What is the perimeter of a rectangle with a length of 8 1/6 feet and a width of 6 2/3 feet

The area of the shaded region in this problem is given as follows:

c. 133 m².

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width.

Hence the area of the entire rectangle in this problem is given as follows:

13 x 11 = 143 m².

The area of the smaller rectangle in this problem is given as follows:

2 x 5 = 10 m².

Hence the area of the shaded region is given as follows:

143 - 10 = 133 m².

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Answer:

C. 8x - 6

Step-by-step explanation:

Step-by-step explanation:

Winston's:

After 3 days: 32 cars

After 5 days: 12 cars

Difference in number of cars = 32 - 12 = 20

Difference in number of days: 5 - 3 = 2

Selling rate: 20/2 = 10 cars per day

Car-Mart:

After 2 days: 43 cars

After 3 days: 32 cars

Difference in number of cars = 43 - 32 = 11

Difference in number of days: 3 - 2 = 1

Selling rate: 11/1 = 11 cars per day

Car-Mart sells 1 car per day more than Winston's.

Starting numbers of cars:

Winston's:

Each day less, there are 10 more cars.

Day 3, 32 cars

Day 2, 42 cars

Day 1, 52 cars

Day 0, 62 cars

Winston's started with 62 cars.

Cart-Mart:

Each day less, there are 11 more cars.

Day 2, 43 cars

Day 1, 54 cars

Day 0, 65 cars

Car-Mart's started with 65 cars.

Car-Mart started with more cars. It had 3 more cars than Winston's

Based on the information given in the table, it should be noted that the number of cars that Car Mart sells is 11 cars per day while Winston sells 10 cars per day.

The difference in number of cars for Winston will be:

= 32 - 12

= 20

Therefore, the selling rate will be:

= 20/2

= 10 cars per day

The difference in the number of cars for Car-Mart will be:

= 43 - 32 = 11 cars per day.

The difference in number of days will be:

= 3 - 2

= 1

The selling rate will be:

= 11/1

= 11 cars per day

Therefore, Car-Mart sells 1 car per day more than Winston.

Also, the starting numbers of cars for Winston is 62 cars while Car-Mart's started with 65 cars. Therefore, Car-Mart had 3 more cars than Winston's.

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Answer:

9.796192

Step-by-step explanation:

square root of 12 = 3.464

square root of 8 = 2.828

3.464 × 2.828

= 9.796192

Hope it helps.

Answer: Choice C.   (3,-2)

A diagram is shown below.

===============================================

Explanation:

There are two approaches we can take. Since we're given a list of choices, we can plug each of the coordinates one at a time into the inequality. If we get a true statement, then it is a solution.

For choice A, we have x = 2 and y = 3 paired up together. Plugging them into the given inequality leads to...

y < (-1/2)*x + 2

3 < (-1/2)*2 + 2

3 < -1 + 2

3 < 1

This is false because 3 is not smaller than 1. So (2,3) is not a solution. You should find that choice B leads to a similar situation because

y < (-1/2)*x + 2

1 < (-1/2)*2 + 2

1 < -1+2

1 < 1

and 1 cannot be smaller than itself. So (2,1) isn't a solution either.

However, choice C is the answer since,

y < (-1/2)*x + 2

-2 < (-1/2)*3 + 2

-2 < -1.5 + 2

-2 < 0.5

This is true because -2 is to the left of 0.5 on the number line. So that's why (3,-2) is a solution.

For choice D, you should find that (-1,3) doesn't make the inequality true.

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

An alternative approach:

As a visual way to solve this problem, we can graph the given inequality by following these steps

We make the boundary line dashed because points on the boundary do not count as solution points. This is due to the lack of "or equal to" in the inequality sign. We shade below the boundary line because of the "less than".

As the diagram below indicates, the blue region consists of every (x,y) solution point that makes y < (-1/2)*x + 2 true.

The diagram also shows that only point C is in that blue region, making it a solution point. Point B on the boundary does not count as a solution. You can think of the dashed line as an electric fence you can only get closer to, but can't touch, in terms of determining a solution point.

