;

C α mr/t^2

Then;

C = kmr/t^2

k = Ct^2/mr

k = 6000 * 2^2/6 * 10

k = 400

Then, to find C;

C = 400 * 18 * 100/3^2

C = 80,000 Dynes

\

Hence, we can see from the calculation that the centrifugal force that is required is 80,000 Dynes.

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It is not possible to determine the greatest number of people Monica can serve with pasta bake based solely on the information provided.

The amount of milk and other ingredients she has does not necessarily indicate how many portions she can make. Other factors such as the recipe she is using, the size of each serving, and the equipment she has available will also impact how many people she can serve. In order to determine the number of portions she can make, more information is needed about the recipe and the serving size she is aiming for.It is not possible to determine the greatest number of people Monica can serve with pasta bake based solely on the information provided.

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By inspection, the following products which are multiples of 30 are:

This is referred to as a number that may be divided by another a certain number of times without a remainder.

The multiple of 30 in the options are those who have 2, 3 and 5 as the common values and is therefore the reason why options A, C and D  were chosen as the correct choice.

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The profit of the company if the company has 1800 customers is 649124 dollars

What is profit ?

A monetary gain, specifically the sum remaining after expenses for purchasing, running, or producing an item have been deducted.

P = 8.5√c³  ------->(1)

c = 1800 customers = 18 hundreds

(1) => P = 8.5√(18)³

           = 8.5 √5832 ( cube of 18=5832

          = 8.5 * 76.3675

          = 649.124 thousands of dollars

( convert into dollars by multiplying by 1000)

          = 649124.025 dollars  

          ≈ 649124 dollars

The profit of the company if the company has 1800 customers is 649124 dollars

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Answer: 48148

Step-by-step explanation:

Answer: D and C

Step-by-step explanation:

To get the value of a market basket you would add up the cost of each year so

2019 market basket = 2.50 + 1.00 + 3.75 = 7.25

2020 market basket = 2.25 + 3.00 + 4.50 = 9.75

2021 market basket = 3.00 + 3.25 + 5.00 = 11.25

now CPI for 2020 would be 9.75 / 7.25 x 100 = 134.828 which is around 135

CPI 2021 would be 11.25 / 7.25 x 100 = 155.172 which is around 155

Answer:

123.88 square units

Step-by-step explanation:

r = radius of circle

  = radius of sector

 = Length of LM

 = Length of MN

 = 13 units

When the angle is measured in degrees:
Area of a sector: [tex]\frac{Angle OfSector}{360^{o}}[/tex]× [tex]\pi r^{2}[/tex]

                = [tex]\frac{84}{360}[/tex]×[tex][\pi (13)^{2}][/tex]

                = 123.883 [tex]units^{2}[/tex]

                = 123.88 square units (Rounded to the nearest hundredth)

Answer: 240 ft²

Step-by-step explanation:

Break the diagram into a rectangle and triangle:

Area of Rectangle + Area of Triangle = Total area of Wall

(20x10) + 1/2(20 x 4) = Area of wall

200 + 40 = Area of wall

240 ft² = Area of wall

Hare Krishna :)

The distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.

What is meant by the speed of an object?

A scalar quantity, speed is defined as the magnitude of the change in an object's location over time. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. Zero speed refers to an object that is not moving at all.

The formula of speed = Distance covered /Time taken

Given,

Distance travelled = 10 miles

Time taken to travel 10 miles = 20 minutes

Speed = Distance/ time = 10/20 = 0.5miles/min

Now given the speed remains constant throughout the journey.

So the distance travelled in 3 hours = 3 * 60 = 180 minutes

Distance = speed * time = 0.5 * 180 = 90 miles.

Therefore the distance travelled by Rahul at a speed of 0.5 miles/min in 180 minutes is 90 miles.

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Maximum number of hours per day that first smokestack can operate 12.5 hours and for second smokestack is 7 hours.

According to the question a  factory has two smokestacks:

Let first smokestack take x  number of hours per day

and second smokestack take y number of hours per day

The rate of particle pollution produced is 12 kg/h for the first smokestack

and rate of particle pollution produced is 32 kg/h for the second.

