Find the exact length of the third side.
63
60

I'll solve for half circle.

Perimeter = πr + 2r

r = 7cm

P = π*7 + 2*7

P = 35.9 cm

The statistics are used to create a visual representation of data distribution, with the box formed by Q1, Q2, and Q3, and the whiskers extending to the minimum and maximum values.

To draw a box plot, you need to have several statistical measures such as the minimum value, the maximum value, the median (or second quartile), the first quartile (Q1), and the third quartile (Q3).

These values are used to create the "box" in the plot, which represents the middle 50% of the data. The lower whisker is drawn from the minimum value to Q1, while the upper whisker is drawn from Q3 to the maximum value. Any data points that fall outside the whiskers are considered outliers and are represented by individual points. The box plot is a useful tool for visualizing the distribution and spread of a dataset.

To draw a box plot, you'll need five key statistics: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. The minimum and maximum represent the lowest and highest data points, respectively. Q1 is the median of the lower half of the data, while Q3 is the median of the upper half. The median (Q2) splits the data into two equal parts. These statistics are used to create a visual representation of data distribution, with the box formed by Q1, Q2, and Q3, and the whiskers extending to the minimum and maximum values.

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Answer:

-1, -7

1, 3

3, -1

5, -5

Step-by-step explanation:

Answer:

69 - 52 = g

(g = 17)

Step-by-step explanation:

69 [total students] - 52 [no role] = g [those who got in]

69 - 52 = g            {simplify/combine like terms}

17 = g

g = 17

So, 17 students will be in the play

(could also be modeled as 52 + g = 69)

(this is because the only possibility for each student is to either not get in, or get in. So, if we add these two values up, we get the total number of students who auditioned).

(if you want to model the equation as such:

52 + g = 69

- 52          -52   {subtract 52 from both sides to isolate g}

g = 17)

The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:

a) Adjacency lists:

In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.

Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.

b) Adjacency matrix:

In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.

c) Incidence matrix:

In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.

Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.

In summary:

a) Adjacency lists: O(n + m)

b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs

c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs

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The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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I'm pretty sure it's 8.5 > 2.97

The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)

Given equation y = 3x + a / 2x - 5

= y(2x - 5) = 3x + a

= 2xy - 5y = 3x + a

= 2xy - 3x = a - 5y

= x(2y-3) = a - 5y

Hence, x = (a - 5y) / (2y - 3)

First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).

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Answer:

67°

Step-by-step explanation:

< EFB = ½× (163-29) = ½×(134) = 67°

In the triangle LMN the length of the side l as per given measures of side and angles is equal to 42.4 inches ( nearest tenth )

In triangle LMN,

Let us consider side length opposite to ∠L, ∠M, and ∠N be l , m , and n respectively.

Measure of side m = 450 inches

Measure of ∠M = 74°

Measure of ∠N = 41°

Sum of all the angles in a triangle is equal to 180°

m ∠M + m ∠N + m ∠L = 180°

⇒ 74° + 41° + m ∠L = 180°

⇒ m ∠L = 180° - 115°

⇒ m ∠L = 65°

Using sine law of triangle we have,

sin L / l  = sin M / m = sin N / n

⇒sin L / l  = sin M / m

Substitute the value we get,

⇒ sin 65° / l  = sin 74° / 450

⇒ l = sin 65° × ( 450 / sin 74°)

⇒ l = 0.9063 × ( 450 / 0.9613 )

⇒ l = 42.43 inches

⇒ l = 42.4 inches ( nearest tenth )

Therefore, the measure of the side length l in a triangle LMN is equal to 42.4 inches ( nearest tenth ).

The above question is incomplete, the complete question is:

In ΔLMN, m = 450 inches,  m ∠M=74° and  m ∠N=41°. Find the length of l, to the nearest 10th of an inch.

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Answer: 424.3

Step-by-step explanation: n ΔLMN, m = 450 inches, m∠M=74° and

m∠N=41°. Find the length of l, to the nearest 10th of an inch.

