Central Park is a rectangular park in New York City. Use the provided ruler to answer the following questions. a. Find the perimeter and the area of Central Park in the scale drawing. Round your measurements for the length and the width to the nearest half centimeter to calculate your answers. The perimeter in the scale drawing is centimeters. The area in the scale drawing is square centimeters. b. Find the actual perimeter and area of Central Park. The actual perimeter is meters. The actual area is square meters.

The answer is (A) The Ratio Test says that the series converges absolutely.

What is the ratio test?

The Ratio Test is a test used to determine whether an infinite series converges or diverges. It involves taking the limit of the absolute value of the ratio of the (n+1)th term to the nth term as n approaches infinity. If the limit is less than 1, then the series converges absolutely.

We have:

[tex]|a_{n+1}/a_{n}| = |(e^(n+7)*sqrt(n+3)/((n+4)!)) / (e^(n+6)*sqrt(n+2)/((n+3)!))|[/tex]

[tex]|a_{n+1}/a_{n}| = e(sqrt(n+3)/sqrt(n+2)) * (n+3)/(n+4)[/tex]

We want to compute:

[tex]L = lim n- > infinity |a_{n+1}/a_{n}| = lim n- > infinity e(sqrt(n+3)/sqrt(n+2)) * (n+3)/(n+4)[/tex]

We can see that the exponent of e goes to 1 as n goes to infinity, and (n+3)/(n+4) goes to 1 as n goes to infinity. Therefore, L = 1.

Since L < 1, by the Ratio Test, the series converges absolutely.

Hence, the answer is (A) The Ratio Test says that the series converges absolutely.

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[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{P = 2 ( x +y)}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{Perimeter_{(rectangle) } = 2 ( Height +Base)\: unit}\\[/tex]

Where-

As per question, we are given that -

We are asked to find out the value of perimeter for the given rectangle. Now that we have all the required values, so we can put them into the formula and solve for the perimeter -

[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{Perimeter_{(rectangle) } = 2 ( Height +Base)\: unit}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf Perimeter_{(rectangle) } = 2\bigg(10+9\bigg)\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf Perimeter_{(rectangle) } = 2 \times 19\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Perimeter_{(rectangle) }=38 \:ft }\\[/tex]

Using division, we can prove that there are models that we can use to prove 7 divided by 2 is = 7/2.

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many groups will be created, for instance, if a sports event requires that 30 students be divided into groups of 5 students. The division operation makes it simple to tackle such issues. Divide 30 by 5 in this case. The outcome is 30 x 5 = 6. There will thus be 6 groups, each with 5 pupils. By multiplying 6 by 5, which yields the initial figure of 30, you can confirm this value.

Here in the question,

We have to model to find 7 divided by 2 = 7/2.

For the two math classes, 7 pizzas have been delivered.

Half of the first pizza is distributed to each class.

A half of the second pizza is distributed to each class.

Third pizza, cut in half, with half going to each class.

Continue until each class receives 7 halves, or 7/2, of the pizzas that were delivered.

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The number οf hοurs fοr Shandra wοrking tο wash car is 2 hοurs.

The number οf hοurs fοr Shandra wοrking tο walking dοgs is 9 hοurs.

Mathematical expressiοn is defined as the cοllectiοn οf the numbers variables and functiοns by using οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Given that;

Shandra is wοrking twο summer jοbs, making $9 per hοur washing cars and $8 per hοur walking dοgs.

Last week Shandra wοrked a tοtal οf 11 hοurs.

Tοtal earned = $90

Nοw,

Tοtal number οf hοurs tο wash car = x

Tοtal number οf hοurs tο walk dοgs = y

Sο, We can fοrmulate;

⇒ 9x + 8y = $90  ... (I)

And, x + y = 11   .. (ii)

Sοlve equatiοn (i) and (ii) we get;

x = 2 hοurs and y = 9 hοurs

Sο, The number οf hοurs fοr Shandra wοrking tο wash car is 2 hοurs.

The number οf hοurs fοr Shandra wοrking tο walking dοgs is 9 hοurs.

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A 14.2 million donation was made to a charity. The overall amount of the charity's contributed funds is 34 million if which amounts to 42% of those monies.

Let x represent the total amount of donations received by the charity.

According to the problem, 14.2 million represents 42% of the charity's donated funds:

14.2 million = 0.42x

We must isolate x on one side of the equation in order to find it. We can do this by dividing both sides of the equation by 0.42:

x = 14.2 million / 0.42

x = 33.80952381 million

Rounding this answer to the nearest million gives:

x ≈ 34 million

Therefore, the total amount of the charity's donated funds is approximately 34 million.