So effectively, this is a quick and easy way to find solutions if you have a graphing calculator or online graphing tools (such as Desmos or GeoGebra).

Answer:

Step-by-step explanation:

640 calories

The annual percent change in the population of town C will be 16.9

From the formula for the annual increase in population, we have

A = P( 1 + r/100 )n

Where, A = new population

r = rate of increase in the population per annum

n = number of years

Since, from the question, we have

n = 7

A = 3P

Therefore,

3P = \(P( 1+ r/100 )^{7}\)

Or, 3 = \(P( 1+ r/100 )^{7}\)

31/7 = 1 + r/100

1.169 = 1 + r/100

0.169 = r/100

r = .169 x 100 = 16.9

Therefore, the annual percent change in the population of town c is 16.9

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The value of x in the ratio 5x : 9 = 7 : 3 is x = 21/5

From the question, the ratio is given as

5x : 9 = 7 : 3

Express the ratio, as a fraction

So, we have the following representation

5x / 9 = 7 / 3

Cross multiply the following expression

So, we have the following representation

3 * 5x = 9 * 7

Evaluate the products

15x = 63

Divide both sides by 15

So, we have

x = 63/15

Simplify the fraction

x = 21/5

Hence, the solution to the ratio is x = 21/5

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The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:

y = 24

Step-by-step explanation:

y - x = 13

x = 11

y - 11 = 13

y = 13 + 11 = 24

The total amount that Adele will have in her account at the end of the 3 years is $2,315.25.

Given that, principal=$2000, rate of interest=5% and time period=3 years.

The compound interest formula is used to calculate compound interest, sometimes known as "interest on interest". The formula for compound interest is \(A = P(1 + \frac{r}{100})^{nt}\), where P= principal balance, r= interest rate, n= number of times interest is compounded per time period and t= number of time periods.

Now, A=2000(1+5/100)³

=2000(1+0.05)³

=2000(1.05)³

=$2,315.25

Therefore, the total amount that Adele will have in her account at the end of the 3 years is $2,315.25.

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Answer:

B. √3

Step-by-step explanation:

Edge 2021

The expression -2(3m - 2) - 5 + 4m should be simplified by applying the distributive property first, followed by combining like terms. The simplified expression is -2m - 1.

To simplify the expression -2(3m - 2) - 5 + 4m, we need to determine whether to apply the distributive property first or combine like terms first.

The distributive property states that when a number is multiplied by a sum or difference inside parentheses, it must be distributed or multiplied by each term inside the parentheses.

In this expression, we have -2 multiplied by the quantity (3m - 2). Applying the distributive property would involve multiplying -2 by both terms inside the parentheses: \(-2 \times 3\) m and \(-2 \times -2.\)

On the other hand, we also have 4m in the expression, which is a term with the variable 'm'. Combining like terms involves simplifying expressions that have the same variable and power.

In this case, we have \(-2 \times 3\) m and 4m, which are both terms with 'm'.

To decide whether to use the distributive property first or combine like terms first, we need to prioritize the order of operations. The order of operations dictates that we should perform multiplication before addition or subtraction.

Therefore, we should first apply the distributive property to -2(3m - 2), resulting in -6m + 4. Then we can combine like terms by adding -6m and 4m, resulting in -2m. Finally, we can combine the constant terms by adding -5 and 4, resulting in -1.

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The square of the length of the chord that is a common external tangent of the other two circles with radii of 3 and 6 is 45.

Given that circles of radii 3 and 6 are externally tangent to each other and internally tangent to a circle of radius 9. The circle of radius 9 has a chord that serves as a common external tangent for the other two circles. The task is to find the square of the length of this chord.

The distance between the centers of the circles of radii 3 and 6 can be found by adding their radii: d1 = 3 + 6 = 9 units.

Since the circles are internally tangent to the circle of radius 9, the distance between their centers can be found by subtracting their radii from the radius of the larger circle: d2 = 9 - 3 - 6 = 0 units.