A.A.S.→Law of Sines

Plug in. Opposite sides go together. 450 sin, 65 sin 74 ≈ 424.2742 ≈ 424.3

l=

sin74

450sin65

​

≈424.2742≈424.3

Answer: 30 straps for 66 is better

Step-by-step explanation:

If its 9 straps for 20.25, then one strap costs 2.25

If its 30 traps for 66, one strap costs 2.2

Therefore, if you buy 30 straps for 66, its a better buy.

Answer:

1. 2.25

2. 2.20

3. 1.02

4. 30 straps

Step-by-step explanation:

1. Divide 20.25 by 9

2. Divide 66 by 30

3. Divide 2.25 by 2.20

Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.

The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:

6x+12x=180

18x=180

x=10°

Therefore, 6x= 6*10=60° and 12x=12*10=120°.

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The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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In math, protractors are essential tools for measuring and determining vertical and adjacent angles.

In the study of geometry, angles play a fundamental role, and accurately measuring them is crucial for solving various mathematical problems. When it comes to vertical and adjacent angles, a key tool used by both students and professionals is the protractor. A protractor is a DIY (do-it-yourself) tool that allows for precise angle measurement and identification.

With a protractor, one can easily determine the size of vertical angles, which are formed by intersecting lines or rays that share the same vertex but point in opposite directions. These angles have equal measures. Similarly, adjacent angles are formed when two angles share a common side and a common vertex but do not overlap. By using a protractor, one can measure the individual angles and determine their relationship to each other.

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Answer:

first of all

11+4=15/3×√64

5×8=40

\((11 + 4) \div 3 \times \sqrt{64} \)

Add the numbers

\(15 \div 3 \times \sqrt{64} \)

Calculate the square root

\(15 \div 3 \times 8\)

Divide the numbers

\(5 \times 8\)

Multiply the numbers

\(40\)

Answer:

Decay

Decay

Growth

Decay

Decay

Growth

Step-by-step explanation:

Answer:

\(200 + 0.07m \leq 230\)

A maximum of \(\approx\) 428 miles is the distance what Divya can travel.

Step-by-step explanation:

Given that:

Rent to be paid for the car in the weekend = $200

Charges to be paid per mile = $0.07

Total money available  with Divya = $230

To find:

The inequality as per her limitations and solution to the problem.

Solution:

Let the number of miles for which Divya can drive = \(m\) miles

Charges for one mile = $0.07

Charges for \(m\) miles = $0.07\(m\)

Total charges for renting and \(m\) miles = Rental charges + Operational charges

Total charges for renting and \(m\) miles = $200 + $0.07\(m\)

These are charges must be lesser than equal to the amount of money available with Divya.

Therefore, we can write:

\(200 + 0.07m \leq 230\)

Subtracting 200 from both the sides:

\(0.07m \leq 30\)

Dividing both sides with 0.07:

\(m \leq \dfrac{30}{0.07}\\m\leq 428.6\)

Therefore, a maximum of \(\approx\) 428 miles is the distance what Divya can travel.

The numbers between 10 and 50  when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have:

The set of numbers between 10 and 50 when they are divided by 5 then the remainder is 2

The numbers are:

12, 17, 22, 27, 32, 37, 42, 47

By description method:

1      2     3    4      5     6      7      8  

12   17   22   27    32    37   42    47  

By set builder form:

s = {12, 17, 22, 27, 32, 37, 42, 47}

Thus, the numbers between 10 and 50  when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.

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The amount of juice the cup can hold given that the cup has diameter of 8 centimeters and a height of 12 centimeters is 602.88 cm³

To know the amount of juice the cup can hold, we shall obtain the volume of the cup.

