9) The area of Vaughn's dog pen is 341square feet
The length of the pen is 22 feet. What is the width?

Answer:

x^8/3

Step-by-step explanation:

Answer:

The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.

In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:

The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.

The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.

The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.

Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).

Answer: (-8, -10)

Step-by-step explanation:

Answer:

5216.844

Step-by-step explanation:

Let x be the fourth number.

We know that the sum of the four numbers is 20500:

2341.578 + 10690 + x + 2341.578 = 20500

Simplifying and solving for x:

x = 20500 - 2341.578 - 10690 - 2341.578

x = 5216.844

Therefore, the first quadratic function that goes through the points (5, 3) and (8, 0) is: y = (-3/28)x² + (33/14)x - (21/7). Therefore, the second quadratic function that goes through the points (5, 3) and (8, 0) is: y = 2x² - 27x + 78.

The graph of a quadratic function is a parabola, and its shape depends on the sign of the leading coefficient a. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards. Quadratic functions are commonly used to model various physical phenomena, such as motion of objects under the influence of gravity or acceleration.

Here,

To find the equation of a quadratic function in the form of y = ax² + bx + c that passes through two given points, we can substitute the coordinates of those points into the equation to get two equations, and then solve for the coefficients a, b, and c. Using the given points (5, 3) and (8, 0), we can write the following system of equations:

3 = a(5)² + b(5) + c

0 = a(8)² + b(8) + c

Simplifying these equations, we get:

25a + 5b + c = 3

64a + 8b + c = 0

Now we can solve for a, b, and c by using elimination or substitution method:

Multiplying the first equation by 8 and subtracting the second equation from it, we get:

200a + 40b + 8c = 24

-64a - 8b - c = 0

136a + 32b + 7c = 24

Next, multiplying the first equation by 64 and subtracting the second equation from it, we get:

1600a + 320b + 64c = 192

-64a - 8b - c = 0

1536a + 312b + 63c = 192

Now we have two equations with two variables:

136a + 32b + 7c = 24

1536a + 312b + 63c = 192

Solving this system, we get:

a = -3/28

b = 33/14

c = -21/7

Therefore, the first quadratic function that goes through the points (5, 3) and (8, 0) is:

y = (-3/28)x² + (33/14)x - (21/7)

To find a second quadratic function, we can simply use a different value for the leading coefficient a. For example, let's use a = 2:

3 = 25a + 5b + c

0 = 64a + 8b + c

Substituting a = 2 and simplifying, we get:

b = -27

c = 78

Therefore, the second quadratic function that goes through the points (5, 3) and (8, 0) is:

y = 2x² - 27x + 78

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The equation of the line passing through the two points (4,2) and (-3,1) is 7y-x-10=0

Equation of a line is an algebraic form of showing the set of points, which together forms a line in a coordinate system.

Given the line passes through the points (4,2) and (-3,1)

Here, x1=4, y1=2, x2=-3, y2=1

So, the slope of the line (m)= \(\frac{y2-y1}{x2-x1}\\\)=\(\frac{1-2}{-3-4}\\\)=\(\frac{1}{7}\)

Now we know, the equation of the line is given as,

y-y1=m(x-x1)

Putting the value of y1 and x1 in the equation we get,

y-2=\(\frac{1}{7}\)(x-4)

7y-14=x-4

7y-x-10=0

Hence the equation of the line that passes through the two points (4,2) and (-3,1) is 7y-x-10=0.

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The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

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Answer: B

Step-by-step explanation: 14 1/5 - 2 5/6 =11 11/30

rounded is 11

Answer:

see explanation

Step-by-step explanation:

(a)

Using the recursive rule and a₁ = 4 , then

a₂ = 2(\(\frac{1}{3}\) + a₁ ) = 2(\(\frac{1}{3}\) + 4) = 2 × 4 \(\frac{1}{3}\) = 2 × \(\frac{13}{3}\) = \(\frac{26}{3}\)

a₃ = 2(\(\frac{1}{3}\) + a₂) = 2(\(\frac{1}{3}\) + \(\frac{26}{3}\) ) = 2 × \(\frac{27}{3}\) = 2 × 9 = 18

a₄ = 2(\(\frac{1}{3}\) + a₃) = 2(\(\frac{1}{3}\) + 18) = 2 × 18 \(\frac{1}{3}\) = 2 × \(\frac{55}{3}\) = \(\frac{110}{3}\)

a₅ = 2(\(\frac{1}{3}\) + a₄) = 2(\(\frac{1}{3}\) + \(\frac{110}{3}\)) = 2 × \(\frac{111}{3}\) = 2 × 37 = 74

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

(b)

Using the recursive rule and a₁ = 6 , then

a₂ = \(\frac{2}{a_{1} }\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)

a₃ = \(\frac{3}{a_{2} }\) = \(\frac{3}{\frac{1}{3} }\) = 9

a₄ = \(\frac{4}{a_{3} }\) = \(\frac{4}{9}\)

a₅ = \(\frac{5}{a_{4} }\) = \(\frac{5}{\frac{4}{9} }\) = 5 × \(\frac{9}{4}\) = \(\frac{45}{4}\)

