(Creating Graphical Representations MC
In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.

{17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3}

Which of the following stem-and-leaf plots correctly graphs the data set?


2021 Riverside Red Dragon Football Season Points

0 0 3
1 1 7 7 7 7
2 0 0 0 2 4 8 8
3 1 3
Key 1|1 = 11

2021 Riverside Red Dragon Football Season Points

0 0 3
1 1 7
2 0 2 4 8
3 1 3
Key 1|1 = 11

2021 Riverside Red Dragon Football Season Points

1 1 7
2 0 2 4 8
3 0 1 3
Key 1|1 = 11

2021 Riverside Red Dragon Football Season Points

1 1 7 7 7 7
2 0 0 0 2 4 8 8
3 0 1 3
Key 1|1 = 11

5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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(c) range, (d) variance, (e) standard deviation and (f) interquartile range measure variability.

Range, The range is the difference between the largest and smallest values in a dataset, indicating how spread out the data are.

Variance, The variance measures how far a set of numbers is spread out from their average. It provides a measure of how much the individual data points deviate from the mean.

Standard deviation, The standard deviation is the square root of the variance and is also a measure of how much the individual data points deviate from the mean. It is a widely used measure of variability, particularly in statistical analysis.

Interquartile range, The interquartile range (IQR) is the difference between the third and first quartiles of a dataset. It gives an idea of the spread of the middle 50% of the data and can help identify outliers.

The mean and median are measures of central tendency and do not directly measure variability.

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Answer:

0

Step-by-step explanation:

First we need to find the value of constant k in equation. To find k we use the formula:

\(\int\limits^{100}_0 {ke^{-0.01x}} \, dx =1\\Integrating:\\k\int\limits^{100}_0 {e^{-0.01x}} \, dx =1\\\frac{k}{-0.01}[e^{-0.01x}]_0^{100}=1\\-100k [e^{-0.01x}]_0^{100}=1\\-100k[e^{-0.01*100}-e^{-100*0}]=1\\-100k[e^{-1}-e^0]=1\\-100k(-0.632)=1\\63.2k = 1\\k=0.0158\)

the probability that a person age 20 will live for at least 20 more years = P(40 ≤ x <∞).

The person would live for at least 40 years

Therefore:

P(40 ≤ x <∞) =

\(\int\limits^{\infty}_{40} 0.0158e^{-0.01x}} \, dx \\Integrating:\\0.0158\int\limits^{\infty}_{40} {e^{-0.01x}} \, dx =\frac{0.0158}{-0.01}[e^{-0.01x}]_{40}^{\infty}\\=-1.58 [e^{-0.01x}]_{40}^{\infty}=-1.58[e^{-\infty}-e^{-100*40}]\\=-1.58[e^{-\infty}-e^{-4000}]=-1.58(0-0)=0\)

Step-by-step explanation:

please mark me as brainlest

Answer

1. 0.8..

2. 0.6..

3. 2.66..

4. 9.55..

5. -17.95..

Answer:

415.67 = (1/3)(13.4)(11.7)h

415.67 = 52.26h

h = about 7.95 feet

The answer is \(2\frac{3}{4}\) more gallons

Answer:

y'=|x-5|-1

Step-by-step explanation:

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Answer:

65 boletos.

Step-by-step explanation:

Sabemos que el precio para un niño es 6 dólares, y el precio para un adulto es 9,20 dólares. Además, el cine se vendió 146 boletos, y recibió 1135,20 dólares.

Vamos a resolver este problema con un sistema, usando 2 varibles.
No sabemos cuantos boletos de niño el cine vendió, entonces el cine vendió <<x>> boletos de niños. Tampoco sabemos cuantos boletos de adultos vendió, entonces vendió <<y>> boletos de adultos.

En total, vendió 146 boletos; el número de los boletos de niños con el número de los boletos de adultos es 146 boletos.

Usando las variables, x + y = 146 boletos.

Esta es una de las equaciones que necesitamos.

Porque todos los boletos de niños es 6 dólares, si el cine vendió <<x>> boletos, su total de ventas (de boletos de niños) es <<6x>> dólares.

Lo mismo es verdad para los boletos de adultos; todos los boletos de adultos es 9,20 dólares, entonces si vendió <<y>> boletos, el total de ventas de boletos de adultos es <<9,20y>> dólares.

En total, las ventas de los boletos de niños + las ventas de los boletos de adultos es 1135,20 dólares.

O, con variables, es 6x + 9,20y = 1135,20

Nuestra sistema es:

x + y = 146

6x + 9,20y = 1135,20

Ahora necesitamos resolver esta sistema.

Podemos usar la sustitución. Vamos a resolver una de las eqaciones para una variable, y después, usar el valor de esa variable para encontrar la solución para una de las variables, y después, usar  esa solución para encontrar la solución de la otra variable.