We shall use the formula for obtaining volume of cylinder to obtain the volume of the cup. Details below:

Volume = πr²h

Volume = 3.14 × 4² × 12

Volume = 3.14 × 16 × 12

Volume = 602.88 cm³

Thus, we can conclude from the above calculation that the amount of juice the cup can hold is 602.88 cm³

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The equation can be used to find the value of m is 5m + 37 = 79.50.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, Yung works 5 hours at a restaurant each Wednesday.

He also earns $37 a week delivering newspapers.

Kyung makes a total of $79.50 each week and 'm' represents the amount he makes per hour at the restaurant.

∴ The equation can be used to find the value of m is 5m + 37 = 79.50.

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Answer:

Question 6 answer is 35

Step-by-step explanation:

using pythagoras theorem, hypotenuse²= opposite²+ adjacent²

since it is said that we're looking for the hypotenuse then the values given are for opposite and adjacent.

therefore, hyp²= 21²+28²

hyp²= 1225 take square root of both sides to eliminate square and find hypotenuse

hyp= 35

The equivalent expression to {(2 3/10)⁴ ÷ (9/10)⁵}⁴ is "2 and three tenths raised to the sixteenth power divided by nine tenths raised to the twentieth power".

The correct answer choice is option B

Exponents refers to the power to which a number, expression or symbol is to be raised. For instance, 4²; the exponent is 2 which is a power.

{(2 3/10)⁴ ÷ (9/10)⁵}⁴

= (2.3⁴ ÷ 0.9⁵)⁴

Multiply the powers

= 2.3¹⁶ ÷ 0.9²⁰

It can also be written as

(2.3)¹⁶ / (0.9)²⁰

Consequently, the expression which is equivalent to 2 and three tenths raised to the fourth power divided by nine tenths raised to the fifth power, all raised to the fourth power is (2.3)¹⁶ / (0.9)²⁰

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Answer:

I am 100% sure it is b

Step-by-step explanation:

I have proof( i did the test) and took a picture

The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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The function simulates exponential decay, and it degrades by 5.1% for every increment in x.

Explosive increase and decay are common in situations where quantities change rapidly. It has been suggested that exponential development and decay follow a geometric progression. Quantities that change exponentially rather than continually are referred to be exponentially growing or decaying.

As per the given data in the question,

An exponential function with the formula y = a\(r^x\) is the function that is given.

a = 330

r = 0.949

The function indicates exponential growth if the base r is larger than 1. The function shows exponential decline if indeed the base r is far less than 1. In this instance, the function depicts exponential decline because the base r is smaller than 1, or 0.949.

If we want to describe the rate of reduction as a percentage, we can remove the base r by 1 and multiply it by 100.

The rate of reduction as a percentage in this instance is:

1 - 0.949 = 0.051 ×100

= 5.1%.

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Difference between interval measurement and ratio measurement is Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point. So, option C is correct.

Interval measurement uses numeric values with equal intervals.

This means that the difference between any two adjacent values on the scale is always constant.

However, the zero point on this scale is arbitrary, meaning it does not represent the absence of the characteristic being measured.

Ratio measurement, on the other hand, also uses numeric values with equal intervals, but it has an absolute zero point.

This means that the zero point on a ratio scale represents the complete absence of the characteristic being measured.

As a result, ratio scales can be used to perform more advanced mathematical operations, such as multiplication and division.
To summarize, the main difference between interval and ratio measurement lies in the zero point of their scales. Interval measurement scales have an arbitrary zero point, whereas ratio measurement scales have an absolute zero point.

The correct choice is option C . Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point.

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Question:-

Which of the following statements describes the difference between interval measurement and ratio measurement?

A) Ratio measurement is used for continuous data, whereas interval measurement is used for noncontinuous data.

B) Interval measurement uses numeric values with equal intervals, whereas ratio measurement uses numeric values with unequal intervals.

C) Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point.

D) Ratio measurement uses numeric values without fixed meaning, whereas interval measurement uses numeric values with fixed meaning.

The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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Answer: A≈1385.44m²

Step-by-step explanation:

A=πr2=π·212≈1385.44236m²

Probability that he will choose debbie and esther as the two representatives is 1/20 .