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Lily increased the amount of protein she eats by 12.5% by eating every day from 48 g to 54 g.

How to calculate percentage for the given problem?

To find the percentage increase in the amount of protein that Lily eats, we can use the following formula:

Percentage increase = ((new value - old value) / old value) x 100%

Using this formula and plugging in the values given in the problem, we get:

Percentage increase = ((54 - 48) / 48) x 100%

Percentage increase = (6 / 48) x 100%

Percentage increase = 0.125 x 100%

Percentage increase = 12.5%

Therefore, Lily increased the amount of protein she eats by 12.5%.

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Answer: Reread the lesson and then you will figure it out

Step-by-step explanation:

Kennedy's average speed was 3554 miles per hour by using the formula of average speed.

Average speed is a measure of how fast something travels over a period of time, calculated by dividing the total distance traveled by the total time taken. It is usually expressed in units of distance per unit of time, such as miles per hour (mph) or kilometers per hour (km/h).

Distance is a measure of the physical space between two points, objects, or locations. It is usually expressed in units such as meters, kilometers, miles, feet, or yards.

To find Kennedy's average speed, we can use the formula:

average speed = total distance / total time

In this case, Kennedy drove 9494 miles in 2 2/3 hours. To convert the mixed number to an improper fraction, we can multiply the whole number by the denominator and add the numerator, then put the result over the denominator:

2 2/3 = (2 × 3 + 2) / 3 = 8/3

So Kennedy's total time was:

total time = 8/3 hours

Using the formula, we get:

average speed = 9494 miles / (8/3 hours)

To divide by a fraction, we can multiply by its reciprocal:

average speed = 9494 miles × (3/8 hours)

Simplifying, we get:

average speed = 3554.25 miles per hour

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Answer: −1.3571428 (with a repeating bar over .3571428)

Step-by-step explanation:

The possible length, width, and perimeter for Small cage's floor is 4 feet, 3 feet and 14 feet respectively; for Medium cage's floor is 12 feet, 2 feet and 28 feet respectively and for Large cage's floor is 18 feet, 2 feet and 40 feet respectively.

What is perimeter?

Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it.

We are given the floor areas of each cage.

For Small cage:

Area is given as 12 square feet which is a product of length and width.

So, here length can be 4 feet and width can be 3 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (Length + width)

⇒ Perimeter = 2 * (4 + 3)

⇒ Perimeter = 2 * 7

⇒ Perimeter = 14 feet

For Medium cage:

Area is given as 24 square feet which is a product of length and width.

So, here length can be 12 feet and width can be 2 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (12 + 2)

⇒ Perimeter = 2 * (14)

⇒ Perimeter = 28 feet

For Large cage:

Area is given as 36 square feet which is a product of length and width.

So, here length can be 18 feet and width can be 2 feet.

Now, we get the perimeter as

⇒ Perimeter = 2 * (18 + 2)

⇒ Perimeter = 2 * (20)

⇒ Perimeter = 40 feet

Hence, the required solution has been obtained but there are many other combinations possible.

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Step-by-step explanation:

(f○g)(x) = f(g(x))

so, we use the expression of g(x) as the "x" in f(x).

(f○g)(x) = f(g(x)) = 3(x² + 3) - 1 = 3x² + 9 - 1 = 3x² + 8

so,

(f○g)(3) = 3×3² + 8 = 27 + 8 = 35

check :

g(3) = 3² + 3 = 9 + 3 = 12

f(g(3)) = f(12) = 3×12 - 1 = 36 - 1 = 35

correct.

Therefore, the length of the side x is approximately 10.76.

A right-angled triangle, also known as a right triangle, is a type of triangle that has one of its angles measuring exactly 90 degrees. The other two angles in a right triangle are acute angles, which means they are less than 90 degrees. The side opposite to the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides of the right triangle are called legs, and they are adjacent to the right angle. The Pythagorean theorem, which states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of its hypotenuse, is a fundamental concept in the study of right triangles. Right triangles have many practical applications in geometry, trigonometry, and physics.

In a right triangle, the sum of the measures of the two acute angles is always 90 degrees. Therefore, the third angle in this triangle is:

90 - 34 = 56 degrees

Now, we can use the trigonometric ratios to find the length of the side x.

We know that the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. Therefore:

[tex]tan(34) = x/18[/tex]

To solve for x, we can multiply both sides by 18:

[tex]18 tan(34) = x[/tex]

Using a calculator, we can find that:

18 tan (34) ≈ 10.76.

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Therefore, Andrey's score was 65.4. Therefore, Susan's score was 79.