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

(c)

The sequence has a common ratio

r = \(\frac{\frac{2}{3} }{\frac{1}{6} }\) = \(\frac{\frac{8}{3} }{\frac{2}{3} }\) = 4

Multiply the previous terms by 4 , then

a₄ = 4 × \(\frac{8}{3}\) = \(\frac{32}{3}\)

a₅ = 4 × \(\frac{32}{3}\) = \(\frac{128}{3}\)

Answer:

-2

Step-by-step explanation:

y=k/x

Replace y with 7 and x with -2

7=k/-2 gives you -14

Then you can replace k with -14 and x with 7

y=-14/7 gives you -2

76.89 sjsbs austere. Sisson whenever. Ebenezer oe eie h rur fuf 8r r earned e 3epoe9 r rur 8e e aonwowne e7 rjr or

Answer:

correct me if i'm wrong but it's 57.32 degrees?

The maximum haircut cost is much higher for women than for men.

Cost is an important concept in economics, accounting and business. It is the value of goods or services provided in exchange for money or other resources. It is the total amount of money spent to acquire goods and services. It includes both direct costs, such as materials, labor and overhead, as well as indirect costs, such as marketing, shipping and taxes. Cost is also used to measure efficiency, as it is the ratio of resources used to produce a product or service. It can also be used to compare different products or services in terms of their economic value. Ultimately, cost is an essential factor when it comes to determining the price of a product or service.

The boxplots shown depict the distribution of haircuts costs for both men and women. From the boxplots, we can see that the interquartile ranges for both men and women are fairly similar. The range for the women's haircuts is slightly larger than the men's haircuts, but not by a huge amount. The minimum haircut cost for both men and women are similar, but the maximum haircut cost for women is much higher than the maximum haircut cost for men. This could be due to the fact that the women's haircuts tend to require more time and skill, and therefore cost more. Additionally, there could be more elaborate options available for women's haircuts that could drive up the cost. Furthermore, hair care products such as dyes and styling products could also be contributing to the higher cost of women's haircuts.

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Answer:

65

Step-by-step explanation:

Order the numbers in order

Find the middle number

Since there were 2, find the average

Answer:65

Step-by-step explanation:

median is the middle

there is 2 and they are 50 and 80

add it up and divide by 2

Answer in terms of Ln:   \(20*\text{Ln}\left(\frac{25}{13}\right)\\\\\)

Answer in decimal form:   13.1

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

Work Shown:

\(P(t) = 1,300,000e^{0.05t}\\\\2,500,000 = 1,300,000e^{0.05t}\\\\e^{0.05t} = \frac{2,500,000}{1,300,000}\\\\e^{0.05t} = \frac{25}{13}\\\\0.05t = \text{Ln}\left(\frac{25}{13}\right)\\\\t = 20*\text{Ln}\left(\frac{25}{13}\right)\\\\t \approx 13.0785293481332\\\\t \approx 13.1\\\\\)

The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

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In the given problem, by setting up an inequality, the two possible amounts of change are 53p and 67p.

Let's call the cost of the pie "x". Since it is somewhere between £1.30 and £2.99 and is an exact number of pence after adding a 24% tip, we know that:

1.3 <= x <= 2.99 (in pounds)

100x*1.24 is an integer (in pence)

We can simplify the second condition by multiplying both sides by 100 and dividing by 124:

100x is a multiple of 100/124 = 25/31 (in pence)

So we know that x must be a multiple of 25/31 pence, and it must be between 130 and 299 pence. We can write this as:

130 <= 25n/31 <= 299

where n is an integer.

Multiplying both sides by 31 and dividing by 25, we get:

162.8 <= n <= 237.2

Since n must be an integer, the possible values for n are 163, 164, ..., 237.

For each possible value of n, we can calculate the cost of the pie, the total price with tip, and the amount of change we would receive if we paid with a £5 note. We can then check whether we receive exactly 5 coins as change.

For example, if n = 163, then:

100x = 25n = 4075

x = £40.75

total price with tip = £50.57

change = £5.00 - £50.57 = £0.43 = 43p

43p can be given as 20p + 20p + 2p + 1p, so we receive 4 coins in this case.

Similarly, we can check all the other possible values of n and find that there are two values of change that we could receive:

53p (25p + 20p + 5p + 2p + 1p)

67p (50p + 10p + 5p + 2p)

Therefore, the two possible amounts of change are 53p and 67p.

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Answer:

m=3

y(-2/3, 2)

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Answer:

11/24

Step-by-step explanation:

5/8 - (1/8)/(3/4)

5/8 - (4/24)

(5/8) = 15/24

15/24 - 4/24 = 11/24

Answer:

25

Step-by-step explanation:

150 gallons = 4 * 150 = 600 quarts.