A local pollution control board has ordered that the factory produce no more than 374 kg of particle pollution per day.

so, equation becomes 12x + 32y = 374

also the first smokestack operates 2 hours longer than 1. 5 times as long as the second.

so, x = 2 + 1.5y

putting value of x in other equation

12(2 + 1.5y) + 32y = 374

24 + 18y + 32y = 374

50y = 350

y = 7 hours

x = 2 + 1.5(7) = 12.5 hours

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Answer:

m<a = 44°

Step-by-step explanation:

Left triangle:

95 + 39 + x = 180

x = 46

Right triangle:

46 + 90 + a = 180

a = 44

The blue box measures about 641.667 cm in length.

The width and length of a figure indicate its breadth and length, respectively. The term "breadth" is also used to describe width. Although breadth and width are synonymous (thus the idiom hair's breadth, denoting a very small width), there are two significant differences between the two.

We are aware that the blue box's width is 18 cm, which is smaller than the green box's width (70cm).

As a result, the value of "k" must be lower than 1. By creating a proportion, we can determine the value of "k":

width of green box / width of blue box = k

70 / 18 = k

k = 70/18

k ≈ 3.8889

So the factor "k" is approximately 3.8889. To find the length of the blue box, we can use this factor to scale the length of the green box:

length of blue box = k * length of green box

length of blue box = 3.8889 * 165cm

length of blue box ≈ 641.667cm

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Answer:

D.) QIII

Step-by-step explanation:

Because 1.2 radians is in between 7π/6 and 5π/4

Answer:

[tex]\sqrt{106}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]LM=\sqrt{(7-(-2))^2+(-1-4)^2}=\sqrt{106}[/tex]

Answer:

It will take Richard 12 minutes to type 720 words.

Step-by-step explanation:

720 ÷ 60 = 12

The exponential function that shows Riley's target mileage is y = 12(1.1)ˣ

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The standard exponential equation is:

y = abˣ

where b is the rate of change and a is the initial value.

Let y represent Riley target mileage x weeks after she starts training.

She plans to run 12 miles in her first week of training and will increase her mileage by about 10% each week after. Hence:

a = 12; b = 100% + 10% = 110% = 1.1

The exponential function is y = 12(1.1)ˣ

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The statistical method that is used for identifying the cost behavior is  (e) Least Squares regression method .

The Least Squares Regression method is defined as a statistical technique that is used to determine the relationship between two variables, which are , "the cost" and its "corresponding activity level" .

This method also involves plotting data points on a scatter diagram and fitting a straight line to data points.

The line that best fits data is line that minimizes sum of squared vertical distances between the data points and the line, this is why it is called the Least Squares regression method.

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The given question is incomplete , the complete question is

A statistical method for identifying cost behavior is the:

(a) Scatter diagram method

(b) High low method

(c) Composite method

(d) CVP charting method

(e) Least Squares regression method

Answer:

75.50 + 14x - (35.50 + 9x) = 40 + 5x

Step-by-step explanation:

The speed of the plane is 135 km/h and wind speed is 23 km/h. The solution has been obtained by forming linear equations.

What is a linear equation?

This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.

Let the plane speed be 'P' and the wind speed be 'W'.

We are given that while flying to Kampala with a tailwind a plane averaged 158 km/h.

So, we get an equation as

P + W = 158       ...(1)

Also, on the return trip plane only averaged 112 km/h while flying back into the same wind.

So, we get another equation as

P - W = 112       ...(2)

Now, on adding the equations we get,

⇒P + W + P - W = 158 + 112

⇒2P = 270

⇒P = 135

Now substituting the value into either equation, we get

⇒P + W = 158

⇒135 + W = 158

⇒W = 23

Hence, the speed of the plane is 135 km/h and wind speed is 23 km/h.

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The transformation that is used to transform the figure P to figure Q is described by (b) (x, y) → (x+5, y+3).

The Transformation of the "figure P" being translated 5 units to the right and 3 units up to create the "figure Q" is called as a type of "translation" in the coordinate plane.

When we shift a point (x, y) by "a" units to the right and "b" units up, the new coordinates become as ⇒  (x + a, y + b).

The coordinates of "figure P" is translated 5 units to the right and 3 units up, that means we will use the rule (x,y) → (x+5, y+3) to describe the transformation.

Therefore, the correct transformation used is  (b) (x, y) → (x+5, y+3).