Standard deviation is a statistical measure that represents the amount of variation or dispersion in a set of data values. It measures the average distance of each data point from the mean of the data set. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are more spread out. It is calculated by taking the square root of the variance, which is the average of the squared differences of each data point from the mean. Standard deviation is commonly used in fields such as finance, engineering, and psychology to analyze and compare data sets.

Here,

a. To find Andrey's score, we need to use the formula:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the score, μ is the mean, and σ is the standard deviation.

Andrey was told that he scored 1.2 standard deviations below the mean, so we have:

z = -1.2

μ = 75

σ = 8

Plugging these values into the formula, we get:

-1.2 = (x - 75) / 8

Multiplying both sides by 8, we get:

-9.6 = x - 75

Adding 75 to both sides, we get:

x = 65.4

b. Similarly, to find Susan's score, we have:

z = 0.5

μ = 75

σ = 8

Plugging these values into the formula, we get:

0.5 = (x - 75) / 8

Multiplying both sides by 8, we get:

4 = x - 75

Adding 75 to both sides, we get:

x = 79

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The surface area of the composite figure is 944 cm².

What is the surface area of a cuboid?

Surface area of a cuboid is (lb+lh+bh) where l,b,h are length, breadth and height of the cuboid.

To find the surface area of the composite figure, we need to calculate the surface area of both cuboids and then subtract the area of any faces that are shared by both cuboids.

Given dimension of first cuboid is 14 cm × 8 cm × 2 cm and dimension of the second cuboid is 8 cm × 6 cm × 4 cm.

Surface area of the first cuboid:

Area of the top and bottom faces = 2(14 x 8) = 224 cm²

Area of the front and back faces = 2(14 x 2) = 28 cm²

Area of the left and right faces = 2(8 x 2) = 32 cm²

Total surface area of the first cuboid = 2(224) + 2(28) + 2(32) = 576 cm²

Surface area of the second cuboid:

Area of the top and bottom faces = 2(8 x 6) = 96 cm²

Area of the front and back faces = 2(8 x 4) = 64 cm²

Area of the left and right faces = 2(6 x 4) = 48 cm²

Total surface area of the second cuboid = 2(96) + 2(64) + 2(48) = 416 cm²

Now we need to identify the faces that are shared by both cuboids. The first cuboid has a bottom face that is the same size as the top face of the second cuboid (6 x 4). The surface area of this shared face is 48 cm².

Therefore, the surface area of the composite figure is total surface area of the first cuboid + Total surface area of the second cuboid - Area of shared face

= 576 + 416 - 48

= 944 cm²

So the surface area of the composite figure is 944 cm².

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The complete statement is: Tina can select and answer the essay questions on her test in 10 ways.

Tina has to answer any 2 of 5 questions, which means she needs to choose 2 questions out of the 5 available questions.

The number of ways to choose r items from a set of n items is given by the combination formula:

C(n,r) = n! / (r!(n-r)!)

In this case, n = 5 (the total number of questions) and r = 2 (the number of questions that Tina needs to choose).

So we can plug in these values to get:

C(5,2) = 5! / (2!(5-2)!)

C(5,2) = (5 x 4 x 3 x 2 x 1) / [(2 x 1) x (3 x 2 x 1)]

C(5,2) = (5 x 4) / (2 x 1)

C(5,2) = 10

Therefore, Tina can select and answer the essay questions on her test in 10 ways.

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The linear inequality for the shaded region with slope [tex]-4[/tex] is:

[tex]y < -4x+4[/tex]

In mathematics, a linear inequality is an inequality involving a linear function in one or more variables. It describes a region in the coordinate plane that satisfies the inequality.

In mathematics, the slope is a measure of the steepness of a line. It describes how much a line rises or falls as we move from left to right along it.

According to the given information

To write the linear inequality for the graph passing through points [tex](0,4)[/tex] and [tex](1,0)[/tex], we need to find the equation of the line first.

The slope of the line passing through these two points is:

[tex]m =(y_{2} -y_{1} )/(x_{2} -x_{1} )\\ = (0-4)/(1-0)\\ = -4[/tex]

Using the slope-intercept form of a linear equation, [tex]y = mx +b[/tex], where m is the slope and b is the y-intercept, we can find the equation of the line passing through these two points:

[tex]y = -4x+4[/tex]

Now, to write the linear inequality for this line, we need to determine which side of the line is shaded. We can use the test point [tex](0,0)[/tex] to check which side of the line contains the solutions to the inequality.

If we plug in [tex](0,0)[/tex] into the equation [tex]y = -4x+4[/tex], we get:

[tex]0= -4(0) +4\\0 = 4[/tex]

Since [tex]0[/tex] is not less than [tex]4[/tex], the point [tex](0,0)[/tex] is not a solution to the inequality. Therefore, we need to shade the side of the line that does not contain the origin [tex](0,0)[/tex].