Podemos mover <<y>> al otro lado.

x + y = 146 => x = 146 - y

Ahora, podemos sustituir <<x>> para 146 - y en 6x + 9,20y = 1135,20

6(146-y) + 9,20y = 1135,20

Multiplica.

876 - 6y + 9,20y = 1135,20

Combina los términos que son los mismos.

876 + 3,20y = 1135,20

Mueva 876 al otro lado.

876 + 3,20y = 1135,20 => 3,20y = 259,20

Divide todo por  3,20.

3,20y/ 3,20 = 259,20/ 3,20

y = 81

Entonces, el cine vendió 81 boletos de adultos.

Recuerda, esta (81 boletos de adultos) no es lo que necesitamos. Necesitamos cuantos boletos de niños vendió.

Entonces, podemos substituir <<y>> con 81 en x = 146 - y. Recuerda que <<x>> es cuantos boletos de niños vendió.

x = 146 - y => x = 146 - 81 => 65

Entonces, el cine vendió 65 boletos de niños.

Answer:

1. is b 2. is a 3. is d

Step-by-step explanation:

:D

Answer:

75 km.

Step-by-step explanation:

Fractions of a number

To get the fraction of a number, we multiply that number by the given fraction.

For example two-thirds of 60 is 2/3 × 60 = 2 × 20 = 40 and one-fifth of 100 is 1/5 × 100 = 100/5 = 20

Now, we are supposed to find a fraction of 100 km. Assume its three-quarters.

So, three-quarters of 100 km is 3/4 × 100 km = 3 × 100 km/4 = 3 × 25 km = 75 km

So, three-quarters of 100 km is 75 km.

Answer:

the explanatory variable is "the amount of practice every year" while the response variable is "the improvement in his game"

Step-by-step explanation:

In simple terms, the difference between explanatory and random variable is that the response variable is usually the focus of a question in a study/experiment while an explanatory variable is a variable that explains changes in the response variable. Which means that the explanatory variable is simply any variable that may affect the response variable.

Now, in this question, the golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.

This means that the amount of practice every year explains how much he improves every year.

Thus, the explanatory variable is "the amount of practice every year" while the response variable is "improvement in his game"

The number of pennies weighing as much s earth is  193 × 10²⁴

Index forms are described as described as those forms that are used to represent numbers that are too large or small in more proper ways.

Other names for index forms are scientific notation and standard forms.

Ratio is described as the comparison of numbers or variables on the basis of their size.

It shows how many times one number contains another.

From the information given, we have that;

The earth weighs = 5. 972 × 10 ²⁴ kilograms

The penny weighs = 3.1 × 10 ⁻³ kilograms

Divide the values

= 5. 972 × 10 ²⁴/3.1 × 10 ⁻³

= 1.93 × 10 ²⁶

= 193 × 10²⁴

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Answer:

6.28

Step-by-step explanation:

\((3.14)(1.5) {}^{2} = 7.065 \)

\((3.14)(0.5) {}^{2} = 0.785\)

\(7.065 - 0.785 = 6.28\)

Answer:

Step-by-step explanation:

First, we multiply 2×2 then the answer we obtain we add to it 6 which in total gives us 10

Answer: The answer is B and C

Step-by-step explanation:

Answer:

c. The quotient of a and b is positive.

Step-by-step explanation:

Answer: \(\dfrac{21}{410}\).

Step-by-step explanation:

Formula : Probability = \(\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}\)

From the given frequency distribution for the class level of students in an introductory statistics course, we have

Number of Junior= 12

Number of Senior = 7

Total students = 6+16+12+7 = 41

Probability that the first student obtained is a junior = \(\dfrac{12}{41}\)

Probability that the the second student obtained is a senior. \(=\dfrac{7}{41-1}=\dfrac{7}{40}\)

Then, the probability that the first student obtained is a junior and the second a senior would be \(\dfrac{12}{41}\times\dfrac{7}{40}=\dfrac{21}{410}\)

Hence, the required probability is \(\dfrac{21}{410}\).

Answer:

Step-by-step explanation:

Hello!

X: Number of chapters per book in the bible.

1.

Mean (X[bar])

X[bar]= ∑X/n= 929/39= 23.82

Median (Me)

To calculate the median you determine its position first, then you have to arrange the data from least to greatest and identify the corresponding value:

Position: (n+1)/2= (39+1)/2= 20

The 20th observation corresponds to the median of this data set:

1 2 3 3 3 3 4 4 4 5 7 8 9 10 10 12 12 13 14 14 21 22 24 24 25 27 29 31 31 34 36 36 40 42 48 50 52 66 150

Me= 14

Mode (Md)

The mode corresponds to the value with the most observed frequency, in this case, if we are studying the numbers of chapters per book so the mode will correspond to the "number of chapters" that is most repeated.