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The given question is incomplete , the complete question is

A "figure P" was translated 5 units to the right and 3 units up to create "figure Q". Which rule describes this transformation ?

(a) (x, y) → (x-5, y-3)

(b) (x, y) → (x+5, y+3)

(c) (x, y) → (x-3, y-5)

(d) (x, y) → (x+3, y+5)

Answer:

B, C, A.

Step-by-step explanation:

In order to find the angles of triangle KLM and their order from least to greatest, we need to use the Law of Cosines and the perimeter equation of the triangle. The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of these sides and the cosine of the angle between them.

Let's assume that the length of sides KL, LM, and KM are x - 4, x + 4, and 2x - 1, respectively. We can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (x - 4)^2 + (2x - 1)^2 - (x + 4)^2 / 2 * (x - 4) * (2x - 1)

Next, we can use the perimeter equation of the triangle, which is

KL + LM + KM = 27, to find the value of x:

x - 4 + x + 4 + 2x - 1 = 27

4x = 36

x = 9

So, the lengths of the sides of the triangle are

KL = x - 4 = 5, LM = x + 4 = 13, and KM = 2x - 1 = 17.

Next, we can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (5)^2 + (17)^2 - (13)^2 / 2 * (5) * (17)

cos A = 74 / 60

A = cos^-1 (74/60) = approximately 49.7°

Finally, we can use the perimeter equation of the triangle and the Law of Sines to find the other two angles of the triangle:

B + C = 180° - 49.7° = 130.3°

B / sin B = LM / sin A

B = sin^-1 (sin B / sin A) * LM / sin A

C = 130.3° - B

The angles of triangle KLM in order from least to greatest are approximately:

B, C, A.

The complete question:

The stem-and-leaf plot shows the test scores for a chemistry class.

How many students had a score greater than 90 points?

A. 6

B. 7

C. 8

D. 9

Solution:

The number of students had a score greater than 90 points is 7. So option B is correct.

A stem-and-leaf plot is a type of data visualization that shows the distribution of a set of data. It is particularly useful for small to medium-sized data sets. In a stem-and-leaf plot, each data point is split into two parts: the stem and the leaf. The stem is the leftmost digit or digits of the data point, and the leaf is the rightmost digit.

To the left of the vertical bar are the tens places.

As we want to find the scores greater than 90, we start at the row in the stem and leaf plot with a 9 to the left.

To the right are 6 values - 1, 2, 3, 4, 6, and 7.

So there are six scores here higher than 90:

91, 92, 93, 94, 96, and 97.

Now we move lower to 10 in the tens place.

There is one score there - 100. (That smart kid.)

Total up the six scores in the 9 row and the 1 in the 10 row to get 7 scores higher than 90 in this stem and leaf plot.

Hence, the number of students is 7

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The account's balance after 5 years is given as follows:

[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]

In which:

The amount of money earned, in compound interest, after t years, is given by:

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

In which:

Quarterly compounding means that the value of n is given as follows:

n = 4.

Then the balance of the account after 5 years, when t = 5, is given as follow:

[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]

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The number of elements in the sample space for this experiment is 969.

If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:

nCr = n! / [r!(n - r)!]

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:

19C3 = 19! / [3!(19 - 3)!]

= 19! / (3!)(16!)

= 969

Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.

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Step-by-step explanation:

9-3 =6

So we have 6 dollars for 3 bracelets

Which means each bracelet costs 2 dollar each

So 9x-3x=6x

The value of ∠4 in the given transversal line image is; 85°

Corresponding angles are defined as the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

In this question, we see that ∠3 is a corresponding angle to 95°. Thus;

∠3 = 95°

Now, ∠4 forms a straight line with ∠3 and as such they will sum up to 180 degrees as sum if angles on a straight line sums up to 180 degrees. Thus;

∠4 = 180 - 95

∠4 = 85°

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The ratio used to find the measurement of angle x is given as follows:

cos(x) = 40/68.

The three trigonometric ratios are defined as follows:

For angle x, we have that:

Hence the ratio is given as follows:

cos(x) = 40/68.

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Answer:

3/4 hour-72

1 hour- 92

Step-by-step explanation:

3/4-

24 x 3= 72

1-

24 x 4 =92