The chord is a common external tangent of the circles, and its length can be found by doubling the distance between the center of the circle of radius 9 and the chord: Chord length = 2 × h.

To find the height (h) of the triangle formed by the chord and the center of the circle of radius 9, we can use the formula h = (r1 + r2 - R) / 2, where r1 and r2 are the radii of the smaller circles, and R is the radius of the larger circle. In this case, h = (3 + 6 - 9) / 2 = 0.
Since h is zero, it means that the chord passes through the center of the circle of radius 9. Therefore, its length will be the diameter of the circle of radius 9.

The square of the length of the chord can be found using the Pythagorean theorem. Let's denote the length of the chord as d.

- We know that r1 + h = R, so h = R - r1 = 9 - 3 = 6.

- Using the Pythagorean theorem: d = sqrt(R² - h²) = √(9² - 6²) = √(81 - 36) = √(45).

Therefore, the square of the length of the chord is d^2 = 45.

In summary, the square of the length of the chord that serves as a common external tangent for the circles of radii 3 and 6, and is internally tangent to a circle of radius 9, is 45.

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Answer:

They started the morning shift with 80 cups of coffee

3 hours into the shift the chef made 40 more cups of coffee

45 minutes into the shift 60 cups of coffee were sold

Explanation:

The graph says that:

1. They started the shift with 80 cups of coffee in stock (point A)

2. 25 minutes later, they had 60 cups of coffee (point B)

3. at 45 minutes, they had 20 cups of coffee (point C)

4. at 2 hours they had 0 cups of coffee. (point D)

5. After 3 hours they had 40 cups of coffee (point E)

6. At the end of the morning they had 10 cups of coffee. (point F)

Therefore, the true statement are:

They started the morning shift with 80 cups of coffee because that is the information showed by point A.

3 hours into the shift the chef made 40 more cups of coffee because at point D there was no cups of coffee, then at point E which is 3 hours into the shift there were 40 cups of coffee.

45 minutes into the shift 60 cups of coffee were sold because they started with 80 cups and 45 minutes later they had 20 cups. It means that they sell 80 - 20 = 60 cups of coffee.

So, the answers are:

They started the morning shift with 80 cups of coffee

3 hours into the shift the chef made 40 more cups of coffee

45 minutes into the shift 60 cups of coffee were sold

Answer:

There would be 2 1/2 servings.

Step-by-step explanation:

So first, you change 1/4 into 2/8 so 2/8 plus 2/8 equals 4/8 and if you add half of that, so 1/8, then you get 5/8 cup.

Answer:

1234567890

Step-by-step explanation:

1234567890

The distance that you have walked around the perfectly circular lake can be determined using the formula for the circumference of a circle, which is C = πd, where C is the circumference

(1 point), π is pi, and d is the diameter.

In this case, the diameter is 500 m, so the circumference of the lake is C = π(500 m) = 1570.8 m. To determine the distance that you have walked, you can use the formula for arc length, which is L = θ/360∘ × C, where L is the arc length, θ is the central angle, and C is the circumference. In this case, θ is 800∘ and C is 1570.8 m, so the distance that you have walked is L = (800∘/360∘) × 1570.8 m = 3489.78 m. Rounded to two decimal places, the distance that you have walked is 3489.78 m, or 3.49 km. Therefore, the answer is 3.49 km.

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\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

Given that,

Now, let's solve & find the area & perimeter of the semi-circle.