Once again you have to arrange the data from least to greatest.

1 2 3 3 3 3 4 4 4 5 7 8 9 10 10 12 12 13 14 14 21 22 24 24 25 27 29 31 31 34 36 36 40 42 48 50 52 66 150

"3 chapters" is repeated 4 times

"4 chapters" is repeated 4 times

"10 chapters" is repeated 2 times

"12 chapters" is repeated 2 times

"14 chapters" is repeated 2 times

"24 chapters" is repeated 2 times

"31 chapters" is repeated 2 times

"36 chapters" is repeated 2 times

This data set has two modes Md₁= 3 and Md₂= 4 and its called "bimodal" distribution.

Range (R)

The range of the distribution is the difference between the maximum and minimum values of the data set:

Minimum: 1 chapter

Maximum: 150 chapters

R=max-min= 150-1= 149

2.

Out of the 5 number summary, I've already identified three: Min, Max, and Me.

To calculate the first (Q₁) and third (Q₃) quartiles you have to calculate their positions first and then identify them in the data set (arranged from least to greatest)

PosQ₁= (n+1)/4= 40/4= 10

PosQ₃= (n+1)*3/4= 40*3/4= 30

1 2 3 3 3 3 4 4 4 5 7 8 9 10 10 12 12 13 14 14 21 22 24 24 25 27 29 31 31 34 36 36 40 42 48 50 52 66 150

Q₁= 5

Q₃= 34

3. Box plot attached.

4. Histogram attached

5.

a. and d.

An outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on statistical analysis.

Considering the 1st quartile (Q₁), the 3rd quartile (Q₃) and the interquartile range IQR, any value X is considered an outlier if:

X < Q₁ - 1.5 IQR

X > Q₃ + 1.5 IQR

Or extreme outliers if:

X < Q₁ - 3 IQR

X > Q₃ + 3 IQR

Q₁= 5

Q₃= 34

IQR= Q₃ - Q₁= 34 - 5= 29

Limits for outliers:

Q₁ - 1.5 IQR = 5-(1.5*29)= -38.5

Q₃ + 1.5 IQR = 34+(1.5*29)= 77.5

Limits for extreme outliers:

Q₁ - 3 IQR = 5 - (3*29)= -82

Q₃ + 3 IQR= 34 + (3*29)= 121

As you can see, comparing the data with the criteria to classify a value as an outlier, there is only one in the data set and, since it is more than 3 IQR away from the third quartile, it is an extreme outlier: 150 chapters

b. and c.

Central tendency measures:

X[bar]= 23.82 ⇒ the mean or average number is also known as the "expected" value of the distribution. This measurement is always a value within the range of definition of the variable but does not necessarily coincide with an observation. Another characteristic of this measurement is that it is greatly affected by outliers and tends to "move" its position towards them.

You can say that on average the books of the bible have 23.82 chapters

If you take the outlier out of the data set and calculate the mean, you'd expect it to be less and closer to the median:

X[bar] (without 150):∑X/n= 779/38= 20.5

Md₁= 3 and Md₂= 4 ⇒ Both modes are on the lower end of the distribution, aside for showing that there are many books with the same amount of chapters, it shows no more information.

Me= 14 ⇒ The median is the value that separates the distribution in halves, considering that there is an outlier that affects the value of the mean, is the median the measure that best describes the distribution.

I hope this helps!

Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Answer:

5(5v+4)=17v+8v+9+9

25v+20=25v+18

25v-25v=18-20

0v=-2

i think soooo

this question is very very irrelevant

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

First you add all of the marbles in the bag which is 16 marbles.  The fraction of red marbles to the total would be 4/16.  In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.

The function represents f ( x ) is f ( x ) = 32 ( 3x - 1 )

Given :

The table represents some points on the graph of linear function f.

Table :

x        -2         1        5       10

f ( x ) -224   64     448   928

take two points ( 5 , 448 ) and ( 1 , 64 )

slope m = 64 - ( 448 ) / 1 - ( 5 )

= 64 - 448 / 1 - 5

= -384 / -4

= 384 / 4

= 192 / 2

= 96

( 1 , 64 ) on

y -  64 = 96 ( x - 1 )

y - 64 = 96x - 96

y = 96x - 96 + 64

y = 96x - 32

take 32 as common

= 32 ( 3x - 1 )

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Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)

Step-by-step explanation:

since you provided 1st and the last terms

the equation can be nth term

n/2 × ( a + l) = nth sum

n/2 × ( 1 + 121) = 671

n/2 × 122 = 671

61 n = 671

n = 11

a) so there are 11 terms

then,

so as 11th term is 121

let's find common diff

a + ( n-1) d = nth term

1 +( 11-1) d= 121

10d = 121 -1

10d = 120

common difference = 12

Answer:

a) Calculate the current price of the corporate bond? (4 marks)

b) Calculate the current price of the ordinary share if the average return of the shares in the same industry is 9%? (3 marks)

c) Calculate the current price of the preferred share if the average return of the shares in the same industry is 10% (3 marks)