Probability is the stream in mathematics in which likeliness of an event to happen is studied.

The range of probability lies between 0 to 1 , where 0 indicates uncertainty and 1 indicates certainty.

It is given that anna, becky, christina, debbie, and esther are the five candidates for student representative for the school board.

two students will be selected, and they will alternate attending the school board meetings.

all five students are equally well qualified, so the school superintendent decides to draw names at random.

probability he will choose debbie and esther as the two representatives = ?

Probability of chosing debbie is 1/5

Probability of choosing Esther is also 1/5

Either of them if chosen first the probability is 1/5

and the either of them chosen second the probability is 1/4

Probability that he will choose debbie and esther as the two representatives = (1/5)*(1/4) = 1/20 .

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The linear equation we want to find is:

z = -250*p + b

And when the price is p = $1.50, the sell 525 items.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

Here we have the points of the form:

(p, z)

And we know two points (3.50, 25) and (3.00, 150), then the slope is:

a = (150 - 25)/(3.00 - 3.50) = -250

Then the linear equation is something like:

z = -250*p + b

To find the y-intercept we can use one of the points, replacing the values of the point (3.50, 25) there we get:

25 = -250*3.50 + b

25 + 250*3.50 = b

900

Then the linear equation is:

z = -250*p + 900

B) now we want to find the number of items sold if the price is $1.50, we will get:

z = -250*1.50 + 900

z = 525

525 will be sold.

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Using the simplex method, we can solve the linear programming problem to maximize P=8x₁+2x₂-x₃ subject to x₁+x₂-x₃≤2 and 2x₁+4x₂+3x₃≤6 . The optimal solution is x₁=0.5, x₂=0.2, and x₃=0.5, which gives a maximum value of P=7/4.

To solve the linear programming problem using the simplex method, we can start by setting up the initial simplex tableau:

| Basic Variables  | x₁  | x₂  | x₃  |   |   |   | RHS |

|------------------|-----|-----|-----|---|---|---|-----|

|       x₂         |  1  |  1  | -1  | ≤ | 2 |   |  0  |

|       x₃         |  2  |  4  |  3  | ≤ | 6 |   |  0  |

|       P          |  8  |  2  | -1  |   |   |   |  0  |

The first step is to select a pivot column, which is the column with the most negative coefficient in the P row. In this case, that is the x₃ column. Next, we need to select a pivot row, which is the row with the smallest non-negative ratio of the RHS to the corresponding coefficient in the pivot column. In this case, that is the x₂ row, since 2/(-1)=-2 is the smallest non-negative ratio.

Using the x₂ row and x₃ column as the pivot element, we can perform row operations to get a new tableau:

We can see that the P row still has a negative coefficient, so we need to repeat the process of selecting a pivot column and pivot row. This time, the pivot column is the x₁ column, since it has the most negative coefficient in the P row. The pivot row is the x₃ row, since 2/1=2 is the smallest non-negative ratio.

Using the x₃ row and x₁ column as the pivot element, we can perform row operations to get a new tableau:

| Basic Variables  | x₁  | x₂      | x₃  |   |              |       | RHS |

|------------------|-----|---------|-----|---|--------------|-------|-----|

|       x₂         | 3/8 |  1/8    |  0  | ≤ | 1/8          | 1/24  |  0  |

|       x₁         | 1/2 |  1/6    | 1/2 | ≤ | 1/3          | 1/6   |  0  |

|       P          | 7/4 |  3/8    | 7/4 |   | 5/8          | 1/24  |  0  |

We can see that all the coefficients in the P row are non-negative, so we have found the optimal solution. The maximum value of P is 7/4, which occurs when x₁=1/2, x₂=1/6, and x₃=1/2.

Therefore, the correct choice is

A. The maximum value of P is when x₁ = 0.5, X₂=0.2 and x3 = 0.5.

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