(1) Radius (r) = 21.5 cm

Area of a semi-circle = πr²/2

\(\downarrow\)

\( \tt \frac{ \pi \: r ^{2} }{2} \\\tt = \frac{3.14 \times (21.5) ^{2} }{2} \\ \tt = \frac{3.14 \times 46.25}{2} \\ \tt = \frac{1451.465}{2} \\ = \boxed{\boxed{\bf 725.73 \: cm ^{2} }}\)

(2) Radius (r) = 21.5 cm

Perimeter of the semi-circle = r (π + 2)

\(\downarrow\)

\(\tt \: r(\pi + 2) \\ = \tt \: 21.5(3.14 + 2) \\ \tt = 21.5(5.14) \\ \tt = 21.5 \times 5.14 \\ = \boxed{\boxed{\bf 110.51 \: cm}}\)

The formula for  \(f^n(x)\) is \(f^n(x)=\frac{(-1)^{n-1}(n-1)! }{(x-1)^n}\).

What does derivative mean?

Calculus defines a derivative as the instantaneous pace at which a function changes in relation to another variable. Finding a function's derivative is the process of differentiation. A function's derivative is the same as its tangent's slope and rate of change.

Given function is \(f(x)=ln(x-1)\).

The first derivative of the function is \(f^1(x)=\frac{1}{x-1}\).

The second derivative of the function is \(f^2(x)=\frac{-1}{(x-1)^2}\).

The third derivative of the function is \(f^3(x)=\frac{2}{(x-1)^3}\).

The fourth derivative of the function is \(f^4(x)=\frac{-6}{(x-1)^4}\).

The fifth derivative of the function is \(f^5(x)=\frac{24}{(x-1)^5}\).

By observing the derivatives we could observe the pattern that

\(f^n(x)=\frac{(-1)^{n-1}(n-1)! }{(x-1)^n}\).

Therefore the formula for  \(f^n(x)\) is \(f^n(x)=\frac{(-1)^{n-1}(n-1)! }{(x-1)^n}\).

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Answer:

The first one and the last two

Answer:

the first one and the 2 last ones!

Answer:

73 then 89 is the prime numbers

Step-by-step explanation:

Answer:

regular

Step-by-step explanation:

because an irregular polyhedron is formed by polygons of different shapes where all the components are not the same.

To make three plates by three machines it will take 05 minutes.

The Production Possibility Frontier (PPF) is a curve on a graph that represents the possible amount that can be produced by two products if they rely on the same finite resource for manufacturing. PPF is also known as the production possibility curve.

Given:

05 machines make 05 plates in 05 hours.

rate of 3 machines is 1 plate per minute,

1 machine makes 5 Plate in = 5 × 5 = 25 minutes.

1 machine makes makes 1 plate in = 25 ÷ 5 = 5 minutes

So, 1 machine can make 03 plates in = 5 × 3 = 15

Thus, 03 machines can make 03 plates in = 15 ÷ 3

                                                                      = 5 minutes.

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Answer:

31.4

Step-by-step explanation:

5 x 2 x 3.14 (pi) = 31.4 rounded.

In statistics, a scatter plot is used to identify a correlation between two variables by visually observing a collection of ordered pairs (x, y) in which two variables are plotted on the X and Y axis. The value of one variable is compared to the value of the other variable. The data can be measured and presented on a graph to determine whether there is a relationship between them. A scatter plot of home run leaders for each league in baseball is one such example.

To construct a scatter plot of home run leaders in baseball, the difference between the smallest and largest number of home runs by leaders for each league must first be calculated. The American League and the National League are the two leagues in baseball that have home run leaders. A scatter plot of home run leaders can be constructed using a graph. The vertical axis represents the number of home runs hit by the leaders in the National League.

The horizontal axis represents the number of home runs hit by the leaders in the American League. The difference between the greatest and smallest number of home runs hit by the leaders in each league will be measured. To get the difference between the smallest and greatest number of home runs in each league, the greatest number of home runs hit by leaders in a league is subtracted from the smallest number of home runs hit by leaders in a league.

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Answer:

34 units

Step-by-step explanation:

The perimeter of a triangle is given by the sum of the lengths of its three sides.

So if the perimeter is 68 units and the sides measure x, 2x and 3x, we have that:

x + 2x + 3x = 68

6x = 68

x = 68/6 units

Now with the value of x we can find the length of EO:

EO = 3x

EO = 3 * (68/6)

EO = 68/2 = 34 units