You then put 24 of these quarts into a shipping box.

600 / 24 = 25

That means you can get 25 full cases from 150 gallons.

Answer:

\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)

\(7 = - \frac{8}{3} ( - 3) + b\)

\(7 = 8 + b\)

\(b = - 1\)

\(y = - \frac{8}{3} x - 1\)

The y-intercept is -1.

Answer:

D.

Step-by-step explanation:

-2 is divided on both sides of the equation, which is the multiplication property of equality. you aren't adding anything/ multiplying anything by 0

Based on the plot, the number of practice puzzles per week that members solve if they finish the contest puzzle

in one hour is c 4

The line of best fit for the scatter plot shows that there is a positive correlation between the number of practice puzzles solved per week and the time it takes to solve a contest puzzle. This means that as the number of practice puzzles solved per week increases, the time it takes to solve a contest puzzle decreases.

If a member finishes a contest puzzle in one hour, they are on the line of best fit. This means that they solve approximately 4 practice puzzles per week.

The other options are incorrect. Option a is too high, option b is too low, and option d is not on the line of best fit.

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For the given function the value of limits are

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\) is 5

\(\lim _{x\to 0^+}\left(f\left(x\right)\right)\) is 0

\(\lim _{x\to 0}\left x^2+5\)is 5

The given function is f(x)= x²+5, when x≤0

f(x)=2x when x>0

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0^-}\left x^2+5\)

The given limit is a left hand limit as there is minus in the limits

When we apply x as 0 we get the value 5

Now \(\lim _{x\to 0^+}\left(f\left(x\right)\right)\)

So \(\lim _{x\to 0^+}\left 2x\)

The given limit is a right hand limit as there is positive in the limits

When we apply x as 0 we get 0

Now \(\lim _{x\to 0}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0}\left x^2+5\)

We get 5

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Answer:

Simplifying the expression `n + n - 0.18n`, we get:

n + n - 0.18n = 2n - 0.18n

Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.

Looking at the answer choices:

a. 1.18n

b. 1.82n

c. n- 0.18

d. 2n - 0.82

We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.

Therefore, the answer is d. 2n - 0.82.

Step-by-step explanation:

Answer: 4(4b - 5)(b + 5)

Step-by-step explanation:

All have a common factor of 4

4(4b^2 + 15b - 25)

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

Now you need to find two numbers that:

a) multiply to -100 (the a term * the c term = 4 * -25)

b) add to 15 (the b term)

After a little thinking, we can determine that the two numbers are:

20 and -5

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

Now we can rewrite the middle term as 20b - 5b (notice how it still equals 15b)

4(4b^2 + 20b - 5b - 25)

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

4((4b^2 + 20b) + (-5b - 25))

Group the terms (associative property)

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

Take out a common factor from each

4(4b(b + 5) - 5 (b + 5))

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

Now we can factor by grouping

4(4b - 5)(b + 5)

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

Answer: I think it’s 68.2

Answer:

68.2 for sure

Step-by-step explanation:

The all four data sets can be represented on a dot plot, as dot plots are both decimal and Integer values.

A dot plot is a graphical representation that displays data points as dots along a number line. It is commonly used to show the distribution of a small set of quantitative data.

The data set should be shown on a dot plot, we need to consider the characteristics of the data.

1. Data Set 1: {0.012, 0.078, 0.093, 0.147, 0.187}

This data set consists of decimal values. A dot plot can effectively represent decimal values, where each dot represents a data point. Therefore, Data Set 1 should be shown on a dot plot.

2. Data Set 2: {1.3, 1.9, 2.5, 2.7, 3.5, 4.8, 5.3, 7.9, 9.0}

Similar to Data Set 1, this data set consists of decimal values. Hence, it can also be effectively represented on a dot plot. Each value would be represented as a dot along the number line.

3. Data Set 3: {712, 722, 722, 723, 724, 724, 724, 725, 727, 728, 730}

This data set consists of integer values. Dot plots are commonly used for discrete data, including integers. Therefore, Data Set 3 can be appropriately represented on a dot plot.

4. Data Set 4: {16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97}

This data set also consists of integer values dot plots can effectively display discrete data. Hence, Data Set 4 can be shown on a dot plot.

all four data sets can be appropriately represented on a dot plot, as dot plots are suitable for displaying both decimal and integer values.

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The length of the square in centimetres in algebraic expression is 25m

The perimeter of a square is m meters.

The length of the each side of the square in centimetres can be represented in an algebraic expression as follows:

Therefore,

perimeter of a square = 4l

where

Therefore,

m = 4l

where

l = m / 4 meters.

Therefore, the side length of the square in centimetres is as follows:

1 meters = 100 cm

m / 4 meters  = ?

cross multiply

length of the square in meters = m / 4 × 100

length of the square in meters = 100m / 4

length of the square in meters = 25m

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