The linear inequality for the shaded region is:

[tex]y < -4x +4[/tex]

Therefore any point below the line [tex]y < -4x +4[/tex] satisfies this inequality.

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Answer:

A/First picture

Step-by-step explanation:

The line touches the y axis at 3, as indicated by the +3 in the equation. In addition, the -1/2x indicated a downwards line.

Answer:

the first photo

Step-by-step explanation:

I hope this helps

The value of x for the intersecting chords is equal to 44°

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

x = (124° - 36°)/2

x = 88°/2

x = 44°

Therefore, the value of x for the intersecting chords is equal to 44°.

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The labelled parts of the circle include:

A secant of a circle is a line that intersects the circle in two distinct points. In other words, a secant is a line that cuts through a circle. The length of a secant segment between the two points of intersection with the circle is called the length of the secant.

An inscribed angle is the angle formed in the interior of a circle by the intersection of two chords on the circle.

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Image transcribed:

CIRCLES ESCAPE Challenge

Directions A circle is given to the left. Parts of this circle are partially named below. Complete the names by dragging and placing the letters over the empty spaces. Though there could be more than one answer, each letter tile can only be used once

Center

Radius

Diameter

Chord

Secant

Tangent

Central Angle

Inscribed Angle

Minor Arc

Major Arc

Answer:

Step-by-step explanation:

(2+3) x 3 + 8/2 = 5 X 3 + 8/2 = 15 + 4 = 19

"The spread of the data distribution for Lake Mockingbird is 5 inches bigger than the spread of the data distribution for Lake Warbler," is the answer to question 2.

The graphs do not support this statement since the difference in spread between the two lakes is not represented as 5 inches. The right answer to question 1 is B: "The spread of the data distribution for Lake Mockingbird is approximately 40% higher than the spread for Lake Warbler." This is due to the fact that the data distribution of the Lake Mockingbird is around 60 inches (from 5 to 65), whereas the data distribution of the Lake Warbler is approximately 43 inches (from 2 to 45). The difference between the two ranges is approximately 60 - 43 = 17. inches. From 43 to 60, the percentage rise is around 39.5%, which is close to 40%. The correct answer to question 3 is B: "The distribution of Lake Mockingbird reveals a center that is 3 inches greater than the distribution of Lake Warbler." This assertion is false since the graphs do not show the center of each distribution and cannot be established with the information supplied. Based on the data in the graphs, the other claims are correct.

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The two cars will be 380 miles apart after 3.5 hours after the first car leaves based on distance formula.

The formula for distance, which is rate times time, must be used to address this issue. Let x be the number of hours following the departure of the first car. The distances between the two cars are increasing since they are moving in different directions.

The first thing we must do is determine how far the first car, which left at 3:00 p.m., drove. When the rate is 55 miles per hour and the time is x hours, we may use the calculation distance = rate x time. Hence, the first car's mileage was 55 miles.

The second step is to determine how far the second car, which left at 4:00 p.m., travelled. When the speed is 75 miles per hour and the time is x - 1 hours, we can apply the same calculation (since the second car left one hour later than the first). Thus, the second car's mileage is 75(x - 1) miles.

The sum of the distances covered by each car is the overall distance between the two vehicles. So that we can create an equation:

distance of first car + distance of second car = total distance

55x + 75(x - 1) = 380

Simplify:

55x + 75x - 75 = 380

Combining:

130x = 455

Divide sides by 130 to obtain:

x = 3.5

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Answer:

There are 10 possible digits that could appear on the license plate: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Half of these digits (1, 3, 5, 7, and 9) are odd.

Since there are three digits on the license plate, there are 10x10x10 = 1000 possible license plates.

To find the probability that the last digit is odd, we need to find the number of license plates where the last digit is odd and divide by the total number of possible license plates:

Number of license plates where last digit is odd = 10x10x5 = 500 (since there are 5 odd digits to choose from for the last digit)

Total number of possible license plates = 10x10x10 = 1000

So the probability of selecting a license plate at random where the last digit is an odd number is:

500/1000 = 0.5 or 50%

Hope This Helps!

Answer:

The tip was $14

The formula you need to use in order to find the volume of a cylinder is [tex]V = \pi r^{2} h[/tex]

Step 1) Take note of the information that has been provided to you.

The height is 8 yards

The radius is 2 years

Step 2) Substitute the information above into the formula.

[tex]V = \pi (2^{2})(8)[/tex]

Step 3) Solve.

[tex]V = \pi (2^{2})(8)[/tex]  [tex]=100.53[/tex]

Step 4) Round if necessary.

[tex]100.53 = 101[/tex]