Step-by-step explanation:

total debt = $3,500,000 par value 10$ coupon with a YTM of 12%

YTM = [coupon + (F - P)/n] / [(F + P)/2]

0.12 = [100 + (1,000 - P)/20] / [(1,000 + P)/2]

0.12(500 + 0.5P) = 100 + 50 - 0.05P

60 + 0.06P = 150 - 0.05P

0.11P = 90

P = 90/0.11 = $818.18

total debt = $818.18 x 3,500

stock price:

Div₀ = $8.50

Div₁ = $8.50 x 104% = $8.84

g = 4%

rrr = 9%

using the perpetuity growth model:

stock price = $8.84 / (9% - 4%) = $8.84 / 5% = $176.80

preferred stock:

Div = $12

rrr = 10%

using the perpetuity formula:

preferred stock = $12 / 10% = $120

The claim that if x is even then 9x - 5 is odd is false for all x < 0, as demonstrated by an example where x = -2 and 9x - 5 = -17, which is an even number.

The smallest counterexample method is used to prove that a claim is false by providing an example that does not follow the claim. To prove the claim that if x is even then 9x 5 is odd, for all x < 0, we can use the smallest counterexample method by finding the smallest value of x that would disprove the claim.

Let x = -2, then 9(-2) - 5 = -17. Since -17 is even, it does not follow the claim that if x is even then 9x - 5 is odd, thus disproving the claim for all x < 0.

To explain this with formula and calculation, let x = -2, then 9x - 5 = 9(-2) - 5 = -17. Since -17 is even, the claim that if x is even then 9x - 5 is odd is false. Therefore, the claim is false for all x < 0.

The claim that if x is even then 9x - 5 is odd is false for all x < 0, as demonstrated by an example where x = -2 and 9x - 5 = -17, which is an even number.

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Answer:

105

Step-by-step explanation:

Assuming A^2 + B^2 = C^2:

C^2 = 4 + 3 = 7

So,

C^2 * 15 = 49(15) = 105

Note: Since the relationship between A, B, and C isn't known, it cannot be said for certain that 105 is the answer.

Step-by-step explanation:

there is no C in the first 2 equations. There is no A or B in the last expression. I do not think you can solve this.

Answer: 754

Step-by-step explanation:

Divide 683/11 to get the unit rate of 58. That means she is driving 58mph.

Multiply that by how many hours you have, 13, and you get 754.

b. The distance between points K and L is 10 units.

c. ΔJKL is not an equilateral triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

Given points as:

J (-5,-3)

K (1,5),

L (7,-3)

b. To determine the distance between points K and L, we can use the distance formula:

distance = √(x₂ – x₁)² + (y₂ – y₁)²

Substituting the coordinates of K and L, we get:

distance = √((7 - 1)² + (-3 - 5)²)

distance = √(36 + 64)

distance = √(100)

distance = 10

Therefore, the distance between points K and L is 10 units.

c. To determine if JKL is an equilateral triangle, we need to check if all three sides have the same length.

We can find the lengths of each side using the distance formula:

JK = √((1 - (-5))² + (5 - (-3))²) = √(6^2 + 8²) = 10

KL = 10 (as we found in part b)

LJ = √((-5 - 7)² + (-3 - (-3))²) = √((-12)²) = 12

Since all three sides have different lengths (JK and KL are 10 units, while LJ is 12 units), JKL is not an equilateral triangle.

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The quotient of\((6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))\) is 2x.

To simplify the expression\((6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10)),\) we can use the rule for dividing fractions, which states that dividing by a fraction is the same as multiplying by its reciprocal.

Let's simplify the expression :

Simplify the numerator and denominator of the first fraction.

The numerator is 6x, and the denominator is (3x+15).

We can factor out a common factor of 3 from the denominator, which gives us 3(x+5).

So the first fraction simplifies to 6x / 3(x+5).

Simplify the numerator and denominator of the second fraction.

The numerator is (x^2+2x), and the denominator is \((x^2+7x+10).\)

We can factor both the numerator and denominator:

Numerator: x(x+2)

Denominator: (x+5)(x+2)

Canceling out the common factor of (x+2), we are left with x / (x+5).

Multiply the two simplified fractions.

Multiplying the fractions, we get:

\((6x / 3(x+5)) \times (x / (x+5))\)

Simplify the resulting expression.

Canceling out the common factor of (x+5) in the numerator and denominator, we are left with:

2x / 1

So the quotient simplifies to 2x.

Therefore, the quotient of \((6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))\) is 